TSTP Solution File: SEU422+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU422+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 : Tue Sep 20 07:29:31 EDT 2022
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU422+1 : TPTP v8.1.0. Released v3.4.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % 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 : Sat Sep 3 13:57:38 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.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(r2_hidden_type, type, (
% 0.19/0.41 r2_hidden: ( $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_A_0_type, type, (
% 0.19/0.41 tptp_fun_A_0: $i)).
% 0.19/0.41 tff(tptp_fun_D_4_type, type, (
% 0.19/0.41 tptp_fun_D_4: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_C_2_type, type, (
% 0.19/0.41 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.19/0.41 tff(a_2_0_relset_2_type, type, (
% 0.19/0.41 a_2_0_relset_2: ( $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_B_1_type, type, (
% 0.19/0.41 tptp_fun_B_1: $i)).
% 0.19/0.41 tff(k1_zfmisc_1_type, type, (
% 0.19/0.41 k1_zfmisc_1: $i > $i)).
% 0.19/0.41 tff(r1_tarski_type, type, (
% 0.19/0.41 r1_tarski: ( $i * $i ) > $o)).
% 0.19/0.41 tff(k1_tarski_type, type, (
% 0.19/0.41 k1_tarski: $i > $i)).
% 0.19/0.41 tff(m1_subset_1_type, type, (
% 0.19/0.41 m1_subset_1: ( $i * $i ) > $o)).
% 0.19/0.41 tff(v1_xboole_0_type, type, (
% 0.19/0.41 v1_xboole_0: $i > $o)).
% 0.19/0.41 tff(1,plain,
% 0.19/0.41 (^[A: $i, B: $i] : refl((r1_tarski(k1_tarski(A), B) <=> r2_hidden(A, B)) <=> (r1_tarski(k1_tarski(A), B) <=> r2_hidden(A, B)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 (![A: $i, B: $i] : (r1_tarski(k1_tarski(A), B) <=> r2_hidden(A, B)) <=> ![A: $i, B: $i] : (r1_tarski(k1_tarski(A), B) <=> r2_hidden(A, B))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (![A: $i, B: $i] : (r1_tarski(k1_tarski(A), B) <=> r2_hidden(A, B)) <=> ![A: $i, B: $i] : (r1_tarski(k1_tarski(A), B) <=> r2_hidden(A, B))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(4,axiom,(![A: $i, B: $i] : (r1_tarski(k1_tarski(A), B) <=> r2_hidden(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t37_zfmisc_1')).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (![A: $i, B: $i] : (r1_tarski(k1_tarski(A), B) <=> r2_hidden(A, B))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.41 tff(6,plain,(
% 0.19/0.41 ![A: $i, B: $i] : (r1_tarski(k1_tarski(A), B) <=> r2_hidden(A, B))),
% 0.19/0.41 inference(skolemize,[status(sab)],[5])).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (![A: $i, B: $i] : (r1_tarski(k1_tarski(A), B) <=> r2_hidden(A, B))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : (r1_tarski(k1_tarski(A), B) <=> r2_hidden(A, B))) | (r1_tarski(k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))), A!0) <=> r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 (r1_tarski(k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))), A!0) <=> r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (^[A: $i, B: $i] : refl((m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) <=> (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) <=> ![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) <=> ![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(13,axiom,(![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_subset')).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.41 tff(15,plain,(
% 0.19/0.41 ![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 0.19/0.41 inference(skolemize,[status(sab)],[14])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))) | (m1_subset_1(k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))), k1_zfmisc_1(A!0)) <=> r1_tarski(k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))), A!0))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (m1_subset_1(k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))), k1_zfmisc_1(A!0)) <=> r1_tarski(k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))), A!0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (^[A: $i, B: $i, C: $i] : refl((v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(B))) | (~((~((~r2_hidden(A, a_2_0_relset_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), B)) | (~(A = k1_tarski(tptp_fun_D_4(C, B, A)))) | (~r2_hidden(tptp_fun_D_4(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : ((~r2_hidden(D, C)) | (~m1_subset_1(D, B)) | (~(A = k1_tarski(D))))))))) <=> (v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(B))) | (~((~((~r2_hidden(A, a_2_0_relset_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), B)) | (~(A = k1_tarski(tptp_fun_D_4(C, B, A)))) | (~r2_hidden(tptp_fun_D_4(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : ((~r2_hidden(D, C)) | (~m1_subset_1(D, B)) | (~(A = k1_tarski(D))))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(B))) | (~((~((~r2_hidden(A, a_2_0_relset_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), B)) | (~(A = k1_tarski(tptp_fun_D_4(C, B, A)))) | (~r2_hidden(tptp_fun_D_4(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : ((~r2_hidden(D, C)) | (~m1_subset_1(D, B)) | (~(A = k1_tarski(D))))))))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(B))) | (~((~((~r2_hidden(A, a_2_0_relset_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), B)) | (~(A = k1_tarski(tptp_fun_D_4(C, B, A)))) | (~r2_hidden(tptp_fun_D_4(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : ((~r2_hidden(D, C)) | (~m1_subset_1(D, B)) | (~(A = k1_tarski(D)))))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (^[A: $i, B: $i, C: $i] : rewrite((v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(B))) | (~((~((~r2_hidden(A, a_2_0_relset_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), B)) | (~(A = k1_tarski(tptp_fun_D_4(C, B, A)))) | (~r2_hidden(tptp_fun_D_4(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : ((~r2_hidden(D, C)) | (~m1_subset_1(D, B)) | (~(A = k1_tarski(D))))))))) <=> (v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(B))) | (~((~((~r2_hidden(A, a_2_0_relset_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), B)) | (~(A = k1_tarski(tptp_fun_D_4(C, B, A)))) | (~r2_hidden(tptp_fun_D_4(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : ((~r2_hidden(D, C)) | (~m1_subset_1(D, B)) | (~(A = k1_tarski(D))))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(B))) | (~((~((~r2_hidden(A, a_2_0_relset_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), B)) | (~(A = k1_tarski(tptp_fun_D_4(C, B, A)))) | (~r2_hidden(tptp_fun_D_4(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : ((~r2_hidden(D, C)) | (~m1_subset_1(D, B)) | (~(A = k1_tarski(D))))))))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(B))) | (~((~((~r2_hidden(A, a_2_0_relset_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), B)) | (~(A = k1_tarski(tptp_fun_D_4(C, B, A)))) | (~r2_hidden(tptp_fun_D_4(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : ((~r2_hidden(D, C)) | (~m1_subset_1(D, B)) | (~(A = k1_tarski(D)))))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(B))) | (~((~((~r2_hidden(A, a_2_0_relset_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), B)) | (~(A = k1_tarski(tptp_fun_D_4(C, B, A)))) | (~r2_hidden(tptp_fun_D_4(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : ((~r2_hidden(D, C)) | (~m1_subset_1(D, B)) | (~(A = k1_tarski(D))))))))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(B))) | (~((~((~r2_hidden(A, a_2_0_relset_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), B)) | (~(A = k1_tarski(tptp_fun_D_4(C, B, A)))) | (~r2_hidden(tptp_fun_D_4(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : ((~r2_hidden(D, C)) | (~m1_subset_1(D, B)) | (~(A = k1_tarski(D)))))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[22, 20])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & m1_subset_1(C, k1_zfmisc_1(B))) <=> (~(v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(B)))))), ((~((~v1_xboole_0(B)) & m1_subset_1(C, k1_zfmisc_1(B)))) <=> (~(~(v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(B)))))))), rewrite((~(~(v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(B)))))) <=> (v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(B))))), ((~((~v1_xboole_0(B)) & m1_subset_1(C, k1_zfmisc_1(B)))) <=> (v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(B)))))), trans(monotonicity(rewrite(((~r2_hidden(A, a_2_0_relset_2(B, C))) | (m1_subset_1(tptp_fun_D_4(C, B, A), B) & (A = k1_tarski(tptp_fun_D_4(C, B, A))) & r2_hidden(tptp_fun_D_4(C, B, A), C))) <=> ((~r2_hidden(A, a_2_0_relset_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), B)) | (~(A = k1_tarski(tptp_fun_D_4(C, B, A)))) | (~r2_hidden(tptp_fun_D_4(C, B, A), C)))))), rewrite((r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : (~(m1_subset_1(D, B) & (A = k1_tarski(D)) & r2_hidden(D, C)))) <=> (r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : ((~r2_hidden(D, C)) | (~m1_subset_1(D, B)) | (~(A = k1_tarski(D)))))), ((((~r2_hidden(A, a_2_0_relset_2(B, C))) | (m1_subset_1(tptp_fun_D_4(C, B, A), B) & (A = k1_tarski(tptp_fun_D_4(C, B, A))) & r2_hidden(tptp_fun_D_4(C, B, A), C))) & (r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : (~(m1_subset_1(D, B) & (A = k1_tarski(D)) & r2_hidden(D, C))))) <=> (((~r2_hidden(A, a_2_0_relset_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), B)) | (~(A = k1_tarski(tptp_fun_D_4(C, B, A)))) | (~r2_hidden(tptp_fun_D_4(C, B, A), C))))) & (r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : ((~r2_hidden(D, C)) | (~m1_subset_1(D, B)) | (~(A = k1_tarski(D)))))))), rewrite((((~r2_hidden(A, a_2_0_relset_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), B)) | (~(A = k1_tarski(tptp_fun_D_4(C, B, A)))) | (~r2_hidden(tptp_fun_D_4(C, B, A), C))))) & (r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : ((~r2_hidden(D, C)) | (~m1_subset_1(D, B)) | (~(A = k1_tarski(D)))))) <=> (~((~((~r2_hidden(A, a_2_0_relset_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), B)) | (~(A = k1_tarski(tptp_fun_D_4(C, B, A)))) | (~r2_hidden(tptp_fun_D_4(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : ((~r2_hidden(D, C)) | (~m1_subset_1(D, B)) | (~(A = k1_tarski(D))))))))), ((((~r2_hidden(A, a_2_0_relset_2(B, C))) | (m1_subset_1(tptp_fun_D_4(C, B, A), B) & (A = k1_tarski(tptp_fun_D_4(C, B, A))) & r2_hidden(tptp_fun_D_4(C, B, A), C))) & (r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : (~(m1_subset_1(D, B) & (A = k1_tarski(D)) & r2_hidden(D, C))))) <=> (~((~((~r2_hidden(A, a_2_0_relset_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), B)) | (~(A = k1_tarski(tptp_fun_D_4(C, B, A)))) | (~r2_hidden(tptp_fun_D_4(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : ((~r2_hidden(D, C)) | (~m1_subset_1(D, B)) | (~(A = k1_tarski(D)))))))))), (((~((~v1_xboole_0(B)) & m1_subset_1(C, k1_zfmisc_1(B)))) | (((~r2_hidden(A, a_2_0_relset_2(B, C))) | (m1_subset_1(tptp_fun_D_4(C, B, A), B) & (A = k1_tarski(tptp_fun_D_4(C, B, A))) & r2_hidden(tptp_fun_D_4(C, B, A), C))) & (r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : (~(m1_subset_1(D, B) & (A = k1_tarski(D)) & r2_hidden(D, C)))))) <=> ((v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(B)))) | (~((~((~r2_hidden(A, a_2_0_relset_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), B)) | (~(A = k1_tarski(tptp_fun_D_4(C, B, A)))) | (~r2_hidden(tptp_fun_D_4(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : ((~r2_hidden(D, C)) | (~m1_subset_1(D, B)) | (~(A = k1_tarski(D))))))))))), rewrite(((v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(B)))) | (~((~((~r2_hidden(A, a_2_0_relset_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), B)) | (~(A = k1_tarski(tptp_fun_D_4(C, B, A)))) | (~r2_hidden(tptp_fun_D_4(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : ((~r2_hidden(D, C)) | (~m1_subset_1(D, B)) | (~(A = k1_tarski(D))))))))) <=> (v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(B))) | (~((~((~r2_hidden(A, a_2_0_relset_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), B)) | (~(A = k1_tarski(tptp_fun_D_4(C, B, A)))) | (~r2_hidden(tptp_fun_D_4(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : ((~r2_hidden(D, C)) | (~m1_subset_1(D, B)) | (~(A = k1_tarski(D)))))))))), (((~((~v1_xboole_0(B)) & m1_subset_1(C, k1_zfmisc_1(B)))) | (((~r2_hidden(A, a_2_0_relset_2(B, C))) | (m1_subset_1(tptp_fun_D_4(C, B, A), B) & (A = k1_tarski(tptp_fun_D_4(C, B, A))) & r2_hidden(tptp_fun_D_4(C, B, A), C))) & (r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : (~(m1_subset_1(D, B) & (A = k1_tarski(D)) & r2_hidden(D, C)))))) <=> (v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(B))) | (~((~((~r2_hidden(A, a_2_0_relset_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), B)) | (~(A = k1_tarski(tptp_fun_D_4(C, B, A)))) | (~r2_hidden(tptp_fun_D_4(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : ((~r2_hidden(D, C)) | (~m1_subset_1(D, B)) | (~(A = k1_tarski(D)))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(25,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(C, k1_zfmisc_1(B)))) | (((~r2_hidden(A, a_2_0_relset_2(B, C))) | (m1_subset_1(tptp_fun_D_4(C, B, A), B) & (A = k1_tarski(tptp_fun_D_4(C, B, A))) & r2_hidden(tptp_fun_D_4(C, B, A), C))) & (r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : (~(m1_subset_1(D, B) & (A = k1_tarski(D)) & r2_hidden(D, C)))))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(B))) | (~((~((~r2_hidden(A, a_2_0_relset_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), B)) | (~(A = k1_tarski(tptp_fun_D_4(C, B, A)))) | (~r2_hidden(tptp_fun_D_4(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : ((~r2_hidden(D, C)) | (~m1_subset_1(D, B)) | (~(A = k1_tarski(D)))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.42 tff(26,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(C, k1_zfmisc_1(B)))) | (r2_hidden(A, a_2_0_relset_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, B) & (A = k1_tarski(D)) & r2_hidden(D, C)))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(C, k1_zfmisc_1(B)))) | (r2_hidden(A, a_2_0_relset_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, B) & (A = k1_tarski(D)) & r2_hidden(D, C))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(27,plain,
% 0.19/0.42 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((r2_hidden(A, a_2_0_relset_2(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, B) & (A = k1_tarski(D))) & r2_hidden(D, C))) <=> (r2_hidden(A, a_2_0_relset_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, B) & (A = k1_tarski(D)) & r2_hidden(D, C)))), ((((~v1_xboole_0(B)) & m1_subset_1(C, k1_zfmisc_1(B))) => (r2_hidden(A, a_2_0_relset_2(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, B) & (A = k1_tarski(D))) & r2_hidden(D, C)))) <=> (((~v1_xboole_0(B)) & m1_subset_1(C, k1_zfmisc_1(B))) => (r2_hidden(A, a_2_0_relset_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, B) & (A = k1_tarski(D)) & r2_hidden(D, C)))))), rewrite((((~v1_xboole_0(B)) & m1_subset_1(C, k1_zfmisc_1(B))) => (r2_hidden(A, a_2_0_relset_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, B) & (A = k1_tarski(D)) & r2_hidden(D, C)))) <=> ((~((~v1_xboole_0(B)) & m1_subset_1(C, k1_zfmisc_1(B)))) | (r2_hidden(A, a_2_0_relset_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, B) & (A = k1_tarski(D)) & r2_hidden(D, C))))), ((((~v1_xboole_0(B)) & m1_subset_1(C, k1_zfmisc_1(B))) => (r2_hidden(A, a_2_0_relset_2(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, B) & (A = k1_tarski(D))) & r2_hidden(D, C)))) <=> ((~((~v1_xboole_0(B)) & m1_subset_1(C, k1_zfmisc_1(B)))) | (r2_hidden(A, a_2_0_relset_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, B) & (A = k1_tarski(D)) & r2_hidden(D, C))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(28,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i] : (((~v1_xboole_0(B)) & m1_subset_1(C, k1_zfmisc_1(B))) => (r2_hidden(A, a_2_0_relset_2(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, B) & (A = k1_tarski(D))) & r2_hidden(D, C)))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(C, k1_zfmisc_1(B)))) | (r2_hidden(A, a_2_0_relset_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, B) & (A = k1_tarski(D)) & r2_hidden(D, C))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.42 tff(29,axiom,(![A: $i, B: $i, C: $i] : (((~v1_xboole_0(B)) & m1_subset_1(C, k1_zfmisc_1(B))) => (r2_hidden(A, a_2_0_relset_2(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, B) & (A = k1_tarski(D))) & r2_hidden(D, C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fraenkel_a_2_0_relset_2')).
% 0.19/0.42 tff(30,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(C, k1_zfmisc_1(B)))) | (r2_hidden(A, a_2_0_relset_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, B) & (A = k1_tarski(D)) & r2_hidden(D, C))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.42 tff(31,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(C, k1_zfmisc_1(B)))) | (r2_hidden(A, a_2_0_relset_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, B) & (A = k1_tarski(D)) & r2_hidden(D, C))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.19/0.42 tff(32,plain,(
% 0.19/0.42 ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(C, k1_zfmisc_1(B)))) | (((~r2_hidden(A, a_2_0_relset_2(B, C))) | (m1_subset_1(tptp_fun_D_4(C, B, A), B) & (A = k1_tarski(tptp_fun_D_4(C, B, A))) & r2_hidden(tptp_fun_D_4(C, B, A), C))) & (r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : (~(m1_subset_1(D, B) & (A = k1_tarski(D)) & r2_hidden(D, C))))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[31])).
% 0.19/0.42 tff(33,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(B))) | (~((~((~r2_hidden(A, a_2_0_relset_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), B)) | (~(A = k1_tarski(tptp_fun_D_4(C, B, A)))) | (~r2_hidden(tptp_fun_D_4(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : ((~r2_hidden(D, C)) | (~m1_subset_1(D, B)) | (~(A = k1_tarski(D)))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.19/0.42 tff(34,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(B))) | (~((~((~r2_hidden(A, a_2_0_relset_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), B)) | (~(A = k1_tarski(tptp_fun_D_4(C, B, A)))) | (~r2_hidden(tptp_fun_D_4(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : ((~r2_hidden(D, C)) | (~m1_subset_1(D, B)) | (~(A = k1_tarski(D)))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[33, 23])).
% 0.19/0.42 tff(35,plain,
% 0.19/0.42 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(a_2_0_relset_2(A, B), k1_zfmisc_1(k1_zfmisc_1(A)))))) <=> (~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(a_2_0_relset_2(A, B), k1_zfmisc_1(k1_zfmisc_1(A))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(36,plain,
% 0.19/0.42 ((~![A: $i] : ((~v1_xboole_0(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => m1_subset_1(a_2_0_relset_2(A, B), k1_zfmisc_1(k1_zfmisc_1(A)))))) <=> (~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(a_2_0_relset_2(A, B), k1_zfmisc_1(k1_zfmisc_1(A))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(37,axiom,(~![A: $i] : ((~v1_xboole_0(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => m1_subset_1(a_2_0_relset_2(A, B), k1_zfmisc_1(k1_zfmisc_1(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t16_relset_2')).
% 0.19/0.42 tff(38,plain,
% 0.19/0.42 (~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(a_2_0_relset_2(A, B), k1_zfmisc_1(k1_zfmisc_1(A)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.42 tff(39,plain,
% 0.19/0.42 (~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(a_2_0_relset_2(A, B), k1_zfmisc_1(k1_zfmisc_1(A)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[38, 35])).
% 0.19/0.42 tff(40,plain,
% 0.19/0.42 (~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(a_2_0_relset_2(A, B), k1_zfmisc_1(k1_zfmisc_1(A)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.19/0.42 tff(41,plain,
% 0.19/0.42 (~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(a_2_0_relset_2(A, B), k1_zfmisc_1(k1_zfmisc_1(A)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[40, 35])).
% 0.19/0.42 tff(42,plain,
% 0.19/0.42 (~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(a_2_0_relset_2(A, B), k1_zfmisc_1(k1_zfmisc_1(A)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[41, 35])).
% 0.19/0.42 tff(43,plain,
% 0.19/0.42 (~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(a_2_0_relset_2(A, B), k1_zfmisc_1(k1_zfmisc_1(A)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.19/0.42 tff(44,plain,
% 0.19/0.42 (~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(a_2_0_relset_2(A, B), k1_zfmisc_1(k1_zfmisc_1(A)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[43, 35])).
% 0.19/0.42 tff(45,plain,
% 0.19/0.42 (~((~m1_subset_1(B!1, k1_zfmisc_1(A!0))) | m1_subset_1(a_2_0_relset_2(A!0, B!1), k1_zfmisc_1(k1_zfmisc_1(A!0))))),
% 0.19/0.42 inference(and_elim,[status(thm)],[44])).
% 0.19/0.42 tff(46,plain,
% 0.19/0.42 (m1_subset_1(B!1, k1_zfmisc_1(A!0))),
% 0.19/0.42 inference(or_elim,[status(thm)],[45])).
% 0.19/0.42 tff(47,plain,
% 0.19/0.42 (~v1_xboole_0(A!0)),
% 0.19/0.42 inference(and_elim,[status(thm)],[44])).
% 0.19/0.42 tff(48,plain,
% 0.19/0.42 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(B))) | (~((~((~r2_hidden(A, a_2_0_relset_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), B)) | (~(A = k1_tarski(tptp_fun_D_4(C, B, A)))) | (~r2_hidden(tptp_fun_D_4(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : ((~r2_hidden(D, C)) | (~m1_subset_1(D, B)) | (~(A = k1_tarski(D)))))))))) | (v1_xboole_0(A!0) | (~m1_subset_1(B!1, k1_zfmisc_1(A!0))) | (~((~((~r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)) = k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))))) | (~r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), B!1)))))) | (~(r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1)) | ![D: $i] : ((~r2_hidden(D, B!1)) | (~m1_subset_1(D, A!0)) | (~(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)) = k1_tarski(D)))))))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(B))) | (~((~((~r2_hidden(A, a_2_0_relset_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), B)) | (~(A = k1_tarski(tptp_fun_D_4(C, B, A)))) | (~r2_hidden(tptp_fun_D_4(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : ((~r2_hidden(D, C)) | (~m1_subset_1(D, B)) | (~(A = k1_tarski(D)))))))))) | v1_xboole_0(A!0) | (~m1_subset_1(B!1, k1_zfmisc_1(A!0))) | (~((~((~r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)) = k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))))) | (~r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), B!1)))))) | (~(r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1)) | ![D: $i] : ((~r2_hidden(D, B!1)) | (~m1_subset_1(D, A!0)) | (~(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)) = k1_tarski(D)))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(49,plain,
% 0.19/0.42 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(B))) | (~((~((~r2_hidden(A, a_2_0_relset_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), B)) | (~(A = k1_tarski(tptp_fun_D_4(C, B, A)))) | (~r2_hidden(tptp_fun_D_4(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : ((~r2_hidden(D, C)) | (~m1_subset_1(D, B)) | (~(A = k1_tarski(D)))))))))) | (v1_xboole_0(A!0) | (~m1_subset_1(B!1, k1_zfmisc_1(A!0))) | (~((~((~r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)) = k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))))) | (~r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), B!1)))))) | (~(r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1)) | ![D: $i] : ((~r2_hidden(D, B!1)) | (~m1_subset_1(D, A!0)) | (~(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)) = k1_tarski(D)))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(50,plain,
% 0.19/0.42 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(B))) | (~((~((~r2_hidden(A, a_2_0_relset_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), B)) | (~(A = k1_tarski(tptp_fun_D_4(C, B, A)))) | (~r2_hidden(tptp_fun_D_4(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_relset_2(B, C)) | ![D: $i] : ((~r2_hidden(D, C)) | (~m1_subset_1(D, B)) | (~(A = k1_tarski(D)))))))))) | v1_xboole_0(A!0) | (~m1_subset_1(B!1, k1_zfmisc_1(A!0))) | (~((~((~r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)) = k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))))) | (~r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), B!1)))))) | (~(r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1)) | ![D: $i] : ((~r2_hidden(D, B!1)) | (~m1_subset_1(D, A!0)) | (~(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)) = k1_tarski(D))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.42 tff(51,plain,
% 0.19/0.42 (~((~((~r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)) = k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))))) | (~r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), B!1)))))) | (~(r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1)) | ![D: $i] : ((~r2_hidden(D, B!1)) | (~m1_subset_1(D, A!0)) | (~(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)) = k1_tarski(D)))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[50, 47, 46, 34])).
% 0.19/0.42 tff(52,plain,
% 0.19/0.42 (((~((~r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)) = k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))))) | (~r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), B!1)))))) | (~(r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1)) | ![D: $i] : ((~r2_hidden(D, B!1)) | (~m1_subset_1(D, A!0)) | (~(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)) = k1_tarski(D))))))) | ((~r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)) = k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))))) | (~r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), B!1)))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(53,plain,
% 0.19/0.43 ((~r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)) = k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))))) | (~r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), B!1))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.19/0.43 tff(54,plain,
% 0.19/0.43 (^[A: $i, B: $i] : refl((~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(55,plain,
% 0.19/0.43 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.43 tff(56,plain,
% 0.19/0.43 (^[A: $i, B: $i] : rewrite((~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(57,plain,
% 0.19/0.43 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[56])).
% 0.19/0.43 tff(58,plain,
% 0.19/0.43 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[57, 55])).
% 0.19/0.43 tff(59,plain,
% 0.19/0.43 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) <=> ((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))), rewrite((r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))) <=> (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))), ((((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))) <=> (((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))))), rewrite((((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))))), ((((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(60,plain,
% 0.19/0.43 (![A: $i, B: $i] : (((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[59])).
% 0.19/0.43 tff(61,plain,
% 0.19/0.43 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) <=> ![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(62,plain,
% 0.19/0.43 (^[A: $i, B: $i] : rewrite((r1_tarski(A, B) <=> ![C: $i] : (r2_hidden(C, A) => r2_hidden(C, B))) <=> (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(63,plain,
% 0.19/0.43 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : (r2_hidden(C, A) => r2_hidden(C, B))) <=> ![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.43 tff(64,axiom,(![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : (r2_hidden(C, A) => r2_hidden(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 0.19/0.43 tff(65,plain,
% 0.19/0.43 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.43 tff(66,plain,
% 0.19/0.43 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.19/0.43 tff(67,plain,(
% 0.19/0.43 ![A: $i, B: $i] : (((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[66])).
% 0.19/0.43 tff(68,plain,
% 0.19/0.43 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.19/0.43 tff(69,plain,
% 0.19/0.43 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[68, 58])).
% 0.19/0.43 tff(70,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))))) | (~((~((~r1_tarski(a_2_0_relset_2(A!0, B!1), k1_zfmisc_1(A!0))) | ![C: $i] : ((~r2_hidden(C, a_2_0_relset_2(A!0, B!1))) | r2_hidden(C, k1_zfmisc_1(A!0))))) | (~(r1_tarski(a_2_0_relset_2(A!0, B!1), k1_zfmisc_1(A!0)) | (~((~r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0))))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(71,plain,
% 0.19/0.43 (~((~((~r1_tarski(a_2_0_relset_2(A!0, B!1), k1_zfmisc_1(A!0))) | ![C: $i] : ((~r2_hidden(C, a_2_0_relset_2(A!0, B!1))) | r2_hidden(C, k1_zfmisc_1(A!0))))) | (~(r1_tarski(a_2_0_relset_2(A!0, B!1), k1_zfmisc_1(A!0)) | (~((~r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0)))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.19/0.43 tff(72,plain,
% 0.19/0.43 (((~((~r1_tarski(a_2_0_relset_2(A!0, B!1), k1_zfmisc_1(A!0))) | ![C: $i] : ((~r2_hidden(C, a_2_0_relset_2(A!0, B!1))) | r2_hidden(C, k1_zfmisc_1(A!0))))) | (~(r1_tarski(a_2_0_relset_2(A!0, B!1), k1_zfmisc_1(A!0)) | (~((~r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0))))))) | (r1_tarski(a_2_0_relset_2(A!0, B!1), k1_zfmisc_1(A!0)) | (~((~r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0)))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(73,plain,
% 0.19/0.43 (r1_tarski(a_2_0_relset_2(A!0, B!1), k1_zfmisc_1(A!0)) | (~((~r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.19/0.43 tff(74,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))) | (m1_subset_1(a_2_0_relset_2(A!0, B!1), k1_zfmisc_1(k1_zfmisc_1(A!0))) <=> r1_tarski(a_2_0_relset_2(A!0, B!1), k1_zfmisc_1(A!0)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(75,plain,
% 0.19/0.43 (m1_subset_1(a_2_0_relset_2(A!0, B!1), k1_zfmisc_1(k1_zfmisc_1(A!0))) <=> r1_tarski(a_2_0_relset_2(A!0, B!1), k1_zfmisc_1(A!0))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[74, 16])).
% 0.19/0.43 tff(76,plain,
% 0.19/0.43 (~m1_subset_1(a_2_0_relset_2(A!0, B!1), k1_zfmisc_1(k1_zfmisc_1(A!0)))),
% 0.19/0.43 inference(or_elim,[status(thm)],[45])).
% 0.19/0.43 tff(77,plain,
% 0.19/0.43 ((~(m1_subset_1(a_2_0_relset_2(A!0, B!1), k1_zfmisc_1(k1_zfmisc_1(A!0))) <=> r1_tarski(a_2_0_relset_2(A!0, B!1), k1_zfmisc_1(A!0)))) | m1_subset_1(a_2_0_relset_2(A!0, B!1), k1_zfmisc_1(k1_zfmisc_1(A!0))) | (~r1_tarski(a_2_0_relset_2(A!0, B!1), k1_zfmisc_1(A!0)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(78,plain,
% 0.19/0.43 ((~(m1_subset_1(a_2_0_relset_2(A!0, B!1), k1_zfmisc_1(k1_zfmisc_1(A!0))) <=> r1_tarski(a_2_0_relset_2(A!0, B!1), k1_zfmisc_1(A!0)))) | (~r1_tarski(a_2_0_relset_2(A!0, B!1), k1_zfmisc_1(A!0)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.19/0.43 tff(79,plain,
% 0.19/0.43 (~r1_tarski(a_2_0_relset_2(A!0, B!1), k1_zfmisc_1(A!0))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[78, 75])).
% 0.19/0.43 tff(80,plain,
% 0.19/0.43 ((~(r1_tarski(a_2_0_relset_2(A!0, B!1), k1_zfmisc_1(A!0)) | (~((~r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0)))))) | r1_tarski(a_2_0_relset_2(A!0, B!1), k1_zfmisc_1(A!0)) | (~((~r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(81,plain,
% 0.19/0.43 ((~(r1_tarski(a_2_0_relset_2(A!0, B!1), k1_zfmisc_1(A!0)) | (~((~r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0)))))) | (~((~r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.19/0.43 tff(82,plain,
% 0.19/0.43 (~((~r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[81, 73])).
% 0.19/0.43 tff(83,plain,
% 0.19/0.43 (((~r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0))) | r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(84,plain,
% 0.19/0.44 (r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.19/0.44 tff(85,plain,
% 0.19/0.44 ((~((~r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)) = k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))))) | (~r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), B!1)))))) | (~r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)) = k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))))) | (~r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), B!1))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(86,plain,
% 0.19/0.44 ((~((~r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)) = k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))))) | (~r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), B!1)))))) | (~((~m1_subset_1(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)) = k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))))) | (~r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), B!1))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.19/0.44 tff(87,plain,
% 0.19/0.44 (~((~m1_subset_1(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)) = k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))))) | (~r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), B!1)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[86, 53])).
% 0.19/0.44 tff(88,plain,
% 0.19/0.44 (((~m1_subset_1(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)) = k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))))) | (~r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), B!1))) | (tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)) = k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(89,plain,
% 0.19/0.44 (tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)) = k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.19/0.44 tff(90,plain,
% 0.19/0.44 (k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))) = tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))),
% 0.19/0.44 inference(symmetry,[status(thm)],[89])).
% 0.19/0.44 tff(91,plain,
% 0.19/0.44 (m1_subset_1(k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))), k1_zfmisc_1(A!0)) <=> m1_subset_1(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[90])).
% 0.19/0.44 tff(92,plain,
% 0.19/0.44 (m1_subset_1(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0)) <=> m1_subset_1(k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))), k1_zfmisc_1(A!0))),
% 0.19/0.44 inference(symmetry,[status(thm)],[91])).
% 0.19/0.44 tff(93,plain,
% 0.19/0.44 ((~m1_subset_1(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0))) <=> (~m1_subset_1(k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))), k1_zfmisc_1(A!0)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[92])).
% 0.19/0.44 tff(94,plain,
% 0.19/0.44 (((~r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), a_2_0_relset_2(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0))) | (~r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(95,plain,
% 0.19/0.44 (~r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[94, 82])).
% 0.19/0.44 tff(96,plain,
% 0.19/0.44 (^[A: $i] : refl((~v1_xboole_0(k1_zfmisc_1(A))) <=> (~v1_xboole_0(k1_zfmisc_1(A))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(97,plain,
% 0.19/0.44 (![A: $i] : (~v1_xboole_0(k1_zfmisc_1(A))) <=> ![A: $i] : (~v1_xboole_0(k1_zfmisc_1(A)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[96])).
% 0.19/0.44 tff(98,plain,
% 0.19/0.44 (![A: $i] : (~v1_xboole_0(k1_zfmisc_1(A))) <=> ![A: $i] : (~v1_xboole_0(k1_zfmisc_1(A)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(99,axiom,(![A: $i] : (~v1_xboole_0(k1_zfmisc_1(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_subset_1')).
% 0.19/0.44 tff(100,plain,
% 0.19/0.44 (![A: $i] : (~v1_xboole_0(k1_zfmisc_1(A)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.19/0.44 tff(101,plain,(
% 0.19/0.44 ![A: $i] : (~v1_xboole_0(k1_zfmisc_1(A)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[100])).
% 0.19/0.44 tff(102,plain,
% 0.19/0.44 (![A: $i] : (~v1_xboole_0(k1_zfmisc_1(A)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.19/0.44 tff(103,plain,
% 0.19/0.44 ((~![A: $i] : (~v1_xboole_0(k1_zfmisc_1(A)))) | (~v1_xboole_0(k1_zfmisc_1(A!0)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(104,plain,
% 0.19/0.44 (~v1_xboole_0(k1_zfmisc_1(A!0))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.19/0.44 tff(105,plain,
% 0.19/0.44 (^[A: $i, B: $i] : refl((r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(106,plain,
% 0.19/0.44 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[105])).
% 0.19/0.44 tff(107,plain,
% 0.19/0.44 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(108,plain,
% 0.19/0.44 (^[A: $i, B: $i] : rewrite((m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B))) <=> (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(109,plain,
% 0.19/0.44 (![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[108])).
% 0.19/0.44 tff(110,axiom,(![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_subset')).
% 0.19/0.44 tff(111,plain,
% 0.19/0.44 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.19/0.44 tff(112,plain,
% 0.19/0.44 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.19/0.44 tff(113,plain,(
% 0.19/0.44 ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[112])).
% 0.19/0.44 tff(114,plain,
% 0.19/0.44 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[113, 106])).
% 0.19/0.44 tff(115,plain,
% 0.19/0.44 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(k1_zfmisc_1(A!0)) | r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0)) | (~m1_subset_1(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(k1_zfmisc_1(A!0)) | r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0)) | (~m1_subset_1(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(116,plain,
% 0.19/0.44 ((r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0)) | v1_xboole_0(k1_zfmisc_1(A!0)) | (~m1_subset_1(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0)))) <=> (v1_xboole_0(k1_zfmisc_1(A!0)) | r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0)) | (~m1_subset_1(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(117,plain,
% 0.19/0.44 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0)) | v1_xboole_0(k1_zfmisc_1(A!0)) | (~m1_subset_1(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(k1_zfmisc_1(A!0)) | r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0)) | (~m1_subset_1(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0)))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[116])).
% 0.19/0.44 tff(118,plain,
% 0.19/0.44 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0)) | v1_xboole_0(k1_zfmisc_1(A!0)) | (~m1_subset_1(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(k1_zfmisc_1(A!0)) | r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0)) | (~m1_subset_1(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[117, 115])).
% 0.19/0.44 tff(119,plain,
% 0.19/0.44 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0)) | v1_xboole_0(k1_zfmisc_1(A!0)) | (~m1_subset_1(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(120,plain,
% 0.19/0.44 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(k1_zfmisc_1(A!0)) | r2_hidden(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0)) | (~m1_subset_1(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.19/0.44 tff(121,plain,
% 0.19/0.44 (~m1_subset_1(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)), k1_zfmisc_1(A!0))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[120, 114, 104, 95])).
% 0.19/0.44 tff(122,plain,
% 0.19/0.44 (~m1_subset_1(k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))), k1_zfmisc_1(A!0))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[121, 93])).
% 0.19/0.44 tff(123,plain,
% 0.19/0.44 ((~(m1_subset_1(k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))), k1_zfmisc_1(A!0)) <=> r1_tarski(k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))), A!0))) | m1_subset_1(k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))), k1_zfmisc_1(A!0)) | (~r1_tarski(k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))), A!0))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(124,plain,
% 0.19/0.44 (~r1_tarski(k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))), A!0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[123, 122, 18])).
% 0.19/0.44 tff(125,plain,
% 0.19/0.44 (((~m1_subset_1(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)) = k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))))) | (~r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), B!1))) | m1_subset_1(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(126,plain,
% 0.19/0.44 (m1_subset_1(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[125, 87])).
% 0.19/0.44 tff(127,plain,
% 0.19/0.44 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(A!0) | (~m1_subset_1(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)) | r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(A!0) | (~m1_subset_1(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)) | r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(128,plain,
% 0.19/0.44 ((r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0) | v1_xboole_0(A!0) | (~m1_subset_1(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0))) <=> (v1_xboole_0(A!0) | (~m1_subset_1(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)) | r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(129,plain,
% 0.19/0.44 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0) | v1_xboole_0(A!0) | (~m1_subset_1(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(A!0) | (~m1_subset_1(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)) | r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[128])).
% 0.19/0.44 tff(130,plain,
% 0.19/0.44 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0) | v1_xboole_0(A!0) | (~m1_subset_1(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(A!0) | (~m1_subset_1(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)) | r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0))),
% 0.19/0.44 inference(transitivity,[status(thm)],[129, 127])).
% 0.19/0.44 tff(131,plain,
% 0.19/0.44 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0) | v1_xboole_0(A!0) | (~m1_subset_1(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(132,plain,
% 0.19/0.44 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(A!0) | (~m1_subset_1(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)) | r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.19/0.44 tff(133,plain,
% 0.19/0.44 (r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[132, 47, 114, 126])).
% 0.19/0.45 tff(134,plain,
% 0.19/0.45 ((~(r1_tarski(k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))), A!0) <=> r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0))) | r1_tarski(k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))), A!0) | (~r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(135,plain,
% 0.19/0.45 ((~(r1_tarski(k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))), A!0) <=> r2_hidden(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1))), A!0))) | r1_tarski(k1_tarski(tptp_fun_D_4(B!1, A!0, tptp_fun_C_2(k1_zfmisc_1(A!0), a_2_0_relset_2(A!0, B!1)))), A!0)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.19/0.45 tff(136,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[135, 124, 9])).
% 0.19/0.45 % SZS output end Proof
%------------------------------------------------------------------------------