TSTP Solution File: SEU448+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU448+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 07:29:45 EDT 2022
% Result : Theorem 205.71s 131.79s
% Output : Proof 205.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU448+1 : TPTP v8.1.0. Released v3.4.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 15:07:30 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33 Usage: tptp [options] [-file:]file
% 0.13/0.33 -h, -? prints this message.
% 0.13/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.33 -m, -model generate model.
% 0.13/0.33 -p, -proof generate proof.
% 0.13/0.33 -c, -core generate unsat core of named formulas.
% 0.13/0.33 -st, -statistics display statistics.
% 0.13/0.33 -t:timeout set timeout (in second).
% 0.13/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33 -<param>:<value> configuration parameter and value.
% 0.13/0.33 -o:<output-file> file to place output in.
% 205.71/131.79 % SZS status Theorem
% 205.71/131.79 % SZS output start Proof
% 205.71/131.79 tff(r1_xboole_0_type, type, (
% 205.71/131.79 r1_xboole_0: ( $i * $i ) > $o)).
% 205.71/131.79 tff(k9_relat_1_type, type, (
% 205.71/131.79 k9_relat_1: ( $i * $i ) > $i)).
% 205.71/131.79 tff(tptp_fun_D_3_type, type, (
% 205.71/131.79 tptp_fun_D_3: $i)).
% 205.71/131.79 tff(k4_relat_1_type, type, (
% 205.71/131.79 k4_relat_1: $i > $i)).
% 205.71/131.79 tff(tptp_fun_E_4_type, type, (
% 205.71/131.79 tptp_fun_E_4: $i)).
% 205.71/131.79 tff(k3_subset_1_type, type, (
% 205.71/131.79 k3_subset_1: ( $i * $i ) > $i)).
% 205.71/131.79 tff(tptp_fun_C_0_type, type, (
% 205.71/131.79 tptp_fun_C_0: $i)).
% 205.71/131.79 tff(tptp_fun_A_2_type, type, (
% 205.71/131.79 tptp_fun_A_2: $i)).
% 205.71/131.79 tff(k6_relset_1_type, type, (
% 205.71/131.79 k6_relset_1: ( $i * $i * $i ) > $i)).
% 205.71/131.79 tff(tptp_fun_B_1_type, type, (
% 205.71/131.79 tptp_fun_B_1: $i)).
% 205.71/131.79 tff(m1_relset_1_type, type, (
% 205.71/131.79 m1_relset_1: ( $i * $i * $i ) > $o)).
% 205.71/131.79 tff(m2_relset_1_type, type, (
% 205.71/131.79 m2_relset_1: ( $i * $i * $i ) > $o)).
% 205.71/131.79 tff(r1_tarski_type, type, (
% 205.71/131.79 r1_tarski: ( $i * $i ) > $o)).
% 205.71/131.79 tff(k10_relset_1_type, type, (
% 205.71/131.79 k10_relset_1: ( $i * $i * $i * $i ) > $i)).
% 205.71/131.79 tff(m1_subset_1_type, type, (
% 205.71/131.79 m1_subset_1: ( $i * $i ) > $o)).
% 205.71/131.79 tff(k1_zfmisc_1_type, type, (
% 205.71/131.79 k1_zfmisc_1: $i > $i)).
% 205.71/131.79 tff(k2_zfmisc_1_type, type, (
% 205.71/131.79 k2_zfmisc_1: ( $i * $i ) > $i)).
% 205.71/131.79 tff(1,plain,
% 205.71/131.79 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)))),
% 205.71/131.79 inference(bind,[status(th)],[])).
% 205.71/131.79 tff(2,plain,
% 205.71/131.79 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 205.71/131.79 inference(quant_intro,[status(thm)],[1])).
% 205.71/131.79 tff(3,plain,
% 205.71/131.79 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 205.71/131.79 inference(rewrite,[status(thm)],[])).
% 205.71/131.79 tff(4,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 205.71/131.79 tff(5,plain,
% 205.71/131.79 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 205.71/131.79 inference(modus_ponens,[status(thm)],[4, 3])).
% 205.71/131.79 tff(6,plain,(
% 205.71/131.79 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 205.71/131.79 inference(skolemize,[status(sab)],[5])).
% 205.71/131.79 tff(7,plain,
% 205.71/131.79 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 205.71/131.79 inference(modus_ponens,[status(thm)],[6, 2])).
% 205.71/131.79 tff(8,plain,
% 205.71/131.79 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(E!4, A!2, B!1) <=> m1_relset_1(E!4, A!2, B!1))),
% 205.71/131.79 inference(quant_inst,[status(thm)],[])).
% 205.71/131.79 tff(9,plain,
% 205.71/131.79 (m2_relset_1(E!4, A!2, B!1) <=> m1_relset_1(E!4, A!2, B!1)),
% 205.71/131.79 inference(unit_resolution,[status(thm)],[8, 7])).
% 205.71/131.79 tff(10,plain,
% 205.71/131.79 ((m1_subset_1(C!0, k1_zfmisc_1(A!2)) & (m1_subset_1(D!3, k1_zfmisc_1(B!1)) & (~((~m2_relset_1(E!4, A!2, B!1)) | (r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)) <=> r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0)))))) <=> (m1_subset_1(C!0, k1_zfmisc_1(A!2)) & m1_subset_1(D!3, k1_zfmisc_1(B!1)) & (~((~m2_relset_1(E!4, A!2, B!1)) | (r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)) <=> r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0)))))),
% 205.71/131.79 inference(rewrite,[status(thm)],[])).
% 205.71/131.79 tff(11,plain,
% 205.71/131.79 (((~(~m1_subset_1(D!3, k1_zfmisc_1(B!1)))) & (~((~m2_relset_1(E!4, A!2, B!1)) | (r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)) <=> r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0))))) <=> (m1_subset_1(D!3, k1_zfmisc_1(B!1)) & (~((~m2_relset_1(E!4, A!2, B!1)) | (r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)) <=> r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0)))))),
% 205.71/131.79 inference(rewrite,[status(thm)],[])).
% 205.71/131.79 tff(12,plain,
% 205.71/131.79 ((~(~m1_subset_1(C!0, k1_zfmisc_1(A!2)))) <=> m1_subset_1(C!0, k1_zfmisc_1(A!2))),
% 205.71/131.79 inference(rewrite,[status(thm)],[])).
% 205.71/131.79 tff(13,plain,
% 205.71/131.79 (((~(~m1_subset_1(C!0, k1_zfmisc_1(A!2)))) & ((~(~m1_subset_1(D!3, k1_zfmisc_1(B!1)))) & (~((~m2_relset_1(E!4, A!2, B!1)) | (r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)) <=> r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0)))))) <=> (m1_subset_1(C!0, k1_zfmisc_1(A!2)) & (m1_subset_1(D!3, k1_zfmisc_1(B!1)) & (~((~m2_relset_1(E!4, A!2, B!1)) | (r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)) <=> r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0))))))),
% 205.75/131.79 inference(monotonicity,[status(thm)],[12, 11])).
% 205.75/131.79 tff(14,plain,
% 205.75/131.79 (((~(~m1_subset_1(C!0, k1_zfmisc_1(A!2)))) & ((~(~m1_subset_1(D!3, k1_zfmisc_1(B!1)))) & (~((~m2_relset_1(E!4, A!2, B!1)) | (r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)) <=> r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0)))))) <=> (m1_subset_1(C!0, k1_zfmisc_1(A!2)) & m1_subset_1(D!3, k1_zfmisc_1(B!1)) & (~((~m2_relset_1(E!4, A!2, B!1)) | (r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)) <=> r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0)))))),
% 205.75/131.79 inference(transitivity,[status(thm)],[13, 10])).
% 205.75/131.79 tff(15,plain,
% 205.75/131.79 ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(k10_relset_1(A, B, E, k3_subset_1(A, C)), k3_subset_1(B, D)) <=> r1_tarski(k10_relset_1(B, A, k6_relset_1(A, B, E), D), C)))))) <=> (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(k10_relset_1(A, B, E, k3_subset_1(A, C)), k3_subset_1(B, D)) <=> r1_tarski(k10_relset_1(B, A, k6_relset_1(A, B, E), D), C))))))),
% 205.75/131.79 inference(rewrite,[status(thm)],[])).
% 205.75/131.79 tff(16,plain,
% 205.75/131.79 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : (m2_relset_1(E, A, B) => (r1_tarski(k10_relset_1(A, B, E, k3_subset_1(A, C)), k3_subset_1(B, D)) <=> r1_tarski(k10_relset_1(B, A, k6_relset_1(A, B, E), D), C)))))) <=> (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(k10_relset_1(A, B, E, k3_subset_1(A, C)), k3_subset_1(B, D)) <=> r1_tarski(k10_relset_1(B, A, k6_relset_1(A, B, E), D), C))))))),
% 205.75/131.79 inference(rewrite,[status(thm)],[])).
% 205.75/131.79 tff(17,axiom,(~![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : (m2_relset_1(E, A, B) => (r1_tarski(k10_relset_1(A, B, E, k3_subset_1(A, C)), k3_subset_1(B, D)) <=> r1_tarski(k10_relset_1(B, A, k6_relset_1(A, B, E), D), C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t62_relset_2')).
% 205.75/131.79 tff(18,plain,
% 205.75/131.79 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(k10_relset_1(A, B, E, k3_subset_1(A, C)), k3_subset_1(B, D)) <=> r1_tarski(k10_relset_1(B, A, k6_relset_1(A, B, E), D), C)))))),
% 205.75/131.79 inference(modus_ponens,[status(thm)],[17, 16])).
% 205.75/131.79 tff(19,plain,
% 205.75/131.79 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(k10_relset_1(A, B, E, k3_subset_1(A, C)), k3_subset_1(B, D)) <=> r1_tarski(k10_relset_1(B, A, k6_relset_1(A, B, E), D), C)))))),
% 205.75/131.79 inference(modus_ponens,[status(thm)],[18, 15])).
% 205.75/131.79 tff(20,plain,
% 205.75/131.79 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(k10_relset_1(A, B, E, k3_subset_1(A, C)), k3_subset_1(B, D)) <=> r1_tarski(k10_relset_1(B, A, k6_relset_1(A, B, E), D), C)))))),
% 205.75/131.79 inference(modus_ponens,[status(thm)],[19, 15])).
% 205.75/131.79 tff(21,plain,
% 205.75/131.79 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(k10_relset_1(A, B, E, k3_subset_1(A, C)), k3_subset_1(B, D)) <=> r1_tarski(k10_relset_1(B, A, k6_relset_1(A, B, E), D), C)))))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[20, 15])).
% 205.75/131.80 tff(22,plain,
% 205.75/131.80 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(k10_relset_1(A, B, E, k3_subset_1(A, C)), k3_subset_1(B, D)) <=> r1_tarski(k10_relset_1(B, A, k6_relset_1(A, B, E), D), C)))))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[21, 15])).
% 205.75/131.80 tff(23,plain,
% 205.75/131.80 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(k10_relset_1(A, B, E, k3_subset_1(A, C)), k3_subset_1(B, D)) <=> r1_tarski(k10_relset_1(B, A, k6_relset_1(A, B, E), D), C)))))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[22, 15])).
% 205.75/131.80 tff(24,plain,
% 205.75/131.80 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m2_relset_1(E, A, B)) | (r1_tarski(k10_relset_1(A, B, E, k3_subset_1(A, C)), k3_subset_1(B, D)) <=> r1_tarski(k10_relset_1(B, A, k6_relset_1(A, B, E), D), C)))))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[23, 15])).
% 205.75/131.80 tff(25,plain,
% 205.75/131.80 (m1_subset_1(C!0, k1_zfmisc_1(A!2)) & m1_subset_1(D!3, k1_zfmisc_1(B!1)) & (~((~m2_relset_1(E!4, A!2, B!1)) | (r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)) <=> r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0))))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[24, 14])).
% 205.75/131.80 tff(26,plain,
% 205.75/131.80 (~((~m2_relset_1(E!4, A!2, B!1)) | (r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)) <=> r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0)))),
% 205.75/131.80 inference(and_elim,[status(thm)],[25])).
% 205.75/131.80 tff(27,plain,
% 205.75/131.80 (m2_relset_1(E!4, A!2, B!1)),
% 205.75/131.80 inference(or_elim,[status(thm)],[26])).
% 205.75/131.80 tff(28,plain,
% 205.75/131.80 ((~(m2_relset_1(E!4, A!2, B!1) <=> m1_relset_1(E!4, A!2, B!1))) | (~m2_relset_1(E!4, A!2, B!1)) | m1_relset_1(E!4, A!2, B!1)),
% 205.75/131.80 inference(tautology,[status(thm)],[])).
% 205.75/131.80 tff(29,plain,
% 205.75/131.80 ((~(m2_relset_1(E!4, A!2, B!1) <=> m1_relset_1(E!4, A!2, B!1))) | m1_relset_1(E!4, A!2, B!1)),
% 205.75/131.80 inference(unit_resolution,[status(thm)],[28, 27])).
% 205.75/131.80 tff(30,plain,
% 205.75/131.80 (m1_relset_1(E!4, A!2, B!1)),
% 205.75/131.80 inference(unit_resolution,[status(thm)],[29, 9])).
% 205.75/131.80 tff(31,plain,
% 205.75/131.80 (^[A: $i, B: $i, C: $i] : refl(((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C))) <=> ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C))))),
% 205.75/131.80 inference(bind,[status(th)],[])).
% 205.75/131.80 tff(32,plain,
% 205.75/131.80 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))),
% 205.75/131.80 inference(quant_intro,[status(thm)],[31])).
% 205.75/131.80 tff(33,plain,
% 205.75/131.80 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))),
% 205.75/131.80 inference(rewrite,[status(thm)],[])).
% 205.75/131.80 tff(34,plain,
% 205.75/131.80 (^[A: $i, B: $i, C: $i] : rewrite((m1_relset_1(C, A, B) => (k6_relset_1(A, B, C) = k4_relat_1(C))) <=> ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C))))),
% 205.75/131.80 inference(bind,[status(th)],[])).
% 205.75/131.80 tff(35,plain,
% 205.75/131.80 (![A: $i, B: $i, C: $i] : (m1_relset_1(C, A, B) => (k6_relset_1(A, B, C) = k4_relat_1(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))),
% 205.75/131.80 inference(quant_intro,[status(thm)],[34])).
% 205.75/131.80 tff(36,axiom,(![A: $i, B: $i, C: $i] : (m1_relset_1(C, A, B) => (k6_relset_1(A, B, C) = k4_relat_1(C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k6_relset_1')).
% 205.75/131.80 tff(37,plain,
% 205.75/131.80 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[36, 35])).
% 205.75/131.80 tff(38,plain,
% 205.75/131.80 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[37, 33])).
% 205.75/131.80 tff(39,plain,(
% 205.75/131.80 ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))),
% 205.75/131.80 inference(skolemize,[status(sab)],[38])).
% 205.75/131.80 tff(40,plain,
% 205.75/131.80 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[39, 32])).
% 205.75/131.80 tff(41,plain,
% 205.75/131.80 (((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))) | ((~m1_relset_1(E!4, A!2, B!1)) | (k6_relset_1(A!2, B!1, E!4) = k4_relat_1(E!4)))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))) | (~m1_relset_1(E!4, A!2, B!1)) | (k6_relset_1(A!2, B!1, E!4) = k4_relat_1(E!4)))),
% 205.75/131.80 inference(rewrite,[status(thm)],[])).
% 205.75/131.80 tff(42,plain,
% 205.75/131.80 ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))) | ((~m1_relset_1(E!4, A!2, B!1)) | (k6_relset_1(A!2, B!1, E!4) = k4_relat_1(E!4)))),
% 205.75/131.80 inference(quant_inst,[status(thm)],[])).
% 205.75/131.80 tff(43,plain,
% 205.75/131.80 ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k6_relset_1(A, B, C) = k4_relat_1(C)))) | (~m1_relset_1(E!4, A!2, B!1)) | (k6_relset_1(A!2, B!1, E!4) = k4_relat_1(E!4))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[42, 41])).
% 205.75/131.80 tff(44,plain,
% 205.75/131.80 ((~m1_relset_1(E!4, A!2, B!1)) | (k6_relset_1(A!2, B!1, E!4) = k4_relat_1(E!4))),
% 205.75/131.80 inference(unit_resolution,[status(thm)],[43, 40])).
% 205.75/131.80 tff(45,plain,
% 205.75/131.80 (k6_relset_1(A!2, B!1, E!4) = k4_relat_1(E!4)),
% 205.75/131.80 inference(unit_resolution,[status(thm)],[44, 30])).
% 205.75/131.80 tff(46,plain,
% 205.75/131.80 (k4_relat_1(E!4) = k6_relset_1(A!2, B!1, E!4)),
% 205.75/131.80 inference(symmetry,[status(thm)],[45])).
% 205.75/131.80 tff(47,plain,
% 205.75/131.80 (k9_relat_1(k4_relat_1(E!4), D!3) = k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3)),
% 205.75/131.80 inference(monotonicity,[status(thm)],[46])).
% 205.75/131.80 tff(48,plain,
% 205.75/131.80 (k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3) = k9_relat_1(k4_relat_1(E!4), D!3)),
% 205.75/131.80 inference(symmetry,[status(thm)],[47])).
% 205.75/131.80 tff(49,plain,
% 205.75/131.80 (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3)) <=> r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3))),
% 205.75/131.80 inference(monotonicity,[status(thm)],[48])).
% 205.75/131.80 tff(50,plain,
% 205.75/131.80 (^[A: $i, B: $i] : refl(((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B)) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B)))),
% 205.75/131.80 inference(bind,[status(th)],[])).
% 205.75/131.80 tff(51,plain,
% 205.75/131.80 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B)) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B))),
% 205.75/131.80 inference(quant_intro,[status(thm)],[50])).
% 205.75/131.80 tff(52,plain,
% 205.75/131.80 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B)) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B))),
% 205.75/131.80 inference(rewrite,[status(thm)],[])).
% 205.75/131.80 tff(53,plain,
% 205.75/131.80 (^[A: $i, B: $i] : rewrite((m1_subset_1(B, k1_zfmisc_1(A)) => (k3_subset_1(A, k3_subset_1(A, B)) = B)) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B)))),
% 205.75/131.80 inference(bind,[status(th)],[])).
% 205.75/131.80 tff(54,plain,
% 205.75/131.80 (![A: $i, B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => (k3_subset_1(A, k3_subset_1(A, B)) = B)) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B))),
% 205.75/131.80 inference(quant_intro,[status(thm)],[53])).
% 205.75/131.80 tff(55,axiom,(![A: $i, B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => (k3_subset_1(A, k3_subset_1(A, B)) = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','involutiveness_k3_subset_1')).
% 205.75/131.80 tff(56,plain,
% 205.75/131.80 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[55, 54])).
% 205.75/131.80 tff(57,plain,
% 205.75/131.80 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[56, 52])).
% 205.75/131.80 tff(58,plain,(
% 205.75/131.80 ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B))),
% 205.75/131.80 inference(skolemize,[status(sab)],[57])).
% 205.75/131.80 tff(59,plain,
% 205.75/131.80 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[58, 51])).
% 205.75/131.80 tff(60,plain,
% 205.75/131.80 (m1_subset_1(C!0, k1_zfmisc_1(A!2))),
% 205.75/131.80 inference(and_elim,[status(thm)],[25])).
% 205.75/131.80 tff(61,plain,
% 205.75/131.80 (((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (k3_subset_1(A!2, k3_subset_1(A!2, C!0)) = C!0))) <=> ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (k3_subset_1(A!2, k3_subset_1(A!2, C!0)) = C!0))),
% 205.75/131.80 inference(rewrite,[status(thm)],[])).
% 205.75/131.80 tff(62,plain,
% 205.75/131.80 ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (k3_subset_1(A!2, k3_subset_1(A!2, C!0)) = C!0))),
% 205.75/131.80 inference(quant_inst,[status(thm)],[])).
% 205.75/131.80 tff(63,plain,
% 205.75/131.80 ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (k3_subset_1(A, k3_subset_1(A, B)) = B))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | (k3_subset_1(A!2, k3_subset_1(A!2, C!0)) = C!0)),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[62, 61])).
% 205.75/131.80 tff(64,plain,
% 205.75/131.80 (k3_subset_1(A!2, k3_subset_1(A!2, C!0)) = C!0),
% 205.75/131.80 inference(unit_resolution,[status(thm)],[63, 60, 59])).
% 205.75/131.80 tff(65,plain,
% 205.75/131.80 (m1_relset_1(k4_relat_1(E!4), B!1, A!2) <=> m1_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)),
% 205.75/131.80 inference(monotonicity,[status(thm)],[46])).
% 205.75/131.80 tff(66,plain,
% 205.75/131.80 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k4_relat_1(E!4), B!1, A!2) <=> m1_relset_1(k4_relat_1(E!4), B!1, A!2))),
% 205.75/131.80 inference(quant_inst,[status(thm)],[])).
% 205.75/131.80 tff(67,plain,
% 205.75/131.80 (m2_relset_1(k4_relat_1(E!4), B!1, A!2) <=> m1_relset_1(k4_relat_1(E!4), B!1, A!2)),
% 205.75/131.80 inference(unit_resolution,[status(thm)],[66, 7])).
% 205.75/131.80 tff(68,plain,
% 205.75/131.80 (m2_relset_1(k4_relat_1(E!4), B!1, A!2) <=> m2_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)),
% 205.75/131.80 inference(monotonicity,[status(thm)],[46])).
% 205.75/131.80 tff(69,plain,
% 205.75/131.80 (m2_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2) <=> m2_relset_1(k4_relat_1(E!4), B!1, A!2)),
% 205.75/131.80 inference(symmetry,[status(thm)],[68])).
% 205.75/131.80 tff(70,plain,
% 205.75/131.80 (^[A: $i, B: $i, C: $i] : refl(((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A)) <=> ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A)))),
% 205.75/131.80 inference(bind,[status(th)],[])).
% 205.75/131.80 tff(71,plain,
% 205.75/131.80 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A)) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))),
% 205.75/131.80 inference(quant_intro,[status(thm)],[70])).
% 205.75/131.80 tff(72,plain,
% 205.75/131.80 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A)) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))),
% 205.75/131.80 inference(rewrite,[status(thm)],[])).
% 205.75/131.80 tff(73,plain,
% 205.75/131.80 (^[A: $i, B: $i, C: $i] : rewrite((m1_relset_1(C, A, B) => m2_relset_1(k6_relset_1(A, B, C), B, A)) <=> ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A)))),
% 205.75/131.80 inference(bind,[status(th)],[])).
% 205.75/131.80 tff(74,plain,
% 205.75/131.80 (![A: $i, B: $i, C: $i] : (m1_relset_1(C, A, B) => m2_relset_1(k6_relset_1(A, B, C), B, A)) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))),
% 205.75/131.80 inference(quant_intro,[status(thm)],[73])).
% 205.75/131.80 tff(75,axiom,(![A: $i, B: $i, C: $i] : (m1_relset_1(C, A, B) => m2_relset_1(k6_relset_1(A, B, C), B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k6_relset_1')).
% 205.75/131.80 tff(76,plain,
% 205.75/131.80 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[75, 74])).
% 205.75/131.80 tff(77,plain,
% 205.75/131.80 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[76, 72])).
% 205.75/131.80 tff(78,plain,(
% 205.75/131.80 ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))),
% 205.75/131.80 inference(skolemize,[status(sab)],[77])).
% 205.75/131.80 tff(79,plain,
% 205.75/131.80 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[78, 71])).
% 205.75/131.80 tff(80,plain,
% 205.75/131.80 (((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))) | ((~m1_relset_1(E!4, A!2, B!1)) | m2_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))) | (~m1_relset_1(E!4, A!2, B!1)) | m2_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2))),
% 205.75/131.80 inference(rewrite,[status(thm)],[])).
% 205.75/131.80 tff(81,plain,
% 205.75/131.80 ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))) | ((~m1_relset_1(E!4, A!2, B!1)) | m2_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2))),
% 205.75/131.80 inference(quant_inst,[status(thm)],[])).
% 205.75/131.80 tff(82,plain,
% 205.75/131.80 ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m2_relset_1(k6_relset_1(A, B, C), B, A))) | (~m1_relset_1(E!4, A!2, B!1)) | m2_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[81, 80])).
% 205.75/131.80 tff(83,plain,
% 205.75/131.80 ((~m1_relset_1(E!4, A!2, B!1)) | m2_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)),
% 205.75/131.80 inference(unit_resolution,[status(thm)],[82, 79])).
% 205.75/131.80 tff(84,plain,
% 205.75/131.80 (m2_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)),
% 205.75/131.80 inference(unit_resolution,[status(thm)],[83, 30])).
% 205.75/131.80 tff(85,plain,
% 205.75/131.80 (m2_relset_1(k4_relat_1(E!4), B!1, A!2)),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[84, 69])).
% 205.75/131.80 tff(86,plain,
% 205.75/131.80 ((~(m2_relset_1(k4_relat_1(E!4), B!1, A!2) <=> m1_relset_1(k4_relat_1(E!4), B!1, A!2))) | (~m2_relset_1(k4_relat_1(E!4), B!1, A!2)) | m1_relset_1(k4_relat_1(E!4), B!1, A!2)),
% 205.75/131.80 inference(tautology,[status(thm)],[])).
% 205.75/131.80 tff(87,plain,
% 205.75/131.80 (m1_relset_1(k4_relat_1(E!4), B!1, A!2)),
% 205.75/131.80 inference(unit_resolution,[status(thm)],[86, 85, 67])).
% 205.75/131.80 tff(88,plain,
% 205.75/131.80 (m1_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[87, 65])).
% 205.75/131.80 tff(89,plain,
% 205.75/131.80 (^[A: $i, B: $i, C: $i, D: $i] : refl(((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D))) <=> ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D))))),
% 205.75/131.80 inference(bind,[status(th)],[])).
% 205.75/131.80 tff(90,plain,
% 205.75/131.80 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))),
% 205.75/131.80 inference(quant_intro,[status(thm)],[89])).
% 205.75/131.80 tff(91,plain,
% 205.75/131.80 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))),
% 205.75/131.80 inference(rewrite,[status(thm)],[])).
% 205.75/131.80 tff(92,plain,
% 205.75/131.80 (^[A: $i, B: $i, C: $i, D: $i] : rewrite((m1_relset_1(C, A, B) => (k10_relset_1(A, B, C, D) = k9_relat_1(C, D))) <=> ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D))))),
% 205.75/131.80 inference(bind,[status(th)],[])).
% 205.75/131.80 tff(93,plain,
% 205.75/131.80 (![A: $i, B: $i, C: $i, D: $i] : (m1_relset_1(C, A, B) => (k10_relset_1(A, B, C, D) = k9_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))),
% 205.75/131.80 inference(quant_intro,[status(thm)],[92])).
% 205.75/131.80 tff(94,axiom,(![A: $i, B: $i, C: $i, D: $i] : (m1_relset_1(C, A, B) => (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k10_relset_1')).
% 205.75/131.80 tff(95,plain,
% 205.75/131.80 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[94, 93])).
% 205.75/131.80 tff(96,plain,
% 205.75/131.80 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[95, 91])).
% 205.75/131.80 tff(97,plain,(
% 205.75/131.80 ![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))),
% 205.75/131.80 inference(skolemize,[status(sab)],[96])).
% 205.75/131.80 tff(98,plain,
% 205.75/131.80 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[97, 90])).
% 205.75/131.80 tff(99,plain,
% 205.75/131.80 (((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))) | ((~m1_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)) | (k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3) = k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))) | (~m1_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)) | (k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3) = k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3)))),
% 205.75/131.80 inference(rewrite,[status(thm)],[])).
% 205.75/131.80 tff(100,plain,
% 205.75/131.80 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))) | ((~m1_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)) | (k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3) = k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3)))),
% 205.75/131.80 inference(quant_inst,[status(thm)],[])).
% 205.75/131.80 tff(101,plain,
% 205.75/131.80 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))) | (~m1_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)) | (k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3) = k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[100, 99])).
% 205.75/131.80 tff(102,plain,
% 205.75/131.80 ((~m1_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)) | (k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3) = k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3))),
% 205.75/131.80 inference(unit_resolution,[status(thm)],[101, 98])).
% 205.75/131.80 tff(103,plain,
% 205.75/131.80 (k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3) = k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3)),
% 205.75/131.80 inference(unit_resolution,[status(thm)],[102, 88])).
% 205.75/131.80 tff(104,plain,
% 205.75/131.80 (k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3) = k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3)),
% 205.75/131.80 inference(symmetry,[status(thm)],[103])).
% 205.75/131.80 tff(105,plain,
% 205.75/131.80 (r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0))) <=> r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0)),
% 205.75/131.80 inference(monotonicity,[status(thm)],[104, 64])).
% 205.75/131.80 tff(106,plain,
% 205.75/131.80 (r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0)))),
% 205.75/131.80 inference(symmetry,[status(thm)],[105])).
% 205.75/131.80 tff(107,plain,
% 205.75/131.80 ((~r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3))) <=> (~r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3)))),
% 205.75/131.80 inference(monotonicity,[status(thm)],[49])).
% 205.75/131.80 tff(108,plain,
% 205.75/131.80 ((~r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0)) <=> (~r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0))))),
% 205.75/131.80 inference(monotonicity,[status(thm)],[106])).
% 205.75/131.80 tff(109,assumption,(~r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0)), introduced(assumption)).
% 205.75/131.80 tff(110,plain,
% 205.75/131.80 (~r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0)))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[109, 108])).
% 205.75/131.80 tff(111,plain,
% 205.75/131.80 (m1_subset_1(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2)) <=> m1_subset_1(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2))),
% 205.75/131.80 inference(monotonicity,[status(thm)],[104])).
% 205.75/131.80 tff(112,plain,
% 205.75/131.80 (m1_subset_1(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2)) <=> m1_subset_1(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2))),
% 205.75/131.80 inference(symmetry,[status(thm)],[111])).
% 205.75/131.80 tff(113,plain,
% 205.75/131.80 (^[A: $i, B: $i, C: $i, D: $i] : refl(((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B))) <=> ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B))))),
% 205.75/131.80 inference(bind,[status(th)],[])).
% 205.75/131.80 tff(114,plain,
% 205.75/131.80 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))),
% 205.75/131.80 inference(quant_intro,[status(thm)],[113])).
% 205.75/131.80 tff(115,plain,
% 205.75/131.80 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))),
% 205.75/131.80 inference(rewrite,[status(thm)],[])).
% 205.75/131.80 tff(116,plain,
% 205.75/131.80 (^[A: $i, B: $i, C: $i, D: $i] : rewrite((m1_relset_1(C, A, B) => m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B))) <=> ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B))))),
% 205.75/131.80 inference(bind,[status(th)],[])).
% 205.75/131.80 tff(117,plain,
% 205.75/131.80 (![A: $i, B: $i, C: $i, D: $i] : (m1_relset_1(C, A, B) => m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))),
% 205.75/131.80 inference(quant_intro,[status(thm)],[116])).
% 205.75/131.80 tff(118,axiom,(![A: $i, B: $i, C: $i, D: $i] : (m1_relset_1(C, A, B) => m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k10_relset_1')).
% 205.75/131.80 tff(119,plain,
% 205.75/131.80 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[118, 117])).
% 205.75/131.80 tff(120,plain,
% 205.75/131.80 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[119, 115])).
% 205.75/131.80 tff(121,plain,(
% 205.75/131.80 ![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))),
% 205.75/131.80 inference(skolemize,[status(sab)],[120])).
% 205.75/131.80 tff(122,plain,
% 205.75/131.80 (![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[121, 114])).
% 205.75/131.80 tff(123,plain,
% 205.75/131.80 (((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))) | ((~m1_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)) | m1_subset_1(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))) | (~m1_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)) | m1_subset_1(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2)))),
% 205.75/131.80 inference(rewrite,[status(thm)],[])).
% 205.75/131.80 tff(124,plain,
% 205.75/131.80 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))) | ((~m1_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)) | m1_subset_1(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2)))),
% 205.75/131.80 inference(quant_inst,[status(thm)],[])).
% 205.75/131.80 tff(125,plain,
% 205.75/131.80 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))) | (~m1_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)) | m1_subset_1(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[124, 123])).
% 205.75/131.80 tff(126,plain,
% 205.75/131.80 ((~m1_relset_1(k6_relset_1(A!2, B!1, E!4), B!1, A!2)) | m1_subset_1(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2))),
% 205.75/131.80 inference(unit_resolution,[status(thm)],[125, 122])).
% 205.75/131.80 tff(127,plain,
% 205.75/131.80 (m1_subset_1(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2))),
% 205.75/131.80 inference(unit_resolution,[status(thm)],[126, 88])).
% 205.75/131.80 tff(128,plain,
% 205.75/131.80 (m1_subset_1(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[127, 112])).
% 205.75/131.80 tff(129,plain,
% 205.75/131.80 (^[A: $i, B: $i] : refl(((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C))))))),
% 205.75/131.80 inference(bind,[status(th)],[])).
% 205.75/131.80 tff(130,plain,
% 205.75/131.80 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C))))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))),
% 205.75/131.80 inference(quant_intro,[status(thm)],[129])).
% 205.75/131.80 tff(131,plain,
% 205.75/131.80 (^[A: $i, B: $i] : rewrite(((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C))))))),
% 205.75/131.80 inference(bind,[status(th)],[])).
% 205.75/131.80 tff(132,plain,
% 205.75/131.80 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C))))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))),
% 205.75/131.80 inference(quant_intro,[status(thm)],[131])).
% 205.75/131.80 tff(133,plain,
% 205.75/131.80 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C))))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))),
% 205.75/131.80 inference(transitivity,[status(thm)],[132, 130])).
% 205.75/131.80 tff(134,plain,
% 205.75/131.80 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C))))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))),
% 205.75/131.80 inference(rewrite,[status(thm)],[])).
% 205.75/131.80 tff(135,plain,
% 205.75/131.80 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((m1_subset_1(C, k1_zfmisc_1(A)) => (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))), (![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))), ((m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C))))) <=> (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C))))))), rewrite((m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))), ((m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))))),
% 205.75/131.80 inference(bind,[status(th)],[])).
% 205.75/131.80 tff(136,plain,
% 205.75/131.80 (![A: $i, B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C))))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))),
% 205.75/131.80 inference(quant_intro,[status(thm)],[135])).
% 205.75/131.80 tff(137,axiom,(![A: $i, B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t43_subset_1')).
% 205.75/131.80 tff(138,plain,
% 205.75/131.80 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[137, 136])).
% 205.75/131.80 tff(139,plain,
% 205.75/131.80 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[138, 134])).
% 205.75/131.80 tff(140,plain,(
% 205.75/131.80 ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))),
% 205.75/131.80 inference(skolemize,[status(sab)],[139])).
% 205.75/131.80 tff(141,plain,
% 205.75/131.80 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[140, 133])).
% 205.75/131.80 tff(142,plain,
% 205.75/131.80 (((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))) | ((~m1_subset_1(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), C) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C)))))) <=> ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))) | (~m1_subset_1(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), C) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C)))))),
% 205.75/131.80 inference(rewrite,[status(thm)],[])).
% 205.75/131.80 tff(143,plain,
% 205.75/131.80 ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))) | ((~m1_subset_1(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), C) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C)))))),
% 205.75/131.80 inference(quant_inst,[status(thm)],[])).
% 205.75/131.80 tff(144,plain,
% 205.75/131.80 ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))) | (~m1_subset_1(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), C) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C))))),
% 205.75/131.80 inference(modus_ponens,[status(thm)],[143, 142])).
% 205.75/131.80 tff(145,plain,
% 205.75/131.80 ((~m1_subset_1(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k1_zfmisc_1(A!2))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), C) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C))))),
% 205.75/131.80 inference(unit_resolution,[status(thm)],[144, 141])).
% 205.75/131.80 tff(146,plain,
% 205.75/131.80 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), C) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C))))),
% 205.75/131.80 inference(unit_resolution,[status(thm)],[145, 128])).
% 205.75/131.80 tff(147,plain,
% 205.75/131.80 (^[A: $i, B: $i] : refl(((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A))))),
% 205.75/131.80 inference(bind,[status(th)],[])).
% 205.75/131.80 tff(148,plain,
% 205.75/131.80 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))),
% 205.75/131.81 inference(quant_intro,[status(thm)],[147])).
% 205.75/131.81 tff(149,plain,
% 205.75/131.81 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))),
% 205.75/131.81 inference(rewrite,[status(thm)],[])).
% 205.75/131.81 tff(150,plain,
% 205.75/131.81 (^[A: $i, B: $i] : rewrite((m1_subset_1(B, k1_zfmisc_1(A)) => m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A))))),
% 205.75/131.81 inference(bind,[status(th)],[])).
% 205.75/131.81 tff(151,plain,
% 205.75/131.81 (![A: $i, B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))),
% 205.75/131.81 inference(quant_intro,[status(thm)],[150])).
% 205.75/131.81 tff(152,axiom,(![A: $i, B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k3_subset_1')).
% 205.75/131.81 tff(153,plain,
% 205.75/131.81 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))),
% 205.75/131.81 inference(modus_ponens,[status(thm)],[152, 151])).
% 205.75/131.81 tff(154,plain,
% 205.75/131.81 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))),
% 205.75/131.81 inference(modus_ponens,[status(thm)],[153, 149])).
% 205.75/131.81 tff(155,plain,(
% 205.75/131.81 ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))),
% 205.75/131.81 inference(skolemize,[status(sab)],[154])).
% 205.75/131.81 tff(156,plain,
% 205.75/131.81 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))),
% 205.75/131.81 inference(modus_ponens,[status(thm)],[155, 148])).
% 205.75/131.81 tff(157,plain,
% 205.75/131.81 (((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | m1_subset_1(k3_subset_1(A!2, C!0), k1_zfmisc_1(A!2)))) <=> ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | m1_subset_1(k3_subset_1(A!2, C!0), k1_zfmisc_1(A!2)))),
% 205.75/131.81 inference(rewrite,[status(thm)],[])).
% 205.75/131.81 tff(158,plain,
% 205.75/131.81 ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))) | ((~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | m1_subset_1(k3_subset_1(A!2, C!0), k1_zfmisc_1(A!2)))),
% 205.75/131.81 inference(quant_inst,[status(thm)],[])).
% 205.75/131.81 tff(159,plain,
% 205.75/131.81 ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A)))) | (~m1_subset_1(C!0, k1_zfmisc_1(A!2))) | m1_subset_1(k3_subset_1(A!2, C!0), k1_zfmisc_1(A!2))),
% 205.75/131.81 inference(modus_ponens,[status(thm)],[158, 157])).
% 205.75/131.81 tff(160,plain,
% 205.75/131.81 (m1_subset_1(k3_subset_1(A!2, C!0), k1_zfmisc_1(A!2))),
% 205.75/131.81 inference(unit_resolution,[status(thm)],[159, 60, 156])).
% 205.75/131.81 tff(161,plain,
% 205.75/131.81 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), C) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C))))) | ((~m1_subset_1(k3_subset_1(A!2, C!0), k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0)) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), C) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C))))) | (~m1_subset_1(k3_subset_1(A!2, C!0), k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0)) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0)))))),
% 205.75/131.81 inference(rewrite,[status(thm)],[])).
% 205.75/131.81 tff(162,plain,
% 205.75/131.81 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), C) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C))))) | ((~m1_subset_1(k3_subset_1(A!2, C!0), k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0)) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0)))))),
% 205.75/131.81 inference(quant_inst,[status(thm)],[])).
% 205.75/131.81 tff(163,plain,
% 205.75/131.81 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), C) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C))))) | (~m1_subset_1(k3_subset_1(A!2, C!0), k1_zfmisc_1(A!2))) | (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0)) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0))))),
% 205.75/131.81 inference(modus_ponens,[status(thm)],[162, 161])).
% 205.75/131.81 tff(164,plain,
% 205.75/131.81 (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0)) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0)))),
% 205.75/131.81 inference(unit_resolution,[status(thm)],[163, 160, 146])).
% 205.75/131.81 tff(165,plain,
% 205.75/131.81 ((~(r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0)) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0))))) | (~r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0))) | r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0)))),
% 205.75/131.81 inference(tautology,[status(thm)],[])).
% 205.75/131.81 tff(166,plain,
% 205.75/131.81 ((~r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0))) | r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0)))),
% 205.75/131.81 inference(unit_resolution,[status(thm)],[165, 164])).
% 205.75/131.81 tff(167,plain,
% 205.75/131.81 (~r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0))),
% 205.75/131.81 inference(unit_resolution,[status(thm)],[166, 110])).
% 205.75/131.81 tff(168,plain,
% 205.75/131.81 (^[A: $i, B: $i] : refl(((~r1_xboole_0(A, B)) | r1_xboole_0(B, A)) <=> ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A)))),
% 205.75/131.81 inference(bind,[status(th)],[])).
% 205.75/131.81 tff(169,plain,
% 205.75/131.81 (![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A)) <=> ![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))),
% 205.75/131.81 inference(quant_intro,[status(thm)],[168])).
% 205.75/131.81 tff(170,plain,
% 205.75/131.81 (![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A)) <=> ![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))),
% 205.75/131.81 inference(rewrite,[status(thm)],[])).
% 205.75/131.81 tff(171,plain,
% 205.75/131.81 (^[A: $i, B: $i] : rewrite((r1_xboole_0(A, B) => r1_xboole_0(B, A)) <=> ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A)))),
% 205.75/131.81 inference(bind,[status(th)],[])).
% 205.75/131.81 tff(172,plain,
% 205.75/131.81 (![A: $i, B: $i] : (r1_xboole_0(A, B) => r1_xboole_0(B, A)) <=> ![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))),
% 205.75/131.81 inference(quant_intro,[status(thm)],[171])).
% 205.75/131.81 tff(173,axiom,(![A: $i, B: $i] : (r1_xboole_0(A, B) => r1_xboole_0(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','symmetry_r1_xboole_0')).
% 205.75/131.81 tff(174,plain,
% 205.75/131.81 (![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))),
% 205.75/131.81 inference(modus_ponens,[status(thm)],[173, 172])).
% 205.75/131.81 tff(175,plain,
% 205.75/131.81 (![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))),
% 205.75/131.81 inference(modus_ponens,[status(thm)],[174, 170])).
% 205.75/131.81 tff(176,plain,(
% 205.75/131.81 ![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))),
% 205.75/131.81 inference(skolemize,[status(sab)],[175])).
% 205.75/131.81 tff(177,plain,
% 205.75/131.81 (![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))),
% 205.75/131.81 inference(modus_ponens,[status(thm)],[176, 169])).
% 205.75/131.81 tff(178,plain,
% 205.75/131.81 (((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | ((~r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3))) | r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0)))) <=> ((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | (~r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3))) | r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0)))),
% 205.75/131.81 inference(rewrite,[status(thm)],[])).
% 205.75/131.81 tff(179,plain,
% 205.75/131.81 ((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | ((~r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3))) | r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0)))),
% 205.75/131.81 inference(quant_inst,[status(thm)],[])).
% 205.75/131.81 tff(180,plain,
% 205.75/131.81 ((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | (~r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3))) | r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0))),
% 205.75/131.81 inference(modus_ponens,[status(thm)],[179, 178])).
% 205.75/131.81 tff(181,plain,
% 205.75/131.81 ((~r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3))) | r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0))),
% 205.75/131.81 inference(unit_resolution,[status(thm)],[180, 177])).
% 205.75/131.81 tff(182,plain,
% 205.75/131.81 (~r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3))),
% 205.75/131.81 inference(unit_resolution,[status(thm)],[181, 167])).
% 205.75/131.81 tff(183,plain,
% 205.75/131.81 (~r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3))),
% 205.75/131.81 inference(modus_ponens,[status(thm)],[182, 107])).
% 205.75/131.81 tff(184,plain,
% 205.75/131.81 (((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))) | ((~m1_relset_1(E!4, A!2, B!1)) | (k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)) = k9_relat_1(E!4, k3_subset_1(A!2, C!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))) | (~m1_relset_1(E!4, A!2, B!1)) | (k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)) = k9_relat_1(E!4, k3_subset_1(A!2, C!0))))),
% 205.75/131.81 inference(rewrite,[status(thm)],[])).
% 205.75/131.81 tff(185,plain,
% 205.75/131.81 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))) | ((~m1_relset_1(E!4, A!2, B!1)) | (k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)) = k9_relat_1(E!4, k3_subset_1(A!2, C!0))))),
% 205.75/131.81 inference(quant_inst,[status(thm)],[])).
% 205.75/131.81 tff(186,plain,
% 205.75/131.81 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | (k10_relset_1(A, B, C, D) = k9_relat_1(C, D)))) | (~m1_relset_1(E!4, A!2, B!1)) | (k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)) = k9_relat_1(E!4, k3_subset_1(A!2, C!0)))),
% 205.75/131.81 inference(modus_ponens,[status(thm)],[185, 184])).
% 205.75/131.81 tff(187,plain,
% 205.75/131.81 ((~m1_relset_1(E!4, A!2, B!1)) | (k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)) = k9_relat_1(E!4, k3_subset_1(A!2, C!0)))),
% 205.75/131.81 inference(unit_resolution,[status(thm)],[186, 98])).
% 205.75/131.81 tff(188,plain,
% 205.75/131.81 (k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)) = k9_relat_1(E!4, k3_subset_1(A!2, C!0))),
% 205.75/131.81 inference(unit_resolution,[status(thm)],[187, 30])).
% 205.75/131.81 tff(189,plain,
% 205.75/131.81 (k9_relat_1(E!4, k3_subset_1(A!2, C!0)) = k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0))),
% 205.75/131.81 inference(symmetry,[status(thm)],[188])).
% 205.75/131.81 tff(190,plain,
% 205.75/131.81 (r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)) <=> r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))),
% 205.75/131.81 inference(monotonicity,[status(thm)],[189])).
% 205.75/131.81 tff(191,plain,
% 205.75/131.81 (r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))),
% 205.75/131.81 inference(symmetry,[status(thm)],[190])).
% 205.75/131.81 tff(192,plain,
% 205.75/131.81 ((~(r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)) <=> r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0))) <=> ((~r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))) <=> r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0))),
% 205.75/131.81 inference(rewrite,[status(thm)],[])).
% 205.75/131.81 tff(193,plain,
% 205.75/131.81 (~(r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)) <=> r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0))),
% 205.75/131.81 inference(or_elim,[status(thm)],[26])).
% 205.75/131.81 tff(194,plain,
% 205.75/131.81 ((~r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))) <=> r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0)),
% 205.75/131.81 inference(modus_ponens,[status(thm)],[193, 192])).
% 205.75/131.81 tff(195,plain,
% 205.75/131.81 (r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)) | r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0) | (~((~r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))) <=> r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0)))),
% 205.75/131.81 inference(tautology,[status(thm)],[])).
% 205.75/131.81 tff(196,plain,
% 205.75/131.81 (r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)) | r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0)),
% 205.75/131.81 inference(unit_resolution,[status(thm)],[195, 194])).
% 205.75/131.81 tff(197,plain,
% 205.75/131.81 (r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))),
% 205.75/131.81 inference(unit_resolution,[status(thm)],[196, 109])).
% 205.75/131.81 tff(198,plain,
% 205.75/131.81 (r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))),
% 205.75/131.81 inference(modus_ponens,[status(thm)],[197, 191])).
% 205.75/131.81 tff(199,plain,
% 205.75/131.81 (m1_subset_1(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1)) <=> m1_subset_1(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1))),
% 205.75/131.81 inference(monotonicity,[status(thm)],[189])).
% 205.75/131.81 tff(200,plain,
% 205.75/131.81 (m1_subset_1(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1)) <=> m1_subset_1(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1))),
% 205.75/131.81 inference(symmetry,[status(thm)],[199])).
% 205.75/131.81 tff(201,plain,
% 205.75/131.81 (((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))) | ((~m1_relset_1(E!4, A!2, B!1)) | m1_subset_1(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))) | (~m1_relset_1(E!4, A!2, B!1)) | m1_subset_1(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1)))),
% 205.75/131.81 inference(rewrite,[status(thm)],[])).
% 205.75/131.81 tff(202,plain,
% 205.75/131.81 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))) | ((~m1_relset_1(E!4, A!2, B!1)) | m1_subset_1(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1)))),
% 205.75/131.81 inference(quant_inst,[status(thm)],[])).
% 205.75/131.81 tff(203,plain,
% 205.75/131.81 ((~![A: $i, B: $i, C: $i, D: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k10_relset_1(A, B, C, D), k1_zfmisc_1(B)))) | (~m1_relset_1(E!4, A!2, B!1)) | m1_subset_1(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1))),
% 205.75/131.81 inference(modus_ponens,[status(thm)],[202, 201])).
% 205.75/131.81 tff(204,plain,
% 205.75/131.81 ((~m1_relset_1(E!4, A!2, B!1)) | m1_subset_1(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1))),
% 205.75/131.81 inference(unit_resolution,[status(thm)],[203, 122])).
% 205.75/131.81 tff(205,plain,
% 205.75/131.81 (m1_subset_1(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1))),
% 205.75/131.81 inference(unit_resolution,[status(thm)],[204, 30])).
% 205.75/131.81 tff(206,plain,
% 205.75/131.81 (m1_subset_1(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1))),
% 205.75/131.81 inference(modus_ponens,[status(thm)],[205, 200])).
% 205.75/131.81 tff(207,plain,
% 205.75/131.81 (((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))) | ((~m1_subset_1(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), C) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, C)))))) <=> ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))) | (~m1_subset_1(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), C) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, C)))))),
% 205.75/131.81 inference(rewrite,[status(thm)],[])).
% 205.75/131.81 tff(208,plain,
% 205.75/131.81 ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))) | ((~m1_subset_1(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), C) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, C)))))),
% 205.75/131.81 inference(quant_inst,[status(thm)],[])).
% 205.75/131.81 tff(209,plain,
% 205.75/131.81 ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_xboole_0(B, C) <=> r1_tarski(B, k3_subset_1(A, C)))))) | (~m1_subset_1(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), C) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, C))))),
% 205.75/131.81 inference(modus_ponens,[status(thm)],[208, 207])).
% 205.75/131.81 tff(210,plain,
% 205.75/131.81 ((~m1_subset_1(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k1_zfmisc_1(B!1))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), C) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, C))))),
% 205.75/131.81 inference(unit_resolution,[status(thm)],[209, 141])).
% 205.75/131.81 tff(211,plain,
% 205.75/131.81 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), C) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, C))))),
% 205.75/131.81 inference(unit_resolution,[status(thm)],[210, 206])).
% 205.75/131.81 tff(212,plain,
% 205.75/131.81 (m1_subset_1(D!3, k1_zfmisc_1(B!1))),
% 205.75/131.81 inference(and_elim,[status(thm)],[25])).
% 205.75/131.81 tff(213,plain,
% 205.75/131.81 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), C) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, C))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), C) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, C))))) | (~m1_subset_1(D!3, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))))),
% 205.75/131.81 inference(rewrite,[status(thm)],[])).
% 205.75/131.81 tff(214,plain,
% 205.75/131.81 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), C) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, C))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))))),
% 205.75/131.81 inference(quant_inst,[status(thm)],[])).
% 205.75/131.81 tff(215,plain,
% 205.75/131.81 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), C) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, C))))) | (~m1_subset_1(D!3, k1_zfmisc_1(B!1))) | (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)))),
% 205.75/131.81 inference(modus_ponens,[status(thm)],[214, 213])).
% 205.75/131.81 tff(216,plain,
% 205.75/131.81 (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))),
% 205.75/131.81 inference(unit_resolution,[status(thm)],[215, 212, 211])).
% 205.75/131.81 tff(217,plain,
% 205.75/131.81 ((~(r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)))) | r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3) | (~r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)))),
% 205.75/131.81 inference(tautology,[status(thm)],[])).
% 205.75/131.81 tff(218,plain,
% 205.75/131.81 (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3) | (~r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)))),
% 205.75/131.81 inference(unit_resolution,[status(thm)],[217, 216])).
% 205.75/131.81 tff(219,plain,
% 205.75/131.81 (r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3)),
% 205.75/131.81 inference(unit_resolution,[status(thm)],[218, 198])).
% 205.75/131.81 tff(220,plain,
% 205.75/131.81 (((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | ((~r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3)) | r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0))))) <=> ((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | (~r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3)) | r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0))))),
% 205.75/131.81 inference(rewrite,[status(thm)],[])).
% 205.75/131.81 tff(221,plain,
% 205.75/131.81 ((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | ((~r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3)) | r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0))))),
% 205.75/131.81 inference(quant_inst,[status(thm)],[])).
% 205.75/131.81 tff(222,plain,
% 205.75/131.81 ((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | (~r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3)) | r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))),
% 205.75/131.81 inference(modus_ponens,[status(thm)],[221, 220])).
% 205.75/131.81 tff(223,plain,
% 205.75/131.81 ((~r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3)) | r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))),
% 205.75/131.81 inference(unit_resolution,[status(thm)],[222, 177])).
% 205.75/131.81 tff(224,plain,
% 205.75/131.81 (r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))),
% 205.75/131.81 inference(unit_resolution,[status(thm)],[223, 219])).
% 205.75/131.81 tff(225,plain,
% 205.75/131.81 (^[A: $i, B: $i, C: $i] : refl(((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))))),
% 205.75/131.81 inference(bind,[status(th)],[])).
% 205.75/131.81 tff(226,plain,
% 205.75/131.81 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))),
% 205.75/131.81 inference(quant_intro,[status(thm)],[225])).
% 205.75/131.81 tff(227,plain,
% 205.75/131.81 (^[A: $i, B: $i, C: $i] : rewrite(((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))))),
% 205.75/131.81 inference(bind,[status(th)],[])).
% 205.75/131.81 tff(228,plain,
% 205.75/131.81 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))),
% 205.75/131.81 inference(quant_intro,[status(thm)],[227])).
% 205.75/131.81 tff(229,plain,
% 205.75/131.81 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))),
% 205.75/131.81 inference(transitivity,[status(thm)],[228, 226])).
% 205.75/131.81 tff(230,plain,
% 205.75/131.81 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))),
% 205.75/131.81 inference(rewrite,[status(thm)],[])).
% 205.75/131.81 tff(231,plain,
% 205.75/131.81 (^[A: $i, B: $i, C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(quant_intro(proof_bind(^[E: $i] : rewrite((m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))) <=> ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))), (![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))) <=> ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))), ((m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))) <=> (m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))), rewrite((m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))) <=> ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))), ((m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))) <=> ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))))), (![D: $i] : (m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))) <=> ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))), ((m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))) <=> (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))))), rewrite((m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))), ((m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))))),
% 205.75/131.82 inference(bind,[status(th)],[])).
% 205.75/131.82 tff(232,plain,
% 205.75/131.82 (![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C)))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))),
% 205.75/131.82 inference(quant_intro,[status(thm)],[231])).
% 205.75/131.82 tff(233,axiom,(![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) => (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t46_relset_2')).
% 205.75/131.82 tff(234,plain,
% 205.75/131.82 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))),
% 205.75/131.82 inference(modus_ponens,[status(thm)],[233, 232])).
% 205.75/131.82 tff(235,plain,
% 205.75/131.82 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))),
% 205.75/131.82 inference(modus_ponens,[status(thm)],[234, 230])).
% 205.75/131.82 tff(236,plain,(
% 205.75/131.82 ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))),
% 205.75/131.82 inference(skolemize,[status(sab)],[235])).
% 205.75/131.82 tff(237,plain,
% 205.75/131.82 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))),
% 205.75/131.82 inference(modus_ponens,[status(thm)],[236, 229])).
% 205.75/131.82 tff(238,plain,
% 205.75/131.82 (((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))) | ((~m1_subset_1(k3_subset_1(A!2, C!0), k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, k3_subset_1(A!2, C!0)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))) | (~m1_subset_1(k3_subset_1(A!2, C!0), k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, k3_subset_1(A!2, C!0)))))))),
% 205.75/131.82 inference(rewrite,[status(thm)],[])).
% 205.75/131.82 tff(239,plain,
% 205.75/131.82 ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))) | ((~m1_subset_1(k3_subset_1(A!2, C!0), k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, k3_subset_1(A!2, C!0)))))))),
% 205.75/131.82 inference(quant_inst,[status(thm)],[])).
% 205.75/131.82 tff(240,plain,
% 205.75/131.82 ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (r1_xboole_0(C, k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, C))))))) | (~m1_subset_1(k3_subset_1(A!2, C!0), k1_zfmisc_1(A!2))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, k3_subset_1(A!2, C!0))))))),
% 205.75/131.82 inference(modus_ponens,[status(thm)],[239, 238])).
% 205.75/131.82 tff(241,plain,
% 205.75/131.82 (![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, k3_subset_1(A!2, C!0))))))),
% 205.75/131.82 inference(unit_resolution,[status(thm)],[240, 237, 160])).
% 205.75/131.82 tff(242,plain,
% 205.75/131.82 (((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, k3_subset_1(A!2, C!0))))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E, k3_subset_1(A!2, C!0))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, k3_subset_1(A!2, C!0))))))) | (~m1_subset_1(D!3, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E, k3_subset_1(A!2, C!0))))))),
% 205.75/131.82 inference(rewrite,[status(thm)],[])).
% 205.75/131.82 tff(243,plain,
% 205.75/131.82 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, k3_subset_1(A!2, C!0))))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E, k3_subset_1(A!2, C!0))))))),
% 205.75/131.82 inference(quant_inst,[status(thm)],[])).
% 205.75/131.82 tff(244,plain,
% 205.75/131.82 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D)) <=> r1_xboole_0(D, k9_relat_1(E, k3_subset_1(A!2, C!0))))))) | (~m1_subset_1(D!3, k1_zfmisc_1(B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E, k3_subset_1(A!2, C!0)))))),
% 205.75/131.82 inference(modus_ponens,[status(thm)],[243, 242])).
% 205.75/131.82 tff(245,plain,
% 205.75/131.82 (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E, k3_subset_1(A!2, C!0)))))),
% 205.75/131.82 inference(unit_resolution,[status(thm)],[244, 212, 241])).
% 205.75/131.82 tff(246,plain,
% 205.75/131.82 (^[A: $i, B: $i, C: $i] : refl(((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 205.75/131.82 inference(bind,[status(th)],[])).
% 205.75/131.82 tff(247,plain,
% 205.75/131.82 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 205.75/131.82 inference(quant_intro,[status(thm)],[246])).
% 205.75/131.82 tff(248,plain,
% 205.75/131.82 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 205.75/131.82 inference(rewrite,[status(thm)],[])).
% 205.75/131.82 tff(249,plain,
% 205.75/131.82 (^[A: $i, B: $i, C: $i] : rewrite((m2_relset_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 205.75/131.82 inference(bind,[status(th)],[])).
% 205.75/131.82 tff(250,plain,
% 205.75/131.82 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 205.75/131.82 inference(quant_intro,[status(thm)],[249])).
% 205.75/131.82 tff(251,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_relset_1')).
% 205.75/131.82 tff(252,plain,
% 205.75/131.82 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 205.75/131.82 inference(modus_ponens,[status(thm)],[251, 250])).
% 205.75/131.82 tff(253,plain,
% 205.75/131.82 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 205.75/131.82 inference(modus_ponens,[status(thm)],[252, 248])).
% 205.75/131.82 tff(254,plain,(
% 205.75/131.82 ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 205.75/131.82 inference(skolemize,[status(sab)],[253])).
% 205.75/131.82 tff(255,plain,
% 205.75/131.82 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 205.75/131.82 inference(modus_ponens,[status(thm)],[254, 247])).
% 205.75/131.82 tff(256,plain,
% 205.75/131.82 (((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | ((~m2_relset_1(E!4, A!2, B!1)) | m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (~m2_relset_1(E!4, A!2, B!1)) | m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))),
% 205.75/131.82 inference(rewrite,[status(thm)],[])).
% 205.75/131.82 tff(257,plain,
% 205.75/131.82 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | ((~m2_relset_1(E!4, A!2, B!1)) | m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))),
% 205.75/131.82 inference(quant_inst,[status(thm)],[])).
% 205.75/131.82 tff(258,plain,
% 205.75/131.82 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (~m2_relset_1(E!4, A!2, B!1)) | m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))),
% 205.75/131.82 inference(modus_ponens,[status(thm)],[257, 256])).
% 205.75/131.82 tff(259,plain,
% 205.75/131.82 (m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))),
% 205.75/131.82 inference(unit_resolution,[status(thm)],[258, 27, 255])).
% 205.75/131.82 tff(260,plain,
% 205.75/131.82 (((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E, k3_subset_1(A!2, C!0)))))) | ((~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))))) <=> ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E, k3_subset_1(A!2, C!0)))))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))))),
% 205.75/131.82 inference(rewrite,[status(thm)],[])).
% 205.75/131.82 tff(261,plain,
% 205.75/131.82 ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E, k3_subset_1(A!2, C!0)))))) | ((~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))))),
% 205.75/131.82 inference(quant_inst,[status(thm)],[])).
% 205.75/131.82 tff(262,plain,
% 205.75/131.82 ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E, k3_subset_1(A!2, C!0)))))) | (~m1_subset_1(E!4, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0))))),
% 205.75/131.82 inference(modus_ponens,[status(thm)],[261, 260])).
% 205.75/131.82 tff(263,plain,
% 205.75/131.82 (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))),
% 205.75/131.82 inference(unit_resolution,[status(thm)],[262, 259, 245])).
% 205.75/131.82 tff(264,plain,
% 205.75/131.82 ((~(r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0))))) | r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3)) | (~r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0))))),
% 205.75/131.82 inference(tautology,[status(thm)],[])).
% 205.75/131.82 tff(265,plain,
% 205.75/131.82 (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3)) | (~r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0))))),
% 205.75/131.82 inference(unit_resolution,[status(thm)],[264, 263])).
% 205.75/131.82 tff(266,plain,
% 205.75/131.82 (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3))),
% 205.75/131.82 inference(unit_resolution,[status(thm)],[265, 224])).
% 205.75/131.82 tff(267,plain,
% 205.75/131.82 ($false),
% 205.75/131.82 inference(unit_resolution,[status(thm)],[266, 183])).
% 205.75/131.82 tff(268,plain,(r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0)), inference(lemma,lemma(discharge,[]))).
% 205.75/131.82 tff(269,plain,
% 205.75/131.82 (r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0)))),
% 205.75/131.82 inference(modus_ponens,[status(thm)],[268, 106])).
% 205.75/131.82 tff(270,plain,
% 205.75/131.82 ((~(r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0)) <=> r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0))))) | r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0)) | (~r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0))))),
% 205.75/131.82 inference(tautology,[status(thm)],[])).
% 205.75/131.82 tff(271,plain,
% 205.75/131.82 (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0)) | (~r1_tarski(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, k3_subset_1(A!2, C!0))))),
% 205.75/131.82 inference(unit_resolution,[status(thm)],[270, 164])).
% 205.75/131.82 tff(272,plain,
% 205.75/131.82 (r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0))),
% 205.75/131.82 inference(unit_resolution,[status(thm)],[271, 269])).
% 205.75/131.82 tff(273,plain,
% 205.75/131.82 (((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | ((~r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0))) | r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3)))) <=> ((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | (~r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0))) | r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3)))),
% 205.75/131.82 inference(rewrite,[status(thm)],[])).
% 205.75/131.82 tff(274,plain,
% 205.75/131.82 ((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | ((~r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0))) | r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3)))),
% 205.75/131.82 inference(quant_inst,[status(thm)],[])).
% 205.75/131.82 tff(275,plain,
% 205.75/131.82 ((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | (~r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0))) | r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3))),
% 205.75/131.82 inference(modus_ponens,[status(thm)],[274, 273])).
% 205.75/131.82 tff(276,plain,
% 205.75/131.82 ((~r1_xboole_0(k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3), k3_subset_1(A!2, C!0))) | r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3))),
% 205.75/131.82 inference(unit_resolution,[status(thm)],[275, 177])).
% 205.75/131.82 tff(277,plain,
% 205.75/131.82 (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k6_relset_1(A!2, B!1, E!4), D!3))),
% 205.75/131.82 inference(unit_resolution,[status(thm)],[276, 272])).
% 205.75/131.82 tff(278,plain,
% 205.75/131.82 (r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3))),
% 205.75/131.82 inference(modus_ponens,[status(thm)],[277, 49])).
% 205.75/131.82 tff(279,plain,
% 205.75/131.82 ((~r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))) <=> (~r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)))),
% 205.75/131.82 inference(monotonicity,[status(thm)],[191])).
% 205.75/131.82 tff(280,plain,
% 205.75/131.82 ((~r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))) | (~r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0)) | (~((~r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))) <=> r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0)))),
% 205.75/131.82 inference(tautology,[status(thm)],[])).
% 205.75/131.82 tff(281,plain,
% 205.75/131.82 ((~r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))) | (~r1_tarski(k10_relset_1(B!1, A!2, k6_relset_1(A!2, B!1, E!4), D!3), C!0))),
% 205.75/131.82 inference(unit_resolution,[status(thm)],[280, 194])).
% 205.75/131.82 tff(282,plain,
% 205.75/131.82 (~r1_tarski(k10_relset_1(A!2, B!1, E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))),
% 205.75/131.82 inference(unit_resolution,[status(thm)],[281, 268])).
% 205.75/131.82 tff(283,plain,
% 205.75/131.82 (~r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))),
% 205.75/131.82 inference(modus_ponens,[status(thm)],[282, 279])).
% 205.75/131.82 tff(284,plain,
% 205.75/131.82 ((~(r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3) <=> r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3)))) | (~r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3)) | r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))),
% 205.75/131.82 inference(tautology,[status(thm)],[])).
% 205.75/131.82 tff(285,plain,
% 205.75/131.82 ((~r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3)) | r1_tarski(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), k3_subset_1(B!1, D!3))),
% 205.75/131.82 inference(unit_resolution,[status(thm)],[284, 216])).
% 205.75/131.82 tff(286,plain,
% 205.75/131.82 (~r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3)),
% 205.75/131.82 inference(unit_resolution,[status(thm)],[285, 283])).
% 205.75/131.82 tff(287,plain,
% 205.75/131.82 (((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | ((~r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))) | r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3))) <=> ((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | (~r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))) | r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3))),
% 205.75/131.82 inference(rewrite,[status(thm)],[])).
% 205.75/131.82 tff(288,plain,
% 205.75/131.82 ((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | ((~r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))) | r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3))),
% 205.75/131.82 inference(quant_inst,[status(thm)],[])).
% 205.75/131.82 tff(289,plain,
% 205.75/131.82 ((~![A: $i, B: $i] : ((~r1_xboole_0(A, B)) | r1_xboole_0(B, A))) | (~r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))) | r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3)),
% 205.75/131.82 inference(modus_ponens,[status(thm)],[288, 287])).
% 205.75/131.82 tff(290,plain,
% 205.75/131.82 ((~r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))) | r1_xboole_0(k9_relat_1(E!4, k3_subset_1(A!2, C!0)), D!3)),
% 205.75/131.82 inference(unit_resolution,[status(thm)],[289, 177])).
% 205.75/131.82 tff(291,plain,
% 205.75/131.82 (~r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))),
% 205.75/131.82 inference(unit_resolution,[status(thm)],[290, 286])).
% 205.75/131.82 tff(292,plain,
% 205.75/131.82 ((~(r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3)) <=> r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0))))) | (~r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3))) | r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))),
% 205.93/131.97 inference(tautology,[status(thm)],[])).
% 205.93/131.97 tff(293,plain,
% 205.93/131.97 ((~r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3))) | r1_xboole_0(D!3, k9_relat_1(E!4, k3_subset_1(A!2, C!0)))),
% 205.93/131.97 inference(unit_resolution,[status(thm)],[292, 263])).
% 205.93/131.97 tff(294,plain,
% 205.93/131.97 (~r1_xboole_0(k3_subset_1(A!2, C!0), k9_relat_1(k4_relat_1(E!4), D!3))),
% 205.93/131.97 inference(unit_resolution,[status(thm)],[293, 291])).
% 205.93/131.97 tff(295,plain,
% 205.93/131.97 ($false),
% 205.93/131.97 inference(unit_resolution,[status(thm)],[294, 278])).
% 205.93/131.97 % SZS output end Proof
%------------------------------------------------------------------------------