TSTP Solution File: SEU437+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU437+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 07:29:40 EDT 2022
% Result : Theorem 67.23s 42.24s
% Output : Proof 67.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU437+1 : TPTP v8.1.0. Released v3.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 14:32:54 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 67.23/42.24 % SZS status Theorem
% 67.23/42.24 % SZS output start Proof
% 67.23/42.24 tff(r2_hidden_type, type, (
% 67.23/42.24 r2_hidden: ( $i * $i ) > $o)).
% 67.23/42.24 tff(tptp_fun_D_3_type, type, (
% 67.23/42.24 tptp_fun_D_3: $i)).
% 67.23/42.24 tff(k4_tarski_type, type, (
% 67.23/42.24 k4_tarski: ( $i * $i ) > $i)).
% 67.23/42.24 tff(tptp_fun_C_5_type, type, (
% 67.23/42.24 tptp_fun_C_5: ( $i * $i ) > $i)).
% 67.23/42.24 tff(k8_relset_2_type, type, (
% 67.23/42.24 k8_relset_2: ( $i * $i * $i * $i ) > $i)).
% 67.23/42.24 tff(tptp_fun_C_0_type, type, (
% 67.23/42.24 tptp_fun_C_0: $i)).
% 67.23/42.24 tff(tptp_fun_B_1_type, type, (
% 67.23/42.24 tptp_fun_B_1: $i)).
% 67.23/42.24 tff(tptp_fun_A_2_type, type, (
% 67.23/42.24 tptp_fun_A_2: $i)).
% 67.23/42.24 tff(tptp_fun_E_4_type, type, (
% 67.23/42.24 tptp_fun_E_4: $i)).
% 67.23/42.24 tff(tptp_fun_F_16_type, type, (
% 67.23/42.24 tptp_fun_F_16: ( $i * $i * $i ) > $i)).
% 67.23/42.24 tff(k9_relat_1_type, type, (
% 67.23/42.24 k9_relat_1: ( $i * $i ) > $i)).
% 67.23/42.24 tff(k1_tarski_type, type, (
% 67.23/42.24 k1_tarski: $i > $i)).
% 67.23/42.24 tff(v1_relat_1_type, type, (
% 67.23/42.24 v1_relat_1: $i > $o)).
% 67.23/42.24 tff(m1_subset_1_type, type, (
% 67.23/42.24 m1_subset_1: ( $i * $i ) > $o)).
% 67.23/42.24 tff(k1_zfmisc_1_type, type, (
% 67.23/42.24 k1_zfmisc_1: $i > $i)).
% 67.23/42.24 tff(k2_zfmisc_1_type, type, (
% 67.23/42.24 k2_zfmisc_1: ( $i * $i ) > $i)).
% 67.23/42.24 tff(r1_tarski_type, type, (
% 67.23/42.24 r1_tarski: ( $i * $i ) > $o)).
% 67.23/42.24 tff(v1_xboole_0_type, type, (
% 67.23/42.24 v1_xboole_0: $i > $o)).
% 67.23/42.24 tff(k7_relset_2_type, type, (
% 67.23/42.24 k7_relset_2: ( $i * $i * $i * $i ) > $i)).
% 67.23/42.24 tff(1,plain,
% 67.23/42.24 (^[A: $i, B: $i, C: $i] : refl((v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))))),
% 67.23/42.24 inference(bind,[status(th)],[])).
% 67.23/42.24 tff(2,plain,
% 67.23/42.24 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 67.23/42.24 inference(quant_intro,[status(thm)],[1])).
% 67.23/42.24 tff(3,plain,
% 67.23/42.24 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 67.23/42.24 inference(rewrite,[status(thm)],[])).
% 67.23/42.24 tff(4,plain,
% 67.23/42.24 (^[A: $i, B: $i, C: $i] : rewrite((m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) <=> (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))))),
% 67.23/42.24 inference(bind,[status(th)],[])).
% 67.23/42.24 tff(5,plain,
% 67.23/42.24 (![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) <=> ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 67.23/42.24 inference(quant_intro,[status(thm)],[4])).
% 67.23/42.24 tff(6,axiom,(![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_relset_1')).
% 67.23/42.24 tff(7,plain,
% 67.23/42.24 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 67.23/42.24 inference(modus_ponens,[status(thm)],[6, 5])).
% 67.23/42.24 tff(8,plain,
% 67.23/42.24 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 67.23/42.24 inference(modus_ponens,[status(thm)],[7, 3])).
% 67.23/42.24 tff(9,plain,(
% 67.23/42.24 ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 67.23/42.24 inference(skolemize,[status(sab)],[8])).
% 67.23/42.24 tff(10,plain,
% 67.23/42.24 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 67.23/42.24 inference(modus_ponens,[status(thm)],[9, 2])).
% 67.23/42.24 tff(11,plain,
% 67.23/42.24 ((m1_subset_1(C!0, k1_zfmisc_1(A!2)) & (m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))) & (~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~r1_tarski(D!3, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))))) <=> (m1_subset_1(C!0, k1_zfmisc_1(A!2)) & m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))) & (~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~r1_tarski(D!3, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))))),
% 67.23/42.24 inference(rewrite,[status(thm)],[])).
% 67.23/42.24 tff(12,plain,
% 67.23/42.24 (((~(~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))) & (~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~r1_tarski(D!3, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))))) <=> (m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))) & (~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~r1_tarski(D!3, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))))),
% 67.23/42.25 inference(rewrite,[status(thm)],[])).
% 67.23/42.25 tff(13,plain,
% 67.23/42.25 ((~(~m1_subset_1(C!0, k1_zfmisc_1(A!2)))) <=> m1_subset_1(C!0, k1_zfmisc_1(A!2))),
% 67.23/42.25 inference(rewrite,[status(thm)],[])).
% 67.23/42.25 tff(14,plain,
% 67.23/42.25 (((~(~m1_subset_1(C!0, k1_zfmisc_1(A!2)))) & ((~(~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))) & (~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~r1_tarski(D!3, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))))) <=> (m1_subset_1(C!0, k1_zfmisc_1(A!2)) & (m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))) & (~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~r1_tarski(D!3, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))))))),
% 67.23/42.25 inference(monotonicity,[status(thm)],[13, 12])).
% 67.23/42.25 tff(15,plain,
% 67.23/42.25 (((~(~m1_subset_1(C!0, k1_zfmisc_1(A!2)))) & ((~(~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))) & (~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~r1_tarski(D!3, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))))) <=> (m1_subset_1(C!0, k1_zfmisc_1(A!2)) & m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))) & (~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~r1_tarski(D!3, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))))),
% 67.23/42.25 inference(transitivity,[status(thm)],[14, 11])).
% 67.23/42.25 tff(16,plain,
% 67.23/42.25 ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | ![E: $i] : (r1_tarski(k8_relset_2(A, B, C, D), k8_relset_2(A, B, C, E)) | (~r1_tarski(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))))))) <=> (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | ![E: $i] : (r1_tarski(k8_relset_2(A, B, C, D), k8_relset_2(A, B, C, E)) | (~r1_tarski(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))))))))),
% 67.23/42.25 inference(rewrite,[status(thm)],[])).
% 67.23/42.25 tff(17,plain,
% 67.23/42.25 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (r1_tarski(D, E) => r1_tarski(k8_relset_2(A, B, C, D), k8_relset_2(A, B, C, E))))))) <=> (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | ![E: $i] : (r1_tarski(k8_relset_2(A, B, C, D), k8_relset_2(A, B, C, E)) | (~r1_tarski(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))))))))),
% 67.23/42.25 inference(rewrite,[status(thm)],[])).
% 67.23/42.25 tff(18,axiom,(~![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (r1_tarski(D, E) => r1_tarski(k8_relset_2(A, B, C, D), k8_relset_2(A, B, C, E))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t40_relset_2')).
% 67.23/42.25 tff(19,plain,
% 67.23/42.25 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | ![E: $i] : (r1_tarski(k8_relset_2(A, B, C, D), k8_relset_2(A, B, C, E)) | (~r1_tarski(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))))))),
% 67.23/42.25 inference(modus_ponens,[status(thm)],[18, 17])).
% 67.23/42.25 tff(20,plain,
% 67.23/42.25 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | ![E: $i] : (r1_tarski(k8_relset_2(A, B, C, D), k8_relset_2(A, B, C, E)) | (~r1_tarski(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))))))),
% 67.23/42.25 inference(modus_ponens,[status(thm)],[19, 16])).
% 67.23/42.25 tff(21,plain,
% 67.23/42.25 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | ![E: $i] : (r1_tarski(k8_relset_2(A, B, C, D), k8_relset_2(A, B, C, E)) | (~r1_tarski(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))))))),
% 67.23/42.25 inference(modus_ponens,[status(thm)],[20, 16])).
% 67.23/42.25 tff(22,plain,
% 67.23/42.25 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | ![E: $i] : (r1_tarski(k8_relset_2(A, B, C, D), k8_relset_2(A, B, C, E)) | (~r1_tarski(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))))))),
% 67.23/42.25 inference(modus_ponens,[status(thm)],[21, 16])).
% 67.23/42.25 tff(23,plain,
% 67.23/42.25 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | ![E: $i] : (r1_tarski(k8_relset_2(A, B, C, D), k8_relset_2(A, B, C, E)) | (~r1_tarski(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))))))),
% 67.23/42.25 inference(modus_ponens,[status(thm)],[22, 16])).
% 67.23/42.25 tff(24,plain,
% 67.23/42.25 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | ![E: $i] : (r1_tarski(k8_relset_2(A, B, C, D), k8_relset_2(A, B, C, E)) | (~r1_tarski(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))))))),
% 67.23/42.25 inference(modus_ponens,[status(thm)],[23, 16])).
% 67.23/42.25 tff(25,plain,
% 67.23/42.25 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | ![E: $i] : (r1_tarski(k8_relset_2(A, B, C, D), k8_relset_2(A, B, C, E)) | (~r1_tarski(D, E)) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))))))),
% 67.23/42.25 inference(modus_ponens,[status(thm)],[24, 16])).
% 67.23/42.25 tff(26,plain,
% 67.23/42.25 (m1_subset_1(C!0, k1_zfmisc_1(A!2)) & m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))) & (~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~r1_tarski(D!3, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))))),
% 67.23/42.25 inference(modus_ponens,[status(thm)],[25, 15])).
% 67.23/42.25 tff(27,plain,
% 67.23/42.25 (~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~r1_tarski(D!3, E!4)) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))),
% 67.23/42.25 inference(and_elim,[status(thm)],[26])).
% 67.23/42.25 tff(28,plain,
% 67.23/42.25 (m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))),
% 67.23/42.25 inference(or_elim,[status(thm)],[27])).
% 67.23/42.25 tff(29,plain,
% 67.23/42.25 (((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (v1_relat_1(E!4) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | v1_relat_1(E!4) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))),
% 67.23/42.25 inference(rewrite,[status(thm)],[])).
% 67.23/42.25 tff(30,plain,
% 67.23/42.25 ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (v1_relat_1(E!4) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))),
% 67.23/42.25 inference(quant_inst,[status(thm)],[])).
% 67.23/42.25 tff(31,plain,
% 67.23/42.25 ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | v1_relat_1(E!4) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))),
% 67.23/42.25 inference(modus_ponens,[status(thm)],[30, 29])).
% 67.23/42.25 tff(32,plain,
% 67.23/42.25 (v1_relat_1(E!4)),
% 67.23/42.25 inference(unit_resolution,[status(thm)],[31, 28, 10])).
% 67.23/42.25 tff(33,plain,
% 67.23/42.25 (^[A: $i, B: $i, C: $i] : refl(((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C))) <=> ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C))))),
% 67.23/42.25 inference(bind,[status(th)],[])).
% 67.23/42.25 tff(34,plain,
% 67.23/42.25 (![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C))) <=> ![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))),
% 67.23/42.25 inference(quant_intro,[status(thm)],[33])).
% 67.23/42.25 tff(35,plain,
% 67.23/42.25 (![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C))) <=> ![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))),
% 67.27/42.25 inference(rewrite,[status(thm)],[])).
% 67.27/42.25 tff(36,plain,
% 67.27/42.25 (^[A: $i, B: $i, C: $i] : rewrite((v1_relat_1(C) => (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C))) <=> ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C))))),
% 67.27/42.25 inference(bind,[status(th)],[])).
% 67.27/42.25 tff(37,plain,
% 67.27/42.25 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) => (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C))) <=> ![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))),
% 67.27/42.25 inference(quant_intro,[status(thm)],[36])).
% 67.27/42.25 tff(38,axiom,(![A: $i, B: $i, C: $i] : (v1_relat_1(C) => (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t9_relset_2')).
% 67.27/42.25 tff(39,plain,
% 67.27/42.25 (![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))),
% 67.27/42.25 inference(modus_ponens,[status(thm)],[38, 37])).
% 67.27/42.25 tff(40,plain,
% 67.27/42.25 (![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))),
% 67.27/42.25 inference(modus_ponens,[status(thm)],[39, 35])).
% 67.27/42.25 tff(41,plain,(
% 67.27/42.25 ![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))),
% 67.27/42.25 inference(skolemize,[status(sab)],[40])).
% 67.27/42.25 tff(42,plain,
% 67.27/42.25 (![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))),
% 67.27/42.25 inference(modus_ponens,[status(thm)],[41, 34])).
% 67.27/42.25 tff(43,plain,
% 67.27/42.25 (((~![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))) | ((~v1_relat_1(E!4)) | (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) <=> r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4)))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))) | (~v1_relat_1(E!4)) | (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) <=> r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4)))),
% 67.27/42.25 inference(rewrite,[status(thm)],[])).
% 67.27/42.25 tff(44,plain,
% 67.27/42.25 ((~![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))) | ((~v1_relat_1(E!4)) | (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) <=> r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4)))),
% 67.27/42.25 inference(quant_inst,[status(thm)],[])).
% 67.27/42.25 tff(45,plain,
% 67.27/42.25 ((~![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))) | (~v1_relat_1(E!4)) | (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) <=> r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4))),
% 67.27/42.25 inference(modus_ponens,[status(thm)],[44, 43])).
% 67.27/42.25 tff(46,plain,
% 67.27/42.25 (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) <=> r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4)),
% 67.27/42.25 inference(unit_resolution,[status(thm)],[45, 42, 32])).
% 67.27/42.25 tff(47,plain,
% 67.27/42.25 (^[A: $i, B: $i, C: $i, D: $i] : refl(((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))),
% 67.27/42.25 inference(bind,[status(th)],[])).
% 67.27/42.25 tff(48,plain,
% 67.27/42.25 (![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 67.27/42.25 inference(quant_intro,[status(thm)],[47])).
% 67.27/42.25 tff(49,plain,
% 67.27/42.25 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> (~((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))), ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> (~(~((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))))), rewrite((~(~((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))), ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))), (((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D))) <=> (((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D))))), rewrite((((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D))) <=> ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), (((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D))) <=> ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))))),
% 67.27/42.25 inference(bind,[status(th)],[])).
% 67.27/42.25 tff(50,plain,
% 67.27/42.25 (![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 67.27/42.25 inference(quant_intro,[status(thm)],[49])).
% 67.27/42.25 tff(51,plain,
% 67.27/42.25 (![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)))),
% 67.27/42.25 inference(rewrite,[status(thm)],[])).
% 67.27/42.25 tff(52,plain,
% 67.27/42.26 (^[A: $i, B: $i, C: $i, D: $i] : rewrite(((m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) => (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D))) <=> ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D))))),
% 67.27/42.26 inference(bind,[status(th)],[])).
% 67.27/42.26 tff(53,plain,
% 67.27/42.26 (![A: $i, B: $i, C: $i, D: $i] : ((m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) => (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)))),
% 67.27/42.26 inference(quant_intro,[status(thm)],[52])).
% 67.27/42.26 tff(54,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) => (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k8_relset_2')).
% 67.27/42.26 tff(55,plain,
% 67.27/42.26 (![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)))),
% 67.27/42.26 inference(modus_ponens,[status(thm)],[54, 53])).
% 67.27/42.26 tff(56,plain,
% 67.27/42.26 (![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)))),
% 67.27/42.26 inference(modus_ponens,[status(thm)],[55, 51])).
% 67.27/42.26 tff(57,plain,(
% 67.27/42.26 ![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)))),
% 67.27/42.26 inference(skolemize,[status(sab)],[56])).
% 67.27/42.26 tff(58,plain,
% 67.27/42.26 (![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 67.27/42.26 inference(modus_ponens,[status(thm)],[57, 50])).
% 67.27/42.26 tff(59,plain,
% 67.27/42.26 (![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 67.27/42.26 inference(modus_ponens,[status(thm)],[58, 48])).
% 67.27/42.26 tff(60,plain,
% 67.27/42.26 (m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))),
% 67.27/42.26 inference(and_elim,[status(thm)],[26])).
% 67.27/42.26 tff(61,plain,
% 67.27/42.26 (m1_subset_1(C!0, k1_zfmisc_1(A!2))),
% 67.27/42.26 inference(and_elim,[status(thm)],[26])).
% 67.27/42.26 tff(62,plain,
% 67.27/42.26 (((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k8_relset_2(A!2, B!1, C!0, D!3) = k7_relset_2(A!2, B!1, C!0, D!3)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k8_relset_2(A!2, B!1, C!0, D!3) = k7_relset_2(A!2, B!1, C!0, D!3)))),
% 67.27/42.26 inference(rewrite,[status(thm)],[])).
% 67.27/42.26 tff(63,plain,
% 67.27/42.26 (((k8_relset_2(A!2, B!1, C!0, D!3) = k7_relset_2(A!2, B!1, C!0, D!3)) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2)))) <=> ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k8_relset_2(A!2, B!1, C!0, D!3) = k7_relset_2(A!2, B!1, C!0, D!3)))),
% 67.27/42.26 inference(rewrite,[status(thm)],[])).
% 67.27/42.26 tff(64,plain,
% 67.27/42.26 (((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k8_relset_2(A!2, B!1, C!0, D!3) = k7_relset_2(A!2, B!1, C!0, D!3)) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k8_relset_2(A!2, B!1, C!0, D!3) = k7_relset_2(A!2, B!1, C!0, D!3))))),
% 67.27/42.26 inference(monotonicity,[status(thm)],[63])).
% 67.27/42.26 tff(65,plain,
% 67.27/42.26 (((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k8_relset_2(A!2, B!1, C!0, D!3) = k7_relset_2(A!2, B!1, C!0, D!3)) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k8_relset_2(A!2, B!1, C!0, D!3) = k7_relset_2(A!2, B!1, C!0, D!3)))),
% 67.27/42.26 inference(transitivity,[status(thm)],[64, 62])).
% 67.27/42.26 tff(66,plain,
% 67.27/42.26 ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k8_relset_2(A!2, B!1, C!0, D!3) = k7_relset_2(A!2, B!1, C!0, D!3)) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))))),
% 67.27/42.26 inference(quant_inst,[status(thm)],[])).
% 67.27/42.26 tff(67,plain,
% 67.27/42.26 ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_relset_2(A, B, C, D) = k7_relset_2(A, B, C, D)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k8_relset_2(A!2, B!1, C!0, D!3) = k7_relset_2(A!2, B!1, C!0, D!3))),
% 67.27/42.26 inference(modus_ponens,[status(thm)],[66, 65])).
% 67.27/42.26 tff(68,plain,
% 67.27/42.26 (k8_relset_2(A!2, B!1, C!0, D!3) = k7_relset_2(A!2, B!1, C!0, D!3)),
% 67.27/42.26 inference(unit_resolution,[status(thm)],[67, 61, 60, 59])).
% 67.27/42.26 tff(69,plain,
% 67.27/42.26 (k7_relset_2(A!2, B!1, C!0, D!3) = k8_relset_2(A!2, B!1, C!0, D!3)),
% 67.27/42.26 inference(symmetry,[status(thm)],[68])).
% 67.27/42.26 tff(70,plain,
% 67.27/42.26 (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3)) <=> r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))),
% 67.27/42.26 inference(monotonicity,[status(thm)],[69])).
% 67.27/42.26 tff(71,plain,
% 67.27/42.26 (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3)) <=> r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))),
% 67.27/42.26 inference(symmetry,[status(thm)],[70])).
% 67.27/42.26 tff(72,plain,
% 67.27/42.26 (^[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_5(B, A), A)) | r2_hidden(tptp_fun_C_5(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_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B))))))))),
% 67.27/42.26 inference(bind,[status(th)],[])).
% 67.27/42.26 tff(73,plain,
% 67.27/42.26 (![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_5(B, A), A)) | r2_hidden(tptp_fun_C_5(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_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B)))))))),
% 67.27/42.26 inference(quant_intro,[status(thm)],[72])).
% 67.27/42.26 tff(74,plain,
% 67.27/42.26 (^[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_5(B, A), A)) | r2_hidden(tptp_fun_C_5(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_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B))))))))),
% 67.27/42.26 inference(bind,[status(th)],[])).
% 67.27/42.26 tff(75,plain,
% 67.27/42.26 (![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_5(B, A), A)) | r2_hidden(tptp_fun_C_5(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_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B)))))))),
% 67.27/42.26 inference(quant_intro,[status(thm)],[74])).
% 67.27/42.26 tff(76,plain,
% 67.27/42.26 (![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_5(B, A), A)) | r2_hidden(tptp_fun_C_5(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_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B)))))))),
% 67.27/42.26 inference(transitivity,[status(thm)],[75, 73])).
% 67.27/42.26 tff(77,plain,
% 67.27/42.26 (^[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_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B)))) <=> (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_5(B, A), A)) | r2_hidden(tptp_fun_C_5(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_5(B, A), A)) | r2_hidden(tptp_fun_C_5(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_5(B, A), A)) | r2_hidden(tptp_fun_C_5(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_5(B, A), A)) | r2_hidden(tptp_fun_C_5(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_5(B, A), A)) | r2_hidden(tptp_fun_C_5(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_5(B, A), A)) | r2_hidden(tptp_fun_C_5(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_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B)))))))))),
% 67.27/42.26 inference(bind,[status(th)],[])).
% 67.27/42.26 tff(78,plain,
% 67.27/42.26 (![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_5(B, A), A)) | r2_hidden(tptp_fun_C_5(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_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B)))))))),
% 67.27/42.26 inference(quant_intro,[status(thm)],[77])).
% 67.27/42.26 tff(79,plain,
% 67.27/42.26 (![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)))),
% 67.27/42.26 inference(rewrite,[status(thm)],[])).
% 67.27/42.26 tff(80,plain,
% 67.27/42.26 (^[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))))),
% 67.27/42.26 inference(bind,[status(th)],[])).
% 67.27/42.26 tff(81,plain,
% 67.27/42.26 (![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)))),
% 67.27/42.26 inference(quant_intro,[status(thm)],[80])).
% 67.27/42.26 tff(82,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')).
% 67.27/42.26 tff(83,plain,
% 67.27/42.26 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 67.27/42.27 inference(modus_ponens,[status(thm)],[82, 81])).
% 67.27/42.27 tff(84,plain,
% 67.27/42.27 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 67.27/42.27 inference(modus_ponens,[status(thm)],[83, 79])).
% 67.27/42.27 tff(85,plain,(
% 67.27/42.27 ![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_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B)))))),
% 67.27/42.27 inference(skolemize,[status(sab)],[84])).
% 67.27/42.27 tff(86,plain,
% 67.27/42.27 (![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_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B)))))))),
% 67.27/42.27 inference(modus_ponens,[status(thm)],[85, 78])).
% 67.27/42.27 tff(87,plain,
% 67.27/42.27 (![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_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B)))))))),
% 67.27/42.27 inference(modus_ponens,[status(thm)],[86, 76])).
% 67.27/42.27 tff(88,plain,
% 67.27/42.27 ((~![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_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B)))))))) | (~((~((~r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4))) | ![C: $i] : ((~r2_hidden(C, k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, k8_relset_2(A!2, B!1, C!0, E!4))))) | (~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))))))))),
% 67.27/42.27 inference(quant_inst,[status(thm)],[])).
% 67.27/42.27 tff(89,plain,
% 67.27/42.27 (~((~((~r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4))) | ![C: $i] : ((~r2_hidden(C, k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, k8_relset_2(A!2, B!1, C!0, E!4))))) | (~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4)))))))),
% 67.27/42.27 inference(unit_resolution,[status(thm)],[88, 87])).
% 67.27/42.27 tff(90,plain,
% 67.27/42.27 (((~((~r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4))) | ![C: $i] : ((~r2_hidden(C, k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, k8_relset_2(A!2, B!1, C!0, E!4))))) | (~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))))))) | (r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4)))))),
% 67.27/42.27 inference(tautology,[status(thm)],[])).
% 67.27/42.27 tff(91,plain,
% 67.27/42.27 (r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))))),
% 67.27/42.27 inference(unit_resolution,[status(thm)],[90, 89])).
% 67.27/42.27 tff(92,plain,
% 67.27/42.27 (~r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4))),
% 67.27/42.27 inference(or_elim,[status(thm)],[27])).
% 67.27/42.27 tff(93,plain,
% 67.27/42.27 ((~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4)))))) | r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))))),
% 67.27/42.27 inference(tautology,[status(thm)],[])).
% 67.27/42.27 tff(94,plain,
% 67.27/42.27 ((~(r1_tarski(k8_relset_2(A!2, B!1, C!0, D!3), k8_relset_2(A!2, B!1, C!0, E!4)) | (~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4)))))) | (~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))))),
% 67.27/42.27 inference(unit_resolution,[status(thm)],[93, 92])).
% 67.27/42.27 tff(95,plain,
% 67.27/42.27 (~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4)))),
% 67.27/42.27 inference(unit_resolution,[status(thm)],[94, 91])).
% 67.27/42.27 tff(96,plain,
% 67.27/42.27 (((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))),
% 67.27/42.27 inference(tautology,[status(thm)],[])).
% 67.27/42.27 tff(97,plain,
% 67.27/42.27 (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))),
% 67.27/42.27 inference(unit_resolution,[status(thm)],[96, 95])).
% 67.27/42.27 tff(98,plain,
% 67.27/42.27 (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))),
% 67.27/42.27 inference(modus_ponens,[status(thm)],[97, 71])).
% 67.27/42.27 tff(99,plain,
% 67.27/42.27 (m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)) <=> m1_subset_1(k8_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))),
% 67.27/42.27 inference(monotonicity,[status(thm)],[69])).
% 67.27/42.27 tff(100,plain,
% 67.27/42.27 (m1_subset_1(k8_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)) <=> m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))),
% 67.27/42.27 inference(symmetry,[status(thm)],[99])).
% 67.27/42.27 tff(101,plain,
% 67.27/42.27 (^[A: $i, B: $i, C: $i, D: $i] : refl((m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))),
% 67.27/42.27 inference(bind,[status(th)],[])).
% 67.27/42.27 tff(102,plain,
% 67.27/42.27 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 67.27/42.27 inference(quant_intro,[status(thm)],[101])).
% 67.27/42.27 tff(103,plain,
% 67.27/42.27 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> (~((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))), ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> (~(~((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))))), rewrite((~(~((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))))), ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))))), (((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B))) <=> (((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B))))), rewrite((((~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B))) <=> (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), (((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B))) <=> (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))))),
% 67.27/42.28 inference(bind,[status(th)],[])).
% 67.27/42.28 tff(104,plain,
% 67.27/42.28 (![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B))) <=> ![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 67.27/42.28 inference(quant_intro,[status(thm)],[103])).
% 67.27/42.28 tff(105,plain,
% 67.27/42.28 (![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)))),
% 67.27/42.28 inference(rewrite,[status(thm)],[])).
% 67.27/42.28 tff(106,plain,
% 67.27/42.28 (^[A: $i, B: $i, C: $i, D: $i] : rewrite(((m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) => m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B))) <=> ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B))))),
% 67.27/42.28 inference(bind,[status(th)],[])).
% 67.27/42.28 tff(107,plain,
% 67.27/42.28 (![A: $i, B: $i, C: $i, D: $i] : ((m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) => m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)))),
% 67.27/42.28 inference(quant_intro,[status(thm)],[106])).
% 67.27/42.28 tff(108,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) => m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k8_relset_2')).
% 67.27/42.28 tff(109,plain,
% 67.27/42.28 (![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)))),
% 67.27/42.28 inference(modus_ponens,[status(thm)],[108, 107])).
% 67.27/42.28 tff(110,plain,
% 67.27/42.28 (![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)))),
% 67.27/42.28 inference(modus_ponens,[status(thm)],[109, 105])).
% 67.27/42.28 tff(111,plain,(
% 67.27/42.28 ![A: $i, B: $i, C: $i, D: $i] : ((~(m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)))),
% 67.27/42.28 inference(skolemize,[status(sab)],[110])).
% 67.27/42.28 tff(112,plain,
% 67.27/42.28 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 67.27/42.28 inference(modus_ponens,[status(thm)],[111, 104])).
% 67.27/42.28 tff(113,plain,
% 67.27/42.28 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 67.27/42.28 inference(modus_ponens,[status(thm)],[112, 102])).
% 67.27/42.28 tff(114,plain,
% 67.27/42.28 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | m1_subset_1(k8_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | m1_subset_1(k8_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)))),
% 67.27/42.28 inference(rewrite,[status(thm)],[])).
% 67.27/42.28 tff(115,plain,
% 67.27/42.28 ((m1_subset_1(k8_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2)))) <=> ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | m1_subset_1(k8_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)))),
% 67.27/42.28 inference(rewrite,[status(thm)],[])).
% 67.27/42.28 tff(116,plain,
% 67.27/42.28 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k8_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | m1_subset_1(k8_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))))),
% 67.27/42.28 inference(monotonicity,[status(thm)],[115])).
% 67.27/42.28 tff(117,plain,
% 67.27/42.28 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k8_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | m1_subset_1(k8_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)))),
% 67.27/42.28 inference(transitivity,[status(thm)],[116, 114])).
% 67.27/42.28 tff(118,plain,
% 67.27/42.28 ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k8_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))))),
% 67.27/42.28 inference(quant_inst,[status(thm)],[])).
% 67.27/42.28 tff(119,plain,
% 67.27/42.28 ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_relset_2(A, B, C, D), k1_zfmisc_1(B)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | m1_subset_1(k8_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))),
% 67.27/42.28 inference(modus_ponens,[status(thm)],[118, 117])).
% 67.27/42.28 tff(120,plain,
% 67.27/42.28 (m1_subset_1(k8_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))),
% 67.27/42.28 inference(unit_resolution,[status(thm)],[119, 61, 60, 113])).
% 67.27/42.28 tff(121,plain,
% 67.27/42.28 (m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))),
% 67.27/42.28 inference(modus_ponens,[status(thm)],[120, 100])).
% 67.27/42.28 tff(122,plain,
% 67.27/42.28 (^[A: $i, B: $i, C: $i] : refl(((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C)))) <=> ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C)))))),
% 67.27/42.28 inference(bind,[status(th)],[])).
% 67.27/42.28 tff(123,plain,
% 67.27/42.28 (![A: $i, B: $i, C: $i] : ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C)))) <=> ![A: $i, B: $i, C: $i] : ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))),
% 67.27/42.28 inference(quant_intro,[status(thm)],[122])).
% 67.27/42.28 tff(124,plain,
% 67.27/42.28 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) <=> (~((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C)))))), ((~(r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C))) <=> (~(~((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C)))))))), rewrite((~(~((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C)))))) <=> ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))), ((~(r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C))) <=> ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))))),
% 67.27/42.28 inference(bind,[status(th)],[])).
% 67.27/42.28 tff(125,plain,
% 67.27/42.28 (![A: $i, B: $i, C: $i] : (~(r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C))) <=> ![A: $i, B: $i, C: $i] : ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))),
% 67.27/42.28 inference(quant_intro,[status(thm)],[124])).
% 67.27/42.28 tff(126,plain,
% 67.27/42.28 (![A: $i, B: $i, C: $i] : (~(r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C))) <=> ![A: $i, B: $i, C: $i] : (~(r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)))),
% 67.27/42.28 inference(rewrite,[status(thm)],[])).
% 67.27/42.28 tff(127,plain,
% 67.27/42.28 (^[A: $i, B: $i, C: $i] : rewrite((~((r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C))) & v1_xboole_0(C))) <=> (~(r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C))))),
% 67.27/42.28 inference(bind,[status(th)],[])).
% 67.27/42.28 tff(128,plain,
% 67.27/42.28 (![A: $i, B: $i, C: $i] : (~((r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C))) & v1_xboole_0(C))) <=> ![A: $i, B: $i, C: $i] : (~(r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)))),
% 67.27/42.28 inference(quant_intro,[status(thm)],[127])).
% 67.27/42.28 tff(129,axiom,(![A: $i, B: $i, C: $i] : (~((r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C))) & v1_xboole_0(C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t5_subset')).
% 67.27/42.28 tff(130,plain,
% 67.27/42.28 (![A: $i, B: $i, C: $i] : (~(r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)))),
% 67.27/42.28 inference(modus_ponens,[status(thm)],[129, 128])).
% 67.27/42.28 tff(131,plain,
% 67.27/42.28 (![A: $i, B: $i, C: $i] : (~(r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)))),
% 67.27/42.28 inference(modus_ponens,[status(thm)],[130, 126])).
% 67.27/42.28 tff(132,plain,(
% 67.27/42.28 ![A: $i, B: $i, C: $i] : (~(r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)))),
% 67.27/42.28 inference(skolemize,[status(sab)],[131])).
% 67.27/42.28 tff(133,plain,
% 67.27/42.28 (![A: $i, B: $i, C: $i] : ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))),
% 67.27/42.28 inference(modus_ponens,[status(thm)],[132, 125])).
% 67.27/42.28 tff(134,plain,
% 67.27/42.28 (![A: $i, B: $i, C: $i] : ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))),
% 67.27/42.28 inference(modus_ponens,[status(thm)],[133, 123])).
% 67.27/42.28 tff(135,plain,
% 67.27/42.28 (((~![A: $i, B: $i, C: $i] : ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))) | ((~m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))) | (~v1_xboole_0(B!1)) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))) | (~m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))) | (~v1_xboole_0(B!1)) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))))),
% 67.27/42.29 inference(rewrite,[status(thm)],[])).
% 67.27/42.29 tff(136,plain,
% 67.27/42.29 (((~v1_xboole_0(B!1)) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))) | (~m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)))) <=> ((~m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))) | (~v1_xboole_0(B!1)) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))))),
% 67.27/42.29 inference(rewrite,[status(thm)],[])).
% 67.27/42.29 tff(137,plain,
% 67.27/42.29 (((~![A: $i, B: $i, C: $i] : ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))) | ((~v1_xboole_0(B!1)) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))) | (~m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))) | ((~m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))) | (~v1_xboole_0(B!1)) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3)))))),
% 67.27/42.29 inference(monotonicity,[status(thm)],[136])).
% 67.27/42.29 tff(138,plain,
% 67.27/42.29 (((~![A: $i, B: $i, C: $i] : ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))) | ((~v1_xboole_0(B!1)) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))) | (~m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))) | (~m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))) | (~v1_xboole_0(B!1)) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))))),
% 67.27/42.29 inference(transitivity,[status(thm)],[137, 135])).
% 67.27/42.29 tff(139,plain,
% 67.27/42.29 ((~![A: $i, B: $i, C: $i] : ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))) | ((~v1_xboole_0(B!1)) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))) | (~m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))))),
% 67.27/42.29 inference(quant_inst,[status(thm)],[])).
% 67.27/42.29 tff(140,plain,
% 67.27/42.29 ((~![A: $i, B: $i, C: $i] : ((~v1_xboole_0(C)) | (~r2_hidden(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(C))))) | (~m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))) | (~v1_xboole_0(B!1)) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3)))),
% 67.27/42.29 inference(modus_ponens,[status(thm)],[139, 138])).
% 67.27/42.29 tff(141,plain,
% 67.27/42.29 ((~m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))) | (~v1_xboole_0(B!1)) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3)))),
% 67.27/42.29 inference(unit_resolution,[status(thm)],[140, 134])).
% 67.27/42.29 tff(142,plain,
% 67.27/42.29 (~v1_xboole_0(B!1)),
% 67.27/42.29 inference(unit_resolution,[status(thm)],[141, 121, 98])).
% 67.27/42.29 tff(143,plain,
% 67.27/42.29 (^[A: $i] : refl((v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))))))))))) <=> (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))))))))))))),
% 67.27/42.29 inference(bind,[status(th)],[])).
% 67.27/42.29 tff(144,plain,
% 67.27/42.29 (![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))),
% 67.27/42.29 inference(quant_intro,[status(thm)],[143])).
% 67.27/42.29 tff(145,plain,
% 67.27/42.29 (^[A: $i] : rewrite((v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))))))))))) <=> (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))))))))))))),
% 67.27/42.29 inference(bind,[status(th)],[])).
% 67.27/42.29 tff(146,plain,
% 67.27/42.29 (![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))),
% 67.27/42.29 inference(quant_intro,[status(thm)],[145])).
% 67.27/42.29 tff(147,plain,
% 67.27/42.29 (![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))),
% 67.27/42.29 inference(transitivity,[status(thm)],[146, 144])).
% 67.27/42.29 tff(148,plain,
% 67.27/42.29 (^[A: $i] : rewrite((v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F))))) & (r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))))))))) <=> (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))))))))))))),
% 67.27/42.29 inference(bind,[status(th)],[])).
% 67.27/42.29 tff(149,plain,
% 67.27/42.29 (![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F))))) & (r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))),
% 67.27/42.29 inference(quant_intro,[status(thm)],[148])).
% 67.27/42.29 tff(150,plain,
% 67.27/42.29 (![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))))),
% 67.27/42.29 inference(rewrite,[status(thm)],[])).
% 67.27/42.29 tff(151,plain,
% 67.27/42.29 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i, C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(rewrite((r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F))))) <=> (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))), ((m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) <=> (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))), rewrite((m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) <=> ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))), ((m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) <=> ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))))), (![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) <=> ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))), ((m1_subset_1(D, A) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))) <=> (m1_subset_1(D, A) => ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))))), rewrite((m1_subset_1(D, A) => ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))) <=> ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))), ((m1_subset_1(D, A) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))) <=> ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))))), (![D: $i] : (m1_subset_1(D, A) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))) <=> ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))))), ((m1_subset_1(C, k1_zfmisc_1(B)) => ![D: $i] : (m1_subset_1(D, A) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))) <=> (m1_subset_1(C, k1_zfmisc_1(B)) => ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))))), rewrite((m1_subset_1(C, k1_zfmisc_1(B)) => ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))))), ((m1_subset_1(C, k1_zfmisc_1(B)) => ![D: $i] : (m1_subset_1(D, A) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))))))), (![B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(B)) => ![D: $i] : (m1_subset_1(D, A) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))) <=> ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))))), (((~v1_xboole_0(A)) => ![B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(B)) => ![D: $i] : (m1_subset_1(D, A) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))))) <=> ((~v1_xboole_0(A)) => ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))))))), rewrite(((~v1_xboole_0(A)) => ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))))) <=> (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))))), (((~v1_xboole_0(A)) => ![B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(B)) => ![D: $i] : (m1_subset_1(D, A) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))))) <=> (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))))))),
% 67.27/42.30 inference(bind,[status(th)],[])).
% 67.27/42.30 tff(152,plain,
% 67.27/42.30 (![A: $i] : ((~v1_xboole_0(A)) => ![B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(B)) => ![D: $i] : (m1_subset_1(D, A) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))))),
% 67.27/42.30 inference(quant_intro,[status(thm)],[151])).
% 67.27/42.30 tff(153,axiom,(![A: $i] : ((~v1_xboole_0(A)) => ![B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(B)) => ![D: $i] : (m1_subset_1(D, A) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A))) => (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : (r2_hidden(F, C) => r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t25_relset_2')).
% 67.27/42.30 tff(154,plain,
% 67.27/42.30 (![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))))),
% 67.27/42.30 inference(modus_ponens,[status(thm)],[153, 152])).
% 67.27/42.30 tff(155,plain,
% 67.27/42.30 (![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (r2_hidden(D, k8_relset_2(B, A, C, E)) <=> ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))))))),
% 67.27/42.30 inference(modus_ponens,[status(thm)],[154, 150])).
% 67.27/42.30 tff(156,plain,(
% 67.27/42.30 ![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F))))) & (r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))),
% 67.27/42.30 inference(skolemize,[status(sab)],[155])).
% 67.27/42.30 tff(157,plain,
% 67.27/42.30 (![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))),
% 67.27/42.30 inference(modus_ponens,[status(thm)],[156, 149])).
% 67.27/42.30 tff(158,plain,
% 67.27/42.30 (![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))),
% 67.27/42.30 inference(modus_ponens,[status(thm)],[157, 147])).
% 67.27/42.30 tff(159,plain,
% 67.27/42.30 (((~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))) | (v1_xboole_0(B!1) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))) | r2_hidden(D, k8_relset_2(B, B!1, C, E))))))))))) <=> ((~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))) | v1_xboole_0(B!1) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))) | r2_hidden(D, k8_relset_2(B, B!1, C, E))))))))))),
% 67.27/42.30 inference(rewrite,[status(thm)],[])).
% 67.27/42.30 tff(160,plain,
% 67.27/42.30 ((v1_xboole_0(B!1) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, B!1, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))))))))))) <=> (v1_xboole_0(B!1) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))) | r2_hidden(D, k8_relset_2(B, B!1, C, E))))))))))),
% 67.27/42.30 inference(rewrite,[status(thm)],[])).
% 67.27/42.30 tff(161,plain,
% 67.27/42.30 (((~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))) | (v1_xboole_0(B!1) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, B!1, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))) <=> ((~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))) | (v1_xboole_0(B!1) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))) | r2_hidden(D, k8_relset_2(B, B!1, C, E)))))))))))),
% 67.27/42.30 inference(monotonicity,[status(thm)],[160])).
% 67.27/42.30 tff(162,plain,
% 67.27/42.30 (((~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))) | (v1_xboole_0(B!1) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, B!1, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))) <=> ((~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))) | v1_xboole_0(B!1) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))) | r2_hidden(D, k8_relset_2(B, B!1, C, E))))))))))),
% 67.27/42.31 inference(transitivity,[status(thm)],[161, 159])).
% 67.27/42.31 tff(163,plain,
% 67.27/42.31 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))) | (v1_xboole_0(B!1) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, B!1, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))),
% 67.27/42.31 inference(quant_inst,[status(thm)],[])).
% 67.27/42.31 tff(164,plain,
% 67.27/42.31 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, A)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) | (~((~((~r2_hidden(D, k8_relset_2(B, A, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~(r2_hidden(D, k8_relset_2(B, A, C, E)) | (~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C))))))))))))))) | v1_xboole_0(B!1) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))) | r2_hidden(D, k8_relset_2(B, B!1, C, E)))))))))),
% 67.27/42.31 inference(modus_ponens,[status(thm)],[163, 162])).
% 67.27/42.31 tff(165,plain,
% 67.27/42.31 (![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))) | r2_hidden(D, k8_relset_2(B, B!1, C, E)))))))))),
% 67.27/42.31 inference(unit_resolution,[status(thm)],[164, 158, 142])).
% 67.27/42.31 tff(166,plain,
% 67.27/42.31 (((~![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))) | r2_hidden(D, k8_relset_2(B, B!1, C, E)))))))))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C!0), C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C!0)))))) | r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E)))))))))) <=> ((~![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))) | r2_hidden(D, k8_relset_2(B, B!1, C, E)))))))))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C!0), C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C!0)))))) | r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E)))))))))),
% 67.27/42.31 inference(rewrite,[status(thm)],[])).
% 67.27/42.31 tff(167,plain,
% 67.27/42.31 ((~![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))) | r2_hidden(D, k8_relset_2(B, B!1, C, E)))))))))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C!0), C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C!0)))))) | r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E)))))))))),
% 67.27/42.31 inference(quant_inst,[status(thm)],[])).
% 67.27/42.31 tff(168,plain,
% 67.27/42.31 ((~![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(B, B!1, C, E))) | ![F: $i] : ((~r2_hidden(F, C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C), C)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C)))))) | r2_hidden(D, k8_relset_2(B, B!1, C, E)))))))))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C!0), C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C!0)))))) | r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))))))))),
% 67.27/42.31 inference(modus_ponens,[status(thm)],[167, 166])).
% 67.27/42.31 tff(169,plain,
% 67.27/42.31 (![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C!0), C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C!0)))))) | r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))))))))),
% 67.27/42.31 inference(unit_resolution,[status(thm)],[168, 61, 165])).
% 67.27/42.31 tff(170,plain,
% 67.27/42.31 ((~![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_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B)))))))) | (~((~((~r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1)) | ![C: $i] : ((~r2_hidden(C, k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, B!1)))) | (~(r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1) | (~((~r2_hidden(tptp_fun_C_5(B!1, k7_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(B!1, k7_relset_2(A!2, B!1, C!0, D!3)), B!1)))))))),
% 67.27/42.31 inference(quant_inst,[status(thm)],[])).
% 67.27/42.31 tff(171,plain,
% 67.27/42.31 (~((~((~r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1)) | ![C: $i] : ((~r2_hidden(C, k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, B!1)))) | (~(r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1) | (~((~r2_hidden(tptp_fun_C_5(B!1, k7_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(B!1, k7_relset_2(A!2, B!1, C!0, D!3)), B!1))))))),
% 67.27/42.31 inference(unit_resolution,[status(thm)],[170, 87])).
% 67.27/42.31 tff(172,plain,
% 67.27/42.31 (((~((~r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1)) | ![C: $i] : ((~r2_hidden(C, k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, B!1)))) | (~(r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1) | (~((~r2_hidden(tptp_fun_C_5(B!1, k7_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(B!1, k7_relset_2(A!2, B!1, C!0, D!3)), B!1)))))) | ((~r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1)) | ![C: $i] : ((~r2_hidden(C, k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, B!1)))),
% 67.27/42.31 inference(tautology,[status(thm)],[])).
% 67.27/42.31 tff(173,plain,
% 67.27/42.31 ((~r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1)) | ![C: $i] : ((~r2_hidden(C, k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, B!1))),
% 67.27/42.31 inference(unit_resolution,[status(thm)],[172, 171])).
% 67.27/42.31 tff(174,plain,
% 67.27/42.31 (^[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)))),
% 67.27/42.31 inference(bind,[status(th)],[])).
% 67.27/42.31 tff(175,plain,
% 67.27/42.31 (![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))),
% 67.27/42.31 inference(quant_intro,[status(thm)],[174])).
% 67.27/42.31 tff(176,plain,
% 67.27/42.31 (![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))),
% 67.27/42.31 inference(rewrite,[status(thm)],[])).
% 67.27/42.31 tff(177,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')).
% 67.27/42.31 tff(178,plain,
% 67.27/42.31 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 67.27/42.31 inference(modus_ponens,[status(thm)],[177, 176])).
% 67.27/42.31 tff(179,plain,(
% 67.27/42.31 ![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 67.27/42.31 inference(skolemize,[status(sab)],[178])).
% 67.27/42.31 tff(180,plain,
% 67.27/42.31 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 67.27/42.31 inference(modus_ponens,[status(thm)],[179, 175])).
% 67.27/42.31 tff(181,plain,
% 67.27/42.31 ((~![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))) | (m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)) <=> r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1))),
% 67.27/42.31 inference(quant_inst,[status(thm)],[])).
% 67.27/42.31 tff(182,plain,
% 67.27/42.31 (m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)) <=> r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1)),
% 67.27/42.31 inference(unit_resolution,[status(thm)],[181, 180])).
% 67.27/42.31 tff(183,plain,
% 67.27/42.31 ((~(m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1)) <=> r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1))) | (~m1_subset_1(k7_relset_2(A!2, B!1, C!0, D!3), k1_zfmisc_1(B!1))) | r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1)),
% 67.27/42.31 inference(tautology,[status(thm)],[])).
% 67.27/42.31 tff(184,plain,
% 67.27/42.31 (r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1)),
% 67.27/42.31 inference(unit_resolution,[status(thm)],[183, 121, 182])).
% 67.27/42.31 tff(185,plain,
% 67.27/42.31 ((~((~r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1)) | ![C: $i] : ((~r2_hidden(C, k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, B!1)))) | (~r1_tarski(k7_relset_2(A!2, B!1, C!0, D!3), B!1)) | ![C: $i] : ((~r2_hidden(C, k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, B!1))),
% 67.27/42.31 inference(tautology,[status(thm)],[])).
% 67.27/42.31 tff(186,plain,
% 67.27/42.31 (![C: $i] : ((~r2_hidden(C, k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, B!1))),
% 67.27/42.31 inference(unit_resolution,[status(thm)],[185, 184, 173])).
% 67.27/42.31 tff(187,plain,
% 67.27/42.31 (((~![C: $i] : ((~r2_hidden(C, k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, B!1))) | ((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1))) <=> ((~![C: $i] : ((~r2_hidden(C, k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, B!1))) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1))),
% 67.27/42.32 inference(rewrite,[status(thm)],[])).
% 67.27/42.32 tff(188,plain,
% 67.27/42.32 ((~![C: $i] : ((~r2_hidden(C, k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, B!1))) | ((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1))),
% 67.27/42.32 inference(quant_inst,[status(thm)],[])).
% 67.27/42.32 tff(189,plain,
% 67.27/42.32 ((~![C: $i] : ((~r2_hidden(C, k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(C, B!1))) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k7_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1)),
% 67.27/42.32 inference(modus_ponens,[status(thm)],[188, 187])).
% 67.27/42.32 tff(190,plain,
% 67.27/42.32 (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1)),
% 67.27/42.32 inference(unit_resolution,[status(thm)],[189, 98, 186])).
% 67.27/42.32 tff(191,plain,
% 67.27/42.32 (^[A: $i, B: $i] : refl(((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 67.27/42.32 inference(bind,[status(th)],[])).
% 67.27/42.32 tff(192,plain,
% 67.27/42.32 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 67.27/42.32 inference(quant_intro,[status(thm)],[191])).
% 67.27/42.32 tff(193,plain,
% 67.27/42.32 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 67.27/42.32 inference(rewrite,[status(thm)],[])).
% 67.27/42.32 tff(194,plain,
% 67.27/42.32 (^[A: $i, B: $i] : rewrite((r2_hidden(A, B) => m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 67.27/42.32 inference(bind,[status(th)],[])).
% 67.27/42.32 tff(195,plain,
% 67.27/42.32 (![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 67.27/42.32 inference(quant_intro,[status(thm)],[194])).
% 67.27/42.32 tff(196,axiom,(![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_subset')).
% 67.27/42.32 tff(197,plain,
% 67.27/42.32 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 67.27/42.32 inference(modus_ponens,[status(thm)],[196, 195])).
% 67.27/42.32 tff(198,plain,
% 67.27/42.32 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 67.27/42.32 inference(modus_ponens,[status(thm)],[197, 193])).
% 67.27/42.32 tff(199,plain,(
% 67.27/42.32 ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 67.27/42.32 inference(skolemize,[status(sab)],[198])).
% 67.27/42.32 tff(200,plain,
% 67.27/42.32 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 67.27/42.32 inference(modus_ponens,[status(thm)],[199, 192])).
% 67.27/42.32 tff(201,plain,
% 67.27/42.32 (((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1)) | m1_subset_1(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1))) <=> ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1)) | m1_subset_1(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1))),
% 67.27/42.32 inference(rewrite,[status(thm)],[])).
% 67.27/42.32 tff(202,plain,
% 67.27/42.32 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1)) | m1_subset_1(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1))),
% 67.27/42.32 inference(quant_inst,[status(thm)],[])).
% 67.27/42.32 tff(203,plain,
% 67.27/42.32 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1)) | m1_subset_1(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1)),
% 67.27/42.32 inference(modus_ponens,[status(thm)],[202, 201])).
% 67.27/42.32 tff(204,plain,
% 67.34/42.32 (m1_subset_1(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1)),
% 67.34/42.32 inference(unit_resolution,[status(thm)],[203, 200, 190])).
% 67.34/42.32 tff(205,plain,
% 67.34/42.32 (((~![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C!0), C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C!0)))))) | r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))))))))) | ((~m1_subset_1(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C!0), C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C!0)))))) | r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))))))))) | (~m1_subset_1(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))))))))),
% 67.34/42.32 inference(rewrite,[status(thm)],[])).
% 67.34/42.32 tff(206,plain,
% 67.34/42.32 ((~![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C!0), C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C!0)))))) | r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))))))))) | ((~m1_subset_1(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))))))))),
% 67.34/42.33 inference(quant_inst,[status(thm)],[])).
% 67.34/42.33 tff(207,plain,
% 67.34/42.33 ((~![D: $i] : ((~m1_subset_1(D, B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, D, C!0), C!0)) | r2_hidden(D, k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, D, C!0)))))) | r2_hidden(D, k8_relset_2(A!2, B!1, C!0, E))))))))) | (~m1_subset_1(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), B!1)) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E)))))))),
% 67.34/42.33 inference(modus_ponens,[status(thm)],[206, 205])).
% 67.34/42.33 tff(208,plain,
% 67.34/42.33 (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E)))))))),
% 67.34/42.33 inference(unit_resolution,[status(thm)],[207, 204, 169])).
% 67.34/42.33 tff(209,plain,
% 67.34/42.33 (((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E)))))))) | ((~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4)))))))) <=> ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E)))))))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4)))))))),
% 67.34/42.34 inference(rewrite,[status(thm)],[])).
% 67.34/42.34 tff(210,plain,
% 67.34/42.34 ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E)))))))) | ((~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4)))))))),
% 67.34/42.34 inference(quant_inst,[status(thm)],[])).
% 67.34/42.34 tff(211,plain,
% 67.34/42.34 ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E)))))))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))))))),
% 67.34/42.34 inference(modus_ponens,[status(thm)],[210, 209])).
% 67.34/42.34 tff(212,plain,
% 67.34/42.34 (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4)))))),
% 67.34/42.34 inference(unit_resolution,[status(thm)],[211, 28, 208])).
% 67.34/42.34 tff(213,plain,
% 67.34/42.34 (((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))))) | ((~((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4)))),
% 67.34/42.34 inference(tautology,[status(thm)],[])).
% 67.34/42.34 tff(214,plain,
% 67.34/42.34 ((~((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))),
% 67.34/42.34 inference(unit_resolution,[status(thm)],[213, 212])).
% 67.34/42.35 tff(215,plain,
% 67.34/42.35 (((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4)))),
% 67.34/42.35 inference(tautology,[status(thm)],[])).
% 67.34/42.35 tff(216,plain,
% 67.34/42.35 (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))),
% 67.34/42.35 inference(unit_resolution,[status(thm)],[215, 95])).
% 67.34/42.35 tff(217,plain,
% 67.34/42.35 ((~((~((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4)))) | (~((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4))),
% 67.34/42.35 inference(tautology,[status(thm)],[])).
% 67.34/42.35 tff(218,plain,
% 67.34/42.35 ((~((~((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E!4)))) | (~((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0))))))),
% 67.34/42.35 inference(unit_resolution,[status(thm)],[217, 216])).
% 67.34/42.35 tff(219,plain,
% 67.34/42.35 (~((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))),
% 67.34/42.35 inference(unit_resolution,[status(thm)],[218, 214])).
% 67.34/42.35 tff(220,plain,
% 67.34/42.35 (((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0))))) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))),
% 67.34/42.35 inference(tautology,[status(thm)],[])).
% 67.34/42.35 tff(221,plain,
% 67.34/42.35 (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0))))),
% 67.34/42.35 inference(unit_resolution,[status(thm)],[220, 219])).
% 67.34/42.35 tff(222,plain,
% 67.34/42.35 ((~(r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) <=> r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) | (~r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4))),
% 67.34/42.35 inference(tautology,[status(thm)],[])).
% 67.34/42.35 tff(223,plain,
% 67.34/42.35 ((~(r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) <=> r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4))) | (~r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4))),
% 67.34/42.35 inference(unit_resolution,[status(thm)],[222, 221])).
% 67.34/42.35 tff(224,plain,
% 67.34/42.35 (~r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4)),
% 67.34/42.35 inference(unit_resolution,[status(thm)],[223, 46])).
% 67.34/42.35 tff(225,plain,
% 67.34/42.35 ((~![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_5(B, A), A)) | r2_hidden(tptp_fun_C_5(B, A), B)))))))) | (~((~((~r1_tarski(D!3, E!4)) | ![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4)))) | (~(r1_tarski(D!3, E!4) | (~((~r2_hidden(tptp_fun_C_5(E!4, D!3), D!3)) | r2_hidden(tptp_fun_C_5(E!4, D!3), E!4)))))))),
% 67.34/42.35 inference(quant_inst,[status(thm)],[])).
% 67.34/42.35 tff(226,plain,
% 67.34/42.35 (~((~((~r1_tarski(D!3, E!4)) | ![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4)))) | (~(r1_tarski(D!3, E!4) | (~((~r2_hidden(tptp_fun_C_5(E!4, D!3), D!3)) | r2_hidden(tptp_fun_C_5(E!4, D!3), E!4))))))),
% 67.34/42.35 inference(unit_resolution,[status(thm)],[225, 87])).
% 67.34/42.35 tff(227,plain,
% 67.34/42.35 (((~((~r1_tarski(D!3, E!4)) | ![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4)))) | (~(r1_tarski(D!3, E!4) | (~((~r2_hidden(tptp_fun_C_5(E!4, D!3), D!3)) | r2_hidden(tptp_fun_C_5(E!4, D!3), E!4)))))) | ((~r1_tarski(D!3, E!4)) | ![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4)))),
% 67.34/42.35 inference(tautology,[status(thm)],[])).
% 67.34/42.35 tff(228,plain,
% 67.34/42.35 ((~r1_tarski(D!3, E!4)) | ![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4))),
% 67.34/42.35 inference(unit_resolution,[status(thm)],[227, 226])).
% 67.34/42.35 tff(229,plain,
% 67.34/42.35 (r1_tarski(D!3, E!4)),
% 67.34/42.35 inference(or_elim,[status(thm)],[27])).
% 67.34/42.35 tff(230,plain,
% 67.34/42.35 ((~((~r1_tarski(D!3, E!4)) | ![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4)))) | (~r1_tarski(D!3, E!4)) | ![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4))),
% 67.34/42.35 inference(tautology,[status(thm)],[])).
% 67.34/42.35 tff(231,plain,
% 67.34/42.35 ((~((~r1_tarski(D!3, E!4)) | ![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4)))) | ![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4))),
% 67.34/42.35 inference(unit_resolution,[status(thm)],[230, 229])).
% 67.34/42.35 tff(232,plain,
% 67.34/42.35 (![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4))),
% 67.34/42.35 inference(unit_resolution,[status(thm)],[231, 228])).
% 67.34/42.35 tff(233,plain,
% 67.34/42.35 (((~![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4))) | ((~r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), D!3)) | r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4))) <=> ((~![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4))) | (~r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), D!3)) | r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4))),
% 67.34/42.36 inference(rewrite,[status(thm)],[])).
% 67.34/42.36 tff(234,plain,
% 67.34/42.36 ((~![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4))) | ((~r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), D!3)) | r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4))),
% 67.34/42.36 inference(quant_inst,[status(thm)],[])).
% 67.34/42.36 tff(235,plain,
% 67.34/42.36 ((~![C: $i] : ((~r2_hidden(C, D!3)) | r2_hidden(C, E!4))) | (~r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), D!3)) | r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), E!4)),
% 67.34/42.36 inference(modus_ponens,[status(thm)],[234, 233])).
% 67.34/42.36 tff(236,plain,
% 67.34/42.36 (~r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), D!3)),
% 67.34/42.36 inference(unit_resolution,[status(thm)],[235, 232, 224])).
% 67.34/42.36 tff(237,plain,
% 67.34/42.36 (((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E!4, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0))))) | r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)),
% 67.34/42.36 inference(tautology,[status(thm)],[])).
% 67.34/42.36 tff(238,plain,
% 67.34/42.36 (r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)),
% 67.34/42.36 inference(unit_resolution,[status(thm)],[237, 219])).
% 67.34/42.36 tff(239,plain,
% 67.34/42.36 (((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E)))))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(D!3, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(D!3, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3)))))))) <=> ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E)))))))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(D!3, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(D!3, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3)))))))),
% 67.34/42.36 inference(rewrite,[status(thm)],[])).
% 67.34/42.36 tff(240,plain,
% 67.34/42.36 ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E)))))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(D!3, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(D!3, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3)))))))),
% 67.34/42.36 inference(quant_inst,[status(thm)],[])).
% 67.34/42.36 tff(241,plain,
% 67.34/42.36 ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(E, k1_tarski(tptp_fun_F_16(E, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, E)))))))) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(D!3, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(D!3, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))))))),
% 67.34/42.37 inference(modus_ponens,[status(thm)],[240, 239])).
% 67.34/42.37 tff(242,plain,
% 67.34/42.37 (~((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(D!3, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(D!3, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3)))))),
% 67.34/42.37 inference(unit_resolution,[status(thm)],[241, 60, 208])).
% 67.34/42.37 tff(243,plain,
% 67.34/42.37 (((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F)))))) | (~((~((~r2_hidden(tptp_fun_F_16(D!3, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(D!3, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))))) | ((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F)))))),
% 67.34/42.37 inference(tautology,[status(thm)],[])).
% 67.34/42.37 tff(244,plain,
% 67.34/42.37 ((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F))))),
% 67.34/42.37 inference(unit_resolution,[status(thm)],[243, 242])).
% 67.34/42.37 tff(245,plain,
% 67.34/42.37 ((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F)))))) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F))))),
% 67.38/42.37 inference(tautology,[status(thm)],[])).
% 67.38/42.37 tff(246,plain,
% 67.38/42.37 ((~((~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k8_relset_2(A!2, B!1, C!0, D!3))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F)))))) | ![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F))))),
% 67.38/42.37 inference(unit_resolution,[status(thm)],[245, 97])).
% 67.38/42.37 tff(247,plain,
% 67.38/42.37 (![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F))))),
% 67.38/42.37 inference(unit_resolution,[status(thm)],[246, 244])).
% 67.38/42.37 tff(248,plain,
% 67.38/42.37 (((~![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F))))) | ((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))) <=> ((~![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F))))) | (~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))),
% 67.38/42.37 inference(rewrite,[status(thm)],[])).
% 67.38/42.37 tff(249,plain,
% 67.38/42.37 ((~![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F))))) | ((~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))))),
% 67.38/42.37 inference(quant_inst,[status(thm)],[])).
% 67.38/42.37 tff(250,plain,
% 67.38/42.37 ((~![F: $i] : ((~r2_hidden(F, C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(F))))) | (~r2_hidden(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), C!0)) | r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0))))),
% 67.38/42.37 inference(modus_ponens,[status(thm)],[249, 248])).
% 67.38/42.37 tff(251,plain,
% 67.38/42.37 (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0))))),
% 67.38/42.37 inference(unit_resolution,[status(thm)],[250, 247, 238])).
% 67.38/42.37 tff(252,plain,
% 67.38/42.37 ((~(r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) <=> r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), D!3))) | (~r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0))))) | r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), D!3)),
% 67.38/42.37 inference(tautology,[status(thm)],[])).
% 67.38/42.37 tff(253,plain,
% 67.38/42.37 (~(r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) <=> r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), D!3))),
% 67.38/42.37 inference(unit_resolution,[status(thm)],[252, 251, 236])).
% 67.38/42.37 tff(254,plain,
% 67.38/42.37 (((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (v1_relat_1(D!3) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | v1_relat_1(D!3) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))),
% 67.38/42.37 inference(rewrite,[status(thm)],[])).
% 67.38/42.37 tff(255,plain,
% 67.38/42.37 ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (v1_relat_1(D!3) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))),
% 67.38/42.37 inference(quant_inst,[status(thm)],[])).
% 67.38/42.37 tff(256,plain,
% 67.38/42.37 ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | v1_relat_1(D!3) | (~m1_subset_1(D!3, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))),
% 67.38/42.37 inference(modus_ponens,[status(thm)],[255, 254])).
% 67.38/42.37 tff(257,plain,
% 67.38/42.37 (v1_relat_1(D!3)),
% 67.38/42.37 inference(unit_resolution,[status(thm)],[256, 60, 10])).
% 67.38/42.37 tff(258,plain,
% 67.38/42.37 (((~![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))) | ((~v1_relat_1(D!3)) | (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) <=> r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), D!3)))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))) | (~v1_relat_1(D!3)) | (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) <=> r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), D!3)))),
% 67.38/42.37 inference(rewrite,[status(thm)],[])).
% 67.38/42.37 tff(259,plain,
% 67.38/42.37 ((~![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))) | ((~v1_relat_1(D!3)) | (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) <=> r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), D!3)))),
% 67.45/42.45 inference(quant_inst,[status(thm)],[])).
% 67.45/42.45 tff(260,plain,
% 67.45/42.45 ((~![A: $i, B: $i, C: $i] : ((~v1_relat_1(C)) | (r2_hidden(A, k9_relat_1(C, k1_tarski(B))) <=> r2_hidden(k4_tarski(B, A), C)))) | (~v1_relat_1(D!3)) | (r2_hidden(tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), k9_relat_1(D!3, k1_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0)))) <=> r2_hidden(k4_tarski(tptp_fun_F_16(E!4, tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3)), C!0), tptp_fun_C_5(k8_relset_2(A!2, B!1, C!0, E!4), k8_relset_2(A!2, B!1, C!0, D!3))), D!3))),
% 67.45/42.45 inference(modus_ponens,[status(thm)],[259, 258])).
% 67.45/42.45 tff(261,plain,
% 67.45/42.45 ($false),
% 67.45/42.45 inference(unit_resolution,[status(thm)],[260, 42, 257, 253])).
% 67.45/42.45 % SZS output end Proof
%------------------------------------------------------------------------------