TSTP Solution File: SEU451+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU451+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:29:47 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU451+1 : TPTP v8.1.0. Released v3.4.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 15:00:46 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(k9_relset_2_type, type, (
% 0.20/0.41 k9_relset_2: ( $i * $i * $i * $i * $i ) > $i)).
% 0.20/0.41 tff(k6_partfun1_type, type, (
% 0.20/0.41 k6_partfun1: $i > $i)).
% 0.20/0.41 tff(tptp_fun_B_1_type, type, (
% 0.20/0.41 tptp_fun_B_1: $i)).
% 0.20/0.41 tff(tptp_fun_C_0_type, type, (
% 0.20/0.41 tptp_fun_C_0: $i)).
% 0.20/0.41 tff(tptp_fun_A_2_type, type, (
% 0.20/0.41 tptp_fun_A_2: $i)).
% 0.20/0.41 tff(k5_relat_1_type, type, (
% 0.20/0.41 k5_relat_1: ( $i * $i ) > $i)).
% 0.20/0.41 tff(k6_relat_1_type, type, (
% 0.20/0.41 k6_relat_1: $i > $i)).
% 0.20/0.41 tff(k7_relset_1_type, type, (
% 0.20/0.41 k7_relset_1: ( $i * $i * $i * $i * $i * $i ) > $i)).
% 0.20/0.41 tff(m1_relset_1_type, type, (
% 0.20/0.41 m1_relset_1: ( $i * $i * $i ) > $o)).
% 0.20/0.41 tff(m2_relset_1_type, type, (
% 0.20/0.41 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.20/0.41 tff(v1_partfun1_type, type, (
% 0.20/0.41 v1_partfun1: ( $i * $i * $i ) > $o)).
% 0.20/0.41 tff(m1_subset_1_type, type, (
% 0.20/0.41 m1_subset_1: ( $i * $i ) > $o)).
% 0.20/0.41 tff(k1_zfmisc_1_type, type, (
% 0.20/0.41 k1_zfmisc_1: $i > $i)).
% 0.20/0.41 tff(k2_zfmisc_1_type, type, (
% 0.20/0.41 k2_zfmisc_1: ( $i * $i ) > $i)).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 ((k5_relat_1(C!0, k6_partfun1(B!1)) = k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1))) <=> (k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1)))),
% 0.20/0.41 inference(commutativity,[status(thm)],[])).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (^[A: $i] : refl((k6_partfun1(A) = k6_relat_1(A)) <=> (k6_partfun1(A) = k6_relat_1(A)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (![A: $i] : (k6_partfun1(A) = k6_relat_1(A)) <=> ![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (![A: $i] : (k6_partfun1(A) = k6_relat_1(A)) <=> ![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(5,axiom,(![A: $i] : (k6_partfun1(A) = k6_relat_1(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k6_partfun1')).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.41 tff(7,plain,(
% 0.20/0.41 ![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 0.20/0.41 inference(skolemize,[status(sab)],[6])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 (![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 ((~![A: $i] : (k6_partfun1(A) = k6_relat_1(A))) | (k6_partfun1(B!1) = k6_relat_1(B!1))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 (k6_partfun1(B!1) = k6_relat_1(B!1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 (k5_relat_1(C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_relat_1(B!1))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[10])).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 (k5_relat_1(C!0, k6_relat_1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1))),
% 0.20/0.41 inference(symmetry,[status(thm)],[11])).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (^[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)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (![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))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (![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))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(16,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')).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.41 tff(18,plain,(
% 0.20/0.41 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.20/0.41 inference(skolemize,[status(sab)],[17])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k6_relat_1(B!1), B!1, B!1) <=> m1_relset_1(k6_relat_1(B!1), B!1, B!1))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (m2_relset_1(k6_relat_1(B!1), B!1, B!1) <=> m1_relset_1(k6_relat_1(B!1), B!1, B!1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (k6_relat_1(B!1) = k6_partfun1(B!1)),
% 0.20/0.41 inference(symmetry,[status(thm)],[10])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 (m2_relset_1(k6_relat_1(B!1), B!1, B!1) <=> m2_relset_1(k6_partfun1(B!1), B!1, B!1)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[22])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (m2_relset_1(k6_partfun1(B!1), B!1, B!1) <=> m2_relset_1(k6_relat_1(B!1), B!1, B!1)),
% 0.20/0.41 inference(symmetry,[status(thm)],[23])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (^[A: $i] : refl((~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A)))) <=> (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 (![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A)))) <=> ![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 (^[A: $i] : rewrite((v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A)) <=> (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A)) <=> ![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A)) <=> ![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(30,axiom,(![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k6_partfun1')).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.41 tff(32,plain,(
% 0.20/0.41 ![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A))),
% 0.20/0.41 inference(skolemize,[status(sab)],[31])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 ((~![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A))))) | (~((~v1_partfun1(k6_partfun1(B!1), B!1, B!1)) | (~m2_relset_1(k6_partfun1(B!1), B!1, B!1))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (~((~v1_partfun1(k6_partfun1(B!1), B!1, B!1)) | (~m2_relset_1(k6_partfun1(B!1), B!1, B!1)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (((~v1_partfun1(k6_partfun1(B!1), B!1, B!1)) | (~m2_relset_1(k6_partfun1(B!1), B!1, B!1))) | m2_relset_1(k6_partfun1(B!1), B!1, B!1)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (m2_relset_1(k6_partfun1(B!1), B!1, B!1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (m2_relset_1(k6_relat_1(B!1), B!1, B!1)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[38, 24])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 ((~(m2_relset_1(k6_relat_1(B!1), B!1, B!1) <=> m1_relset_1(k6_relat_1(B!1), B!1, B!1))) | (~m2_relset_1(k6_relat_1(B!1), B!1, B!1)) | m1_relset_1(k6_relat_1(B!1), B!1, B!1)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (m1_relset_1(k6_relat_1(B!1), B!1, B!1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[40, 39, 21])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(C!0, A!2, B!1) <=> m1_relset_1(C!0, A!2, B!1))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (m2_relset_1(C!0, A!2, B!1) <=> m1_relset_1(C!0, A!2, B!1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[42, 19])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (k9_relset_2(A, A, B, k6_partfun1(A), C) = k9_relset_2(A, B, B, C, k6_partfun1(B))))) <=> (~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (k9_relset_2(A, A, B, k6_partfun1(A), C) = k9_relset_2(A, B, B, C, k6_partfun1(B)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => (k9_relset_2(A, A, B, k6_partfun1(A), C) = k9_relset_2(A, B, B, C, k6_partfun1(B))))) <=> (~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (k9_relset_2(A, A, B, k6_partfun1(A), C) = k9_relset_2(A, B, B, C, k6_partfun1(B)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(46,axiom,(~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => (k9_relset_2(A, A, B, k6_partfun1(A), C) = k9_relset_2(A, B, B, C, k6_partfun1(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t65_relset_2')).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (k9_relset_2(A, A, B, k6_partfun1(A), C) = k9_relset_2(A, B, B, C, k6_partfun1(B))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (k9_relset_2(A, A, B, k6_partfun1(A), C) = k9_relset_2(A, B, B, C, k6_partfun1(B))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[47, 44])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (k9_relset_2(A, A, B, k6_partfun1(A), C) = k9_relset_2(A, B, B, C, k6_partfun1(B))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (k9_relset_2(A, A, B, k6_partfun1(A), C) = k9_relset_2(A, B, B, C, k6_partfun1(B))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[49, 44])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (k9_relset_2(A, A, B, k6_partfun1(A), C) = k9_relset_2(A, B, B, C, k6_partfun1(B))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[50, 44])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (k9_relset_2(A, A, B, k6_partfun1(A), C) = k9_relset_2(A, B, B, C, k6_partfun1(B))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 (~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (k9_relset_2(A, A, B, k6_partfun1(A), C) = k9_relset_2(A, B, B, C, k6_partfun1(B))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[52, 44])).
% 0.20/0.41 tff(54,plain,(
% 0.20/0.41 ~((~m2_relset_1(C!0, A!2, B!1)) | (k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[53])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (m2_relset_1(C!0, A!2, B!1)),
% 0.20/0.41 inference(or_elim,[status(thm)],[54])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 ((~(m2_relset_1(C!0, A!2, B!1) <=> m1_relset_1(C!0, A!2, B!1))) | (~m2_relset_1(C!0, A!2, B!1)) | m1_relset_1(C!0, A!2, B!1)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 ((~(m2_relset_1(C!0, A!2, B!1) <=> m1_relset_1(C!0, A!2, B!1))) | m1_relset_1(C!0, A!2, B!1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (m1_relset_1(C!0, A!2, B!1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[57, 43])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : refl(((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))) <=> ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_relset_1(E, A, B) & m1_relset_1(F, C, D)) <=> (~((~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))))), ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) <=> (~(~((~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))))))), rewrite((~(~((~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))))) <=> ((~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))), ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) <=> ((~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))))), (((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> (((~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))))), rewrite((((~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))), (((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : rewrite(((m1_relset_1(E, A, B) & m1_relset_1(F, C, D)) => (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((m1_relset_1(E, A, B) & m1_relset_1(F, C, D)) => (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.41 tff(66,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((m1_relset_1(E, A, B) & m1_relset_1(F, C, D)) => (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k7_relset_1')).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.20/0.41 tff(69,plain,(
% 0.20/0.41 ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[68])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[70, 60])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(B!1), B!1, B!1)) | (k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1)) = k5_relat_1(C!0, k6_relat_1(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | (~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(B!1), B!1, B!1)) | (k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1)) = k5_relat_1(C!0, k6_relat_1(B!1))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(73,plain,
% 0.20/0.42 (((k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1)) = k5_relat_1(C!0, k6_relat_1(B!1))) | (~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(B!1), B!1, B!1))) <=> ((~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(B!1), B!1, B!1)) | (k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1)) = k5_relat_1(C!0, k6_relat_1(B!1))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1)) = k5_relat_1(C!0, k6_relat_1(B!1))) | (~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(B!1), B!1, B!1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(B!1), B!1, B!1)) | (k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1)) = k5_relat_1(C!0, k6_relat_1(B!1)))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[73])).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1)) = k5_relat_1(C!0, k6_relat_1(B!1))) | (~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(B!1), B!1, B!1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | (~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(B!1), B!1, B!1)) | (k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1)) = k5_relat_1(C!0, k6_relat_1(B!1))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[74, 72])).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1)) = k5_relat_1(C!0, k6_relat_1(B!1))) | (~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(B!1), B!1, B!1)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | (~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(B!1), B!1, B!1)) | (k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1)) = k5_relat_1(C!0, k6_relat_1(B!1)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.42 tff(78,plain,
% 0.20/0.42 ((~m1_relset_1(k6_relat_1(B!1), B!1, B!1)) | (k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1)) = k5_relat_1(C!0, k6_relat_1(B!1)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[77, 71, 58])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 (k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1)) = k5_relat_1(C!0, k6_relat_1(B!1))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[78, 41])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 (k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1)) = k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_partfun1(B!1))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[22])).
% 0.20/0.42 tff(81,plain,
% 0.20/0.42 (k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_partfun1(B!1)) = k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1))),
% 0.20/0.42 inference(symmetry,[status(thm)],[80])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 (^[A: $i, B: $i, C: $i] : refl(((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))))) <=> ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[82])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 (^[A: $i, B: $i, C: $i] : rewrite(((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))) <=> ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 (^[A: $i, B: $i, C: $i] : rewrite((m2_relset_1(C, A, B) => ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))) <=> ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[87])).
% 0.20/0.42 tff(89,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t23_funct_2')).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.20/0.42 tff(92,plain,(
% 0.20/0.42 ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[91])).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[93, 83])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 (((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))) | ((~m2_relset_1(C!0, A!2, B!1)) | (~((~(k7_relset_1(A!2, A!2, A!2, B!1, k6_partfun1(A!2), C!0) = C!0)) | (~(k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_partfun1(B!1)) = C!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))) | (~m2_relset_1(C!0, A!2, B!1)) | (~((~(k7_relset_1(A!2, A!2, A!2, B!1, k6_partfun1(A!2), C!0) = C!0)) | (~(k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_partfun1(B!1)) = C!0)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))) | ((~m2_relset_1(C!0, A!2, B!1)) | (~((~(k7_relset_1(A!2, A!2, A!2, B!1, k6_partfun1(A!2), C!0) = C!0)) | (~(k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_partfun1(B!1)) = C!0)))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(97,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))) | (~m2_relset_1(C!0, A!2, B!1)) | (~((~(k7_relset_1(A!2, A!2, A!2, B!1, k6_partfun1(A!2), C!0) = C!0)) | (~(k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_partfun1(B!1)) = C!0))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.42 tff(98,plain,
% 0.20/0.42 (~((~(k7_relset_1(A!2, A!2, A!2, B!1, k6_partfun1(A!2), C!0) = C!0)) | (~(k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_partfun1(B!1)) = C!0)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[97, 55, 94])).
% 0.20/0.42 tff(99,plain,
% 0.20/0.42 (((~(k7_relset_1(A!2, A!2, A!2, B!1, k6_partfun1(A!2), C!0) = C!0)) | (~(k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_partfun1(B!1)) = C!0))) | (k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_partfun1(B!1)) = C!0)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(100,plain,
% 0.20/0.42 (k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_partfun1(B!1)) = C!0),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 (C!0 = k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_partfun1(B!1))),
% 0.20/0.42 inference(symmetry,[status(thm)],[100])).
% 0.20/0.42 tff(102,plain,
% 0.20/0.42 (((~(k7_relset_1(A!2, A!2, A!2, B!1, k6_partfun1(A!2), C!0) = C!0)) | (~(k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_partfun1(B!1)) = C!0))) | (k7_relset_1(A!2, A!2, A!2, B!1, k6_partfun1(A!2), C!0) = C!0)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(103,plain,
% 0.20/0.42 (k7_relset_1(A!2, A!2, A!2, B!1, k6_partfun1(A!2), C!0) = C!0),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[102, 98])).
% 0.20/0.42 tff(104,plain,
% 0.20/0.42 ((~![A: $i] : (k6_partfun1(A) = k6_relat_1(A))) | (k6_partfun1(A!2) = k6_relat_1(A!2))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(105,plain,
% 0.20/0.42 (k6_partfun1(A!2) = k6_relat_1(A!2)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[104, 8])).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 (k6_relat_1(A!2) = k6_partfun1(A!2)),
% 0.20/0.42 inference(symmetry,[status(thm)],[105])).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 (k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0) = k7_relset_1(A!2, A!2, A!2, B!1, k6_partfun1(A!2), C!0)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[106])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k6_relat_1(A!2), A!2, A!2) <=> m1_relset_1(k6_relat_1(A!2), A!2, A!2))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 (m2_relset_1(k6_relat_1(A!2), A!2, A!2) <=> m1_relset_1(k6_relat_1(A!2), A!2, A!2)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[108, 19])).
% 0.20/0.43 tff(110,plain,
% 0.20/0.43 (m2_relset_1(k6_relat_1(A!2), A!2, A!2) <=> m2_relset_1(k6_partfun1(A!2), A!2, A!2)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[106])).
% 0.20/0.43 tff(111,plain,
% 0.20/0.43 (m2_relset_1(k6_partfun1(A!2), A!2, A!2) <=> m2_relset_1(k6_relat_1(A!2), A!2, A!2)),
% 0.20/0.43 inference(symmetry,[status(thm)],[110])).
% 0.20/0.43 tff(112,plain,
% 0.20/0.43 ((~![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A))))) | (~((~v1_partfun1(k6_partfun1(A!2), A!2, A!2)) | (~m2_relset_1(k6_partfun1(A!2), A!2, A!2))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(113,plain,
% 0.20/0.43 (~((~v1_partfun1(k6_partfun1(A!2), A!2, A!2)) | (~m2_relset_1(k6_partfun1(A!2), A!2, A!2)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[112, 34])).
% 0.20/0.43 tff(114,plain,
% 0.20/0.43 (((~v1_partfun1(k6_partfun1(A!2), A!2, A!2)) | (~m2_relset_1(k6_partfun1(A!2), A!2, A!2))) | m2_relset_1(k6_partfun1(A!2), A!2, A!2)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(115,plain,
% 0.20/0.43 (m2_relset_1(k6_partfun1(A!2), A!2, A!2)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.20/0.43 tff(116,plain,
% 0.20/0.43 (m2_relset_1(k6_relat_1(A!2), A!2, A!2)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.20/0.43 tff(117,plain,
% 0.20/0.43 ((~(m2_relset_1(k6_relat_1(A!2), A!2, A!2) <=> m1_relset_1(k6_relat_1(A!2), A!2, A!2))) | (~m2_relset_1(k6_relat_1(A!2), A!2, A!2)) | m1_relset_1(k6_relat_1(A!2), A!2, A!2)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(118,plain,
% 0.20/0.43 (m1_relset_1(k6_relat_1(A!2), A!2, A!2)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[117, 116, 109])).
% 0.20/0.43 tff(119,plain,
% 0.20/0.43 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(A!2), A!2, A!2)) | (k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0) = k5_relat_1(k6_relat_1(A!2), C!0)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | (~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(A!2), A!2, A!2)) | (k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0) = k5_relat_1(k6_relat_1(A!2), C!0)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(120,plain,
% 0.20/0.43 (((k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0) = k5_relat_1(k6_relat_1(A!2), C!0)) | (~m1_relset_1(k6_relat_1(A!2), A!2, A!2)) | (~m1_relset_1(C!0, A!2, B!1))) <=> ((~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(A!2), A!2, A!2)) | (k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0) = k5_relat_1(k6_relat_1(A!2), C!0)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(121,plain,
% 0.20/0.43 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0) = k5_relat_1(k6_relat_1(A!2), C!0)) | (~m1_relset_1(k6_relat_1(A!2), A!2, A!2)) | (~m1_relset_1(C!0, A!2, B!1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(A!2), A!2, A!2)) | (k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0) = k5_relat_1(k6_relat_1(A!2), C!0))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[120])).
% 0.20/0.43 tff(122,plain,
% 0.20/0.43 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0) = k5_relat_1(k6_relat_1(A!2), C!0)) | (~m1_relset_1(k6_relat_1(A!2), A!2, A!2)) | (~m1_relset_1(C!0, A!2, B!1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | (~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(A!2), A!2, A!2)) | (k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0) = k5_relat_1(k6_relat_1(A!2), C!0)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[121, 119])).
% 0.20/0.43 tff(123,plain,
% 0.20/0.43 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0) = k5_relat_1(k6_relat_1(A!2), C!0)) | (~m1_relset_1(k6_relat_1(A!2), A!2, A!2)) | (~m1_relset_1(C!0, A!2, B!1)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(124,plain,
% 0.20/0.43 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | (~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(A!2), A!2, A!2)) | (k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0) = k5_relat_1(k6_relat_1(A!2), C!0))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.20/0.43 tff(125,plain,
% 0.20/0.43 ((~m1_relset_1(k6_relat_1(A!2), A!2, A!2)) | (k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0) = k5_relat_1(k6_relat_1(A!2), C!0))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[124, 71, 58])).
% 0.20/0.43 tff(126,plain,
% 0.20/0.43 (k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0) = k5_relat_1(k6_relat_1(A!2), C!0)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[125, 118])).
% 0.20/0.43 tff(127,plain,
% 0.20/0.43 (k5_relat_1(k6_relat_1(A!2), C!0) = k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0)),
% 0.20/0.43 inference(symmetry,[status(thm)],[126])).
% 0.20/0.43 tff(128,plain,
% 0.20/0.43 (k5_relat_1(k6_partfun1(A!2), C!0) = k5_relat_1(k6_relat_1(A!2), C!0)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[105])).
% 0.20/0.43 tff(129,plain,
% 0.20/0.43 (^[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)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(130,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[129])).
% 0.20/0.43 tff(131,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(132,plain,
% 0.20/0.43 (^[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)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(133,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[132])).
% 0.20/0.43 tff(134,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')).
% 0.20/0.43 tff(135,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.20/0.43 tff(136,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[135, 131])).
% 0.20/0.43 tff(137,plain,(
% 0.20/0.43 ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[136])).
% 0.20/0.43 tff(138,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[137, 130])).
% 0.20/0.43 tff(139,plain,
% 0.20/0.43 (((~![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(C!0, A!2, B!1)) | m1_subset_1(C!0, 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(C!0, A!2, B!1)) | m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(140,plain,
% 0.20/0.43 ((~![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(C!0, A!2, B!1)) | m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(141,plain,
% 0.20/0.43 ((~![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(C!0, A!2, B!1)) | m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.20/0.43 tff(142,plain,
% 0.20/0.43 (m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[141, 55, 138])).
% 0.20/0.43 tff(143,plain,
% 0.20/0.43 (m1_subset_1(k6_relat_1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2))) <=> m1_subset_1(k6_partfun1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[106])).
% 0.20/0.43 tff(144,plain,
% 0.20/0.43 (((~![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(k6_relat_1(A!2), A!2, A!2)) | m1_subset_1(k6_relat_1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2))))) <=> ((~![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(k6_relat_1(A!2), A!2, A!2)) | m1_subset_1(k6_relat_1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(145,plain,
% 0.20/0.43 ((~![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(k6_relat_1(A!2), A!2, A!2)) | m1_subset_1(k6_relat_1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(146,plain,
% 0.20/0.43 ((~![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(k6_relat_1(A!2), A!2, A!2)) | m1_subset_1(k6_relat_1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.20/0.43 tff(147,plain,
% 0.20/0.43 ((~m2_relset_1(k6_relat_1(A!2), A!2, A!2)) | m1_subset_1(k6_relat_1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[146, 138])).
% 0.20/0.43 tff(148,plain,
% 0.20/0.43 (m1_subset_1(k6_relat_1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[147, 116])).
% 0.20/0.43 tff(149,plain,
% 0.20/0.43 (m1_subset_1(k6_partfun1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[148, 143])).
% 0.20/0.43 tff(150,plain,
% 0.20/0.43 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : refl(((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) <=> ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(151,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[150])).
% 0.20/0.43 tff(152,plain,
% 0.20/0.43 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) <=> (~((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))))), ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) <=> (~(~((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))))))), rewrite((~(~((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))))) <=> ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))), ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) <=> ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))))), (((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> (((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E))))), rewrite((((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))), (((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(153,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[152])).
% 0.20/0.44 tff(154,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(155,plain,
% 0.20/0.44 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : rewrite(((m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) => (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(156,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) => (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[155])).
% 0.20/0.44 tff(157,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i] : ((m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) => (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k9_relset_2')).
% 0.20/0.44 tff(158,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.20/0.44 tff(159,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[158, 154])).
% 0.20/0.44 tff(160,plain,(
% 0.20/0.44 ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[159])).
% 0.20/0.44 tff(161,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[160, 153])).
% 0.20/0.44 tff(162,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[161, 151])).
% 0.20/0.44 tff(163,plain,
% 0.20/0.44 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | ((~m1_subset_1(k6_partfun1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k5_relat_1(k6_partfun1(A!2), C!0)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | (~m1_subset_1(k6_partfun1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k5_relat_1(k6_partfun1(A!2), C!0)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(164,plain,
% 0.20/0.44 (((k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k5_relat_1(k6_partfun1(A!2), C!0)) | (~m1_subset_1(k6_partfun1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))) <=> ((~m1_subset_1(k6_partfun1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k5_relat_1(k6_partfun1(A!2), C!0)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(165,plain,
% 0.20/0.44 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | ((k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k5_relat_1(k6_partfun1(A!2), C!0)) | (~m1_subset_1(k6_partfun1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | ((~m1_subset_1(k6_partfun1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k5_relat_1(k6_partfun1(A!2), C!0))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[164])).
% 0.20/0.44 tff(166,plain,
% 0.20/0.44 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | ((k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k5_relat_1(k6_partfun1(A!2), C!0)) | (~m1_subset_1(k6_partfun1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | (~m1_subset_1(k6_partfun1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k5_relat_1(k6_partfun1(A!2), C!0)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[165, 163])).
% 0.20/0.44 tff(167,plain,
% 0.20/0.44 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | ((k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k5_relat_1(k6_partfun1(A!2), C!0)) | (~m1_subset_1(k6_partfun1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(168,plain,
% 0.20/0.44 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | (~m1_subset_1(k6_partfun1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k5_relat_1(k6_partfun1(A!2), C!0))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.20/0.44 tff(169,plain,
% 0.20/0.44 ((~m1_subset_1(k6_partfun1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k5_relat_1(k6_partfun1(A!2), C!0))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[168, 162])).
% 0.20/0.44 tff(170,plain,
% 0.20/0.44 (k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k5_relat_1(k6_partfun1(A!2), C!0)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[169, 149, 142])).
% 0.20/0.44 tff(171,plain,
% 0.20/0.44 (k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k5_relat_1(C!0, k6_partfun1(B!1))),
% 0.20/0.44 inference(transitivity,[status(thm)],[170, 128, 127, 107, 103, 101, 81, 79, 12])).
% 0.20/0.44 tff(172,plain,
% 0.20/0.44 ((k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1))) <=> (k5_relat_1(C!0, k6_partfun1(B!1)) = k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[171])).
% 0.20/0.44 tff(173,plain,
% 0.20/0.44 ((k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1))) <=> (k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[172, 1])).
% 0.20/0.44 tff(174,plain,
% 0.20/0.44 ((k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1))) <=> (k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)))),
% 0.20/0.44 inference(symmetry,[status(thm)],[173])).
% 0.20/0.44 tff(175,plain,
% 0.20/0.44 (m1_subset_1(k6_relat_1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1))) <=> m1_subset_1(k6_partfun1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[22])).
% 0.20/0.44 tff(176,plain,
% 0.20/0.44 (((~![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(k6_relat_1(B!1), B!1, B!1)) | m1_subset_1(k6_relat_1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, 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(k6_relat_1(B!1), B!1, B!1)) | m1_subset_1(k6_relat_1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(177,plain,
% 0.20/0.44 ((~![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(k6_relat_1(B!1), B!1, B!1)) | m1_subset_1(k6_relat_1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(178,plain,
% 0.20/0.44 ((~![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(k6_relat_1(B!1), B!1, B!1)) | m1_subset_1(k6_relat_1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.20/0.44 tff(179,plain,
% 0.20/0.44 ((~m2_relset_1(k6_relat_1(B!1), B!1, B!1)) | m1_subset_1(k6_relat_1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[178, 138])).
% 0.20/0.44 tff(180,plain,
% 0.20/0.44 (m1_subset_1(k6_relat_1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[179, 39])).
% 0.20/0.44 tff(181,plain,
% 0.20/0.44 (m1_subset_1(k6_partfun1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[180, 175])).
% 0.20/0.44 tff(182,plain,
% 0.20/0.44 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | ((~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k6_partfun1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))) | (k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k6_partfun1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))) | (k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(183,plain,
% 0.20/0.45 (((k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k6_partfun1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1))))) <=> ((~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k6_partfun1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))) | (k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(184,plain,
% 0.20/0.45 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | ((k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k6_partfun1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | ((~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k6_partfun1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))) | (k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1)))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[183])).
% 0.20/0.45 tff(185,plain,
% 0.20/0.45 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | ((k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k6_partfun1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k6_partfun1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))) | (k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[184, 182])).
% 0.20/0.45 tff(186,plain,
% 0.20/0.45 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | ((k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k6_partfun1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(187,plain,
% 0.20/0.45 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k6_partfun1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))) | (k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.20/0.45 tff(188,plain,
% 0.20/0.45 ((~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k6_partfun1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))) | (k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[187, 162])).
% 0.20/0.45 tff(189,plain,
% 0.20/0.45 (k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[188, 181, 142])).
% 0.20/0.45 tff(190,plain,
% 0.20/0.45 (k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[189, 174])).
% 0.20/0.45 tff(191,plain,
% 0.20/0.45 (~(k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)))),
% 0.20/0.45 inference(or_elim,[status(thm)],[54])).
% 0.20/0.45 tff(192,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.20/0.45 % SZS output end Proof
%------------------------------------------------------------------------------