TSTP Solution File: SEU429+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU429+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 : Tue Sep 20 07:29:36 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU429+1 : TPTP v8.1.0. Released v3.4.0.
% 0.12/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Sep 3 14:09:48 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(m1_subset_1_type, type, (
% 0.20/0.41 m1_subset_1: ( $i * $i ) > $o)).
% 0.20/0.41 tff(k1_zfmisc_1_type, type, (
% 0.20/0.41 k1_zfmisc_1: $i > $i)).
% 0.20/0.41 tff(m2_relset_1_type, type, (
% 0.20/0.41 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.20/0.41 tff(v1_xboole_0_type, type, (
% 0.20/0.41 v1_xboole_0: $i > $o)).
% 0.20/0.41 tff(a_4_1_relset_2_type, type, (
% 0.20/0.41 a_4_1_relset_2: ( $i * $i * $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_B_2_type, type, (
% 0.20/0.41 tptp_fun_B_2: $i)).
% 0.20/0.41 tff(tptp_fun_D_3_type, type, (
% 0.20/0.41 tptp_fun_D_3: $i)).
% 0.20/0.41 tff(tptp_fun_C_1_type, type, (
% 0.20/0.41 tptp_fun_C_1: $i)).
% 0.20/0.41 tff(tptp_fun_A_0_type, type, (
% 0.20/0.41 tptp_fun_A_0: $i)).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 (^[A: $i, B: $i, C: $i, D: $i] : refl((m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))))) <=> (m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B)) <=> (~(v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))))))), ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))) <=> (~(~(v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))))))))), rewrite((~(~(v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))))))) <=> (v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))), ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))) <=> (v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))))))), (((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> ((v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))))) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))))), rewrite(((v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))))) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> (m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))), (((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> (m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(rewrite((((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) & m2_relset_1(D, A, B)) <=> ((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))), (((((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) & m2_relset_1(D, A, B)) => m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> (((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B)) => m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))))), rewrite((((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B)) => m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))), (((((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) & m2_relset_1(D, A, B)) => m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(7,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i, D: $i] : ((((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) & m2_relset_1(D, A, B)) => m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.42 tff(8,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) & m2_relset_1(D, A, B)) => m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','s8_domain_1__e1_38__relset_2')).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.42 tff(10,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.42 tff(11,plain,(
% 0.20/0.42 ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[10])).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (((~v1_xboole_0(A!0)) & (m1_subset_1(C!1, k1_zfmisc_1(k1_zfmisc_1(A!0))) & (~((~m2_relset_1(D!3, A!0, B!2)) | m1_subset_1(a_4_1_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))))))) <=> ((~v1_xboole_0(A!0)) & m1_subset_1(C!1, k1_zfmisc_1(k1_zfmisc_1(A!0))) & (~((~m2_relset_1(D!3, A!0, B!2)) | m1_subset_1(a_4_1_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 (((~(~m1_subset_1(C!1, k1_zfmisc_1(k1_zfmisc_1(A!0))))) & (~((~m2_relset_1(D!3, A!0, B!2)) | m1_subset_1(a_4_1_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2)))))) <=> (m1_subset_1(C!1, k1_zfmisc_1(k1_zfmisc_1(A!0))) & (~((~m2_relset_1(D!3, A!0, B!2)) | m1_subset_1(a_4_1_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (((~v1_xboole_0(A!0)) & ((~(~m1_subset_1(C!1, k1_zfmisc_1(k1_zfmisc_1(A!0))))) & (~((~m2_relset_1(D!3, A!0, B!2)) | m1_subset_1(a_4_1_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))))))) <=> ((~v1_xboole_0(A!0)) & (m1_subset_1(C!1, k1_zfmisc_1(k1_zfmisc_1(A!0))) & (~((~m2_relset_1(D!3, A!0, B!2)) | m1_subset_1(a_4_1_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2)))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[15])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (((~v1_xboole_0(A!0)) & ((~(~m1_subset_1(C!1, k1_zfmisc_1(k1_zfmisc_1(A!0))))) & (~((~m2_relset_1(D!3, A!0, B!2)) | m1_subset_1(a_4_1_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))))))) <=> ((~v1_xboole_0(A!0)) & m1_subset_1(C!1, k1_zfmisc_1(k1_zfmisc_1(A!0))) & (~((~m2_relset_1(D!3, A!0, B!2)) | m1_subset_1(a_4_1_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[16, 14])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))) <=> (~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 ((~![A: $i] : ((~v1_xboole_0(A)) => ![B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) => ![D: $i] : (m2_relset_1(D, A, B) => m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))) <=> (~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(20,axiom,(~![A: $i] : ((~v1_xboole_0(A)) => ![B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) => ![D: $i] : (m2_relset_1(D, A, B) => m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t28_relset_2')).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 (~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 (~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 (~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 (~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[24, 18])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[26, 18])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 ((~v1_xboole_0(A!0)) & m1_subset_1(C!1, k1_zfmisc_1(k1_zfmisc_1(A!0))) & (~((~m2_relset_1(D!3, A!0, B!2)) | m1_subset_1(a_4_1_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 (~((~m2_relset_1(D!3, A!0, B!2)) | m1_subset_1(a_4_1_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))))),
% 0.20/0.42 inference(and_elim,[status(thm)],[28])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 (~m1_subset_1(a_4_1_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2)))),
% 0.20/0.42 inference(or_elim,[status(thm)],[29])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (m2_relset_1(D!3, A!0, B!2)),
% 0.20/0.42 inference(or_elim,[status(thm)],[29])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (m1_subset_1(C!1, k1_zfmisc_1(k1_zfmisc_1(A!0)))),
% 0.20/0.42 inference(and_elim,[status(thm)],[28])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 (~v1_xboole_0(A!0)),
% 0.20/0.42 inference(and_elim,[status(thm)],[28])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))) | ((~m1_subset_1(C!1, k1_zfmisc_1(k1_zfmisc_1(A!0)))) | (~m2_relset_1(D!3, A!0, B!2)) | m1_subset_1(a_4_1_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))) | v1_xboole_0(A!0))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))) | (~m1_subset_1(C!1, k1_zfmisc_1(k1_zfmisc_1(A!0)))) | (~m2_relset_1(D!3, A!0, B!2)) | m1_subset_1(a_4_1_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))) | v1_xboole_0(A!0))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 ((m1_subset_1(a_4_1_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))) | v1_xboole_0(A!0) | (~m2_relset_1(D!3, A!0, B!2)) | (~m1_subset_1(C!1, k1_zfmisc_1(k1_zfmisc_1(A!0))))) <=> ((~m1_subset_1(C!1, k1_zfmisc_1(k1_zfmisc_1(A!0)))) | (~m2_relset_1(D!3, A!0, B!2)) | m1_subset_1(a_4_1_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))) | v1_xboole_0(A!0))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))) | (m1_subset_1(a_4_1_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))) | v1_xboole_0(A!0) | (~m2_relset_1(D!3, A!0, B!2)) | (~m1_subset_1(C!1, k1_zfmisc_1(k1_zfmisc_1(A!0)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))) | ((~m1_subset_1(C!1, k1_zfmisc_1(k1_zfmisc_1(A!0)))) | (~m2_relset_1(D!3, A!0, B!2)) | m1_subset_1(a_4_1_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))) | v1_xboole_0(A!0)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[35])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))) | (m1_subset_1(a_4_1_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))) | v1_xboole_0(A!0) | (~m2_relset_1(D!3, A!0, B!2)) | (~m1_subset_1(C!1, k1_zfmisc_1(k1_zfmisc_1(A!0)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))) | (~m1_subset_1(C!1, k1_zfmisc_1(k1_zfmisc_1(A!0)))) | (~m2_relset_1(D!3, A!0, B!2)) | m1_subset_1(a_4_1_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))) | v1_xboole_0(A!0))),
% 0.20/0.43 inference(transitivity,[status(thm)],[36, 34])).
% 0.20/0.43 tff(38,plain,
% 0.20/0.43 ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))) | (m1_subset_1(a_4_1_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))) | v1_xboole_0(A!0) | (~m2_relset_1(D!3, A!0, B!2)) | (~m1_subset_1(C!1, k1_zfmisc_1(k1_zfmisc_1(A!0)))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(39,plain,
% 0.20/0.43 ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(a_4_1_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))))) | (~m1_subset_1(C!1, k1_zfmisc_1(k1_zfmisc_1(A!0)))) | (~m2_relset_1(D!3, A!0, B!2)) | m1_subset_1(a_4_1_relset_2(A!0, B!2, C!1, D!3), k1_zfmisc_1(k1_zfmisc_1(B!2))) | v1_xboole_0(A!0)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.20/0.43 tff(40,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[39, 33, 32, 31, 30, 13])).
% 0.20/0.43 % SZS output end Proof
%------------------------------------------------------------------------------