%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM742^4 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:16:59 AM UTC 2026
% Result : Theorem 253.42s 36.95s
% Output : CNFRefutation 253.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM742^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 % Computer : n008.cluster.edu
% 0.07/0.22 % Model : x86_64 x86_64
% 0.07/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.22 % Memory : 8046.5625MB
% 0.07/0.22 % OS : Linux 6.8.0-71-generic
% 0.07/0.22 % CPULimit : 300
% 0.07/0.22 % WCLimit : 300
% 0.07/0.22 % DateTime : Tue Sep 29 12:48:39 UTC 2026
% 0.07/0.22 % CPUTime :
% 0.07/0.22 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.29 Running higher-order theorem proving
% 0.24/0.38 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p
% 253.42/36.95 % Version: 3.5.1-ho
% 253.42/36.95 % Preprocessing class: HSLMSMSMLLLCHSA.
% 253.42/36.95 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 253.42/36.95 % Starting pre_casc_4 with 1200s (4) cores
% 253.42/36.95 % Starting full_lambda_6 with 300s (1) cores
% 253.42/36.95 % Starting sh10 with 300s (1) cores
% 253.42/36.95 % Starting post_as_ho9 with 300s (1) cores
% 253.42/36.95 % Starting post_as_ho8 with 300s (1) cores
% 253.42/36.95 % post_as_ho9 with pid 3095820 completed with status 0
% 253.42/36.95 % Result found by post_as_ho9
% 253.42/36.95 % Preprocessing class: HSLMSMSMLLLCHSA.
% 253.42/36.95 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 253.42/36.95 % Starting pre_casc_4 with 1200s (4) cores
% 253.42/36.95 % Starting full_lambda_6 with 300s (1) cores
% 253.42/36.95 % Starting sh10 with 300s (1) cores
% 253.42/36.95 % Starting post_as_ho9 with 300s (1) cores
% 253.42/36.95 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,,true,1,0,2,20000,1.0,true))
% 253.42/36.95 % SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true)
% 253.42/36.95 % Search class: HGUNF-FSLM21-DHSMMFBN
% 253.42/36.95 % partial match(5): HGUSM-FSLM31-DHSFFFBN
% 253.42/36.95 % Scheduled 7 strats onto 1 cores with 299 seconds (299 total)
% 253.42/36.95 % Starting SubtermCWHack with 27s (1) cores
% 253.42/36.95 % SubtermCWHack with pid 3095829 completed with status 8
% 253.42/36.95 % Starting post_as_ho9 with 30s (1) cores
% 253.42/36.95 % post_as_ho9 with pid 3095906 completed with status 0
% 253.42/36.95 % Result found by post_as_ho9
% 253.42/36.95 % Preprocessing class: HSLMSMSMLLLCHSA.
% 253.42/36.95 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 253.42/36.95 % Starting pre_casc_4 with 1200s (4) cores
% 253.42/36.95 % Starting full_lambda_6 with 300s (1) cores
% 253.42/36.95 % Starting sh10 with 300s (1) cores
% 253.42/36.95 % Starting post_as_ho9 with 300s (1) cores
% 253.42/36.95 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,,true,1,0,2,20000,1.0,true))
% 253.42/36.95 % SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true)
% 253.42/36.95 % Search class: HGUNF-FSLM21-DHSMMFBN
% 253.42/36.95 % partial match(5): HGUSM-FSLM31-DHSFFFBN
% 253.42/36.95 % Scheduled 7 strats onto 1 cores with 299 seconds (299 total)
% 253.42/36.95 % Starting SubtermCWHack with 27s (1) cores
% 253.42/36.95 % SubtermCWHack with pid 3095829 completed with status 8
% 253.42/36.95 % Starting post_as_ho9 with 30s (1) cores
% 253.42/36.95 % Preprocessing time : 0.054 s
% 253.42/36.95 % Presaturation interreduction done
% 253.42/36.95
% 253.42/36.95 % Proof found!
% 253.42/36.95 % SZS status Theorem
% 253.42/36.95 % SZS output start CNFRefutation
% 253.42/36.95 thf(decl_23, type, is_of: $i > ($i > $o) > $o).
% 253.42/36.95 thf(decl_24, type, all_of: ($i > $o) > ($i > $o) > $o).
% 253.42/36.95 thf(decl_26, type, in: $i > $i > $o).
% 253.42/36.95 thf(decl_28, type, emptyset: $i).
% 253.42/36.95 thf(decl_43, type, d_Sep: $i > ($i > $o) > $i).
% 253.42/36.95 thf(decl_48, type, ordsucc: $i > $i).
% 253.42/36.95 thf(decl_50, type, omega: $i).
% 253.42/36.95 thf(decl_59, type, ap: $i > $i > $i).
% 253.42/36.95 thf(decl_61, type, d_Pi: $i > ($i > $i) > $i).
% 253.42/36.95 thf(decl_62, type, imp: $o > $o > $o).
% 253.42/36.95 thf(decl_63, type, d_not: $o > $o).
% 253.42/36.95 thf(decl_68, type, l_or: $o > $o > $o).
% 253.42/36.95 thf(decl_124, type, nat: $i).
% 253.42/36.95 thf(decl_125, type, n_is: $i > $i > $o).
% 253.42/36.95 thf(decl_128, type, n_some: ($i > $o) > $o).
% 253.42/36.95 thf(decl_131, type, n_1: $i).
% 253.42/36.95 thf(decl_148, type, diffprop: $i > $i > $i > $o).
% 253.42/36.95 thf(decl_149, type, d_29_ii: $i > $i > $o).
% 253.42/36.95 thf(decl_150, type, iii: $i > $i > $o).
% 253.42/36.95 thf(decl_153, type, lessis: $i > $i > $o).
% 253.42/36.95 thf(decl_162, type, times: $i > $i).
% 253.42/36.95 thf(decl_163, type, n_ts: $i > $i > $i).
% 253.42/36.95 thf(decl_168, type, d_1to: $i > $i).
% 253.42/36.95 thf(decl_173, type, n_2: $i).
% 253.42/36.95 thf(decl_177, type, pair1type: $i > $i).
% 253.42/36.95 thf(decl_179, type, first1: $i > $i > $i).
% 253.42/36.95 thf(decl_180, type, second1: $i > $i > $i).
% 253.42/36.95 thf(decl_190, type, frac: $i).
% 253.42/36.95 thf(decl_192, type, num: $i > $i).
% 253.42/36.95 thf(decl_193, type, den: $i > $i).
% 253.42/36.95 thf(decl_194, type, n_eq: $i > $i > $o).
% 253.42/36.95 thf(decl_195, type, moref: $i > $i > $o).
% 253.42/36.95 thf(decl_196, type, lessf: $i > $i > $o).
% 253.42/36.95 thf(decl_198, type, lesseq: $i > $i > $o).
% 253.42/36.95 thf(decl_199, type, epred1_2: $i > $i > $o).
% 253.42/36.95 thf(decl_200, type, epred2_2: $i > $i > $o).
% 253.42/36.95 thf(decl_202, type, epred4_2: $i > $i > $o).
% 253.42/36.95 thf(decl_203, type, epred5_2: $i > $i > $o).
% 253.42/36.95 thf(decl_205, type, epred7_2: $i > $i > $o).
% 253.42/36.95 thf(decl_206, type, epred8_2: $i > $i > $o).
% 253.42/36.95 thf(decl_209, type, esk1_0: $i).
% 253.42/36.95 thf(decl_210, type, esk2_0: $i).
% 253.42/36.95 thf(decl_211, type, esk3_0: $i).
% 253.42/36.95 thf(def_l_or, axiom, ((l_or)=(^[X83:$o]:(imp @ ((d_not @ ((X83))))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', def_l_or)).
% 253.42/36.95 thf(def_d_not, axiom, ((d_not)=(^[X76:$o]:((imp @ ((X76)) @ (~($true)))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', def_d_not)).
% 253.42/36.95 thf(def_lessis, axiom, ((lessis)=(^[X1:$i, X230:$i]:((l_or @ ((iii @ X1 @ X230)) @ ((n_is @ X1 @ X230)))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', def_lessis)).
% 253.42/36.95 thf(def_iii, axiom, ((iii)=(^[X1:$i, X211:$i]:((n_some @ (diffprop @ X211 @ X1))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', def_iii)).
% 253.42/36.95 thf(def_all_of, axiom, ((all_of)=(^[X3:$i > $o, X2:$i > $o]:(![X4:$i]:((((is_of @ X4 @ X3))=>((X2 @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', def_all_of)).
% 253.42/36.95 thf(def_is_of, axiom, ((is_of)=(^[X1:$i, X2:$i > $o]:((X2 @ X1)))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', def_is_of)).
% 253.42/36.95 thf(def_nat, axiom, ((nat)=(d_Sep @ omega @ (^[X1:$i]:(((X1)!=(emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', def_nat)).
% 253.42/36.95 thf(def_n_ts, axiom, ((n_ts)=(^[X1:$i]:(ap @ (times @ X1)))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', def_n_ts)).
% 253.42/36.95 thf(def_n_eq, axiom, ((n_eq)=(^[X1:$i, X436:$i]:((n_is @ (n_ts @ (num @ X1) @ (den @ X436)) @ (n_ts @ (num @ X436) @ (den @ X1)))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', def_n_eq)).
% 253.42/36.95 thf(def_num, axiom, ((num)=(first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', def_num)).
% 253.42/36.95 thf(def_den, axiom, ((den)=(second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', def_den)).
% 253.42/36.95 thf(def_lessf, axiom, ((lessf)=(^[X1:$i, X450:$i]:((iii @ (n_ts @ (num @ X1) @ (den @ X450)) @ (n_ts @ (num @ X450) @ (den @ X1)))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', def_lessf)).
% 253.42/36.95 thf(satz10e, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((all_of @ (^[X239:$i]:((in @ X239 @ nat))) @ (^[X240:$i]:((((d_not @ ((d_29_ii @ X1 @ X240))))=>((lessis @ X1 @ X240))))))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', satz10e)).
% 253.42/36.95 thf(satz29, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((all_of @ (^[X363:$i]:((in @ X363 @ nat))) @ (^[X364:$i]:((n_is @ (n_ts @ X1 @ X364) @ (n_ts @ X364 @ X1)))))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', satz29)).
% 253.42/36.95 thf(def_pair1type, axiom, ((pair1type)=(^[X1:$i]:(d_Pi @ (d_1to @ n_2) @ (^[X425:$i]:(X1))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', def_pair1type)).
% 253.42/36.95 thf(def_lesseq, axiom, ((lesseq)=(^[X1:$i, X466:$i]:((l_or @ ((lessf @ X1 @ X466)) @ ((n_eq @ X1 @ X466)))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', def_lesseq)).
% 253.42/36.95 thf(suc_p, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((is_of @ (ordsucc @ X1) @ (^[X166:$i]:((in @ X166 @ nat))))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', suc_p)).
% 253.42/36.95 thf(n_1_p, axiom, (is_of @ n_1 @ (^[X1:$i]:((in @ X1 @ nat)))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', n_1_p)).
% 253.42/36.95 thf(def_frac, axiom, ((frac)=(d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', def_frac)).
% 253.42/36.95 thf(satz51a, conjecture, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X493:$i]:((in @ X493 @ frac))) @ (^[X494:$i]:((all_of @ (^[X4:$i]:((in @ X4 @ frac))) @ (^[X4:$i]:((((lesseq @ X1 @ X494))=>((((lessf @ X494 @ X4))=>((lessf @ X1 @ X4)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', satz51a)).
% 253.42/36.95 thf(satz33b, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((all_of @ (^[X401:$i]:((in @ X401 @ nat))) @ (^[X402:$i]:((all_of @ (^[X4:$i]:((in @ X4 @ nat))) @ (^[X4:$i]:((((n_is @ (n_ts @ X1 @ X4) @ (n_ts @ X402 @ X4)))=>((n_is @ X1 @ X402)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', satz33b)).
% 253.42/36.95 thf(def_moref, axiom, ((moref)=(^[X1:$i, X449:$i]:((d_29_ii @ (n_ts @ (num @ X1) @ (den @ X449)) @ (n_ts @ (num @ X449) @ (den @ X1)))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', def_moref)).
% 253.42/36.95 thf(satz10g, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((all_of @ (^[X243:$i]:((in @ X243 @ nat))) @ (^[X244:$i]:((((d_29_ii @ X1 @ X244))=>((d_not @ ((lessis @ X1 @ X244))))))))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', satz10g)).
% 253.42/36.95 thf(satz10d, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((all_of @ (^[X237:$i]:((in @ X237 @ nat))) @ (^[X238:$i]:((((lessis @ X1 @ X238))=>((d_not @ ((d_29_ii @ X1 @ X238))))))))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', satz10d)).
% 253.42/36.95 thf(satz50, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X491:$i]:((in @ X491 @ frac))) @ (^[X492:$i]:((all_of @ (^[X4:$i]:((in @ X4 @ frac))) @ (^[X4:$i]:((((lessf @ X1 @ X492))=>((((lessf @ X492 @ X4))=>((lessf @ X1 @ X4)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', satz50)).
% 253.42/36.95 thf(satz41k, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X481:$i]:((in @ X481 @ frac))) @ (^[X482:$i]:((((d_not @ ((lesseq @ X1 @ X482))))=>((moref @ X1 @ X482))))))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', satz41k)).
% 253.42/36.95 thf(satz41d, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X469:$i]:((in @ X469 @ frac))) @ (^[X470:$i]:((((lesseq @ X1 @ X470))=>((d_not @ ((moref @ X1 @ X470))))))))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', satz41d)).
% 253.42/36.95 thf(satz38, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X437:$i]:((in @ X437 @ frac))) @ (^[X438:$i]:((((n_eq @ X1 @ X438))=>((n_eq @ X438 @ X1))))))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', satz38)).
% 253.42/36.95 thf(satz43, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X459:$i]:((in @ X459 @ frac))) @ (^[X460:$i]:((((lessf @ X1 @ X460))=>((moref @ X460 @ X1))))))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', satz43)).
% 253.42/36.95 thf(satz42, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X457:$i]:((in @ X457 @ frac))) @ (^[X458:$i]:((((moref @ X1 @ X458))=>((lessf @ X458 @ X1))))))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', satz42)).
% 253.42/36.95 thf(satz37, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((n_eq @ X1 @ X1)))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', satz37)).
% 253.42/36.95 thf(satz41e, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X471:$i]:((in @ X471 @ frac))) @ (^[X472:$i]:((((d_not @ ((moref @ X1 @ X472))))=>((lesseq @ X1 @ X472))))))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', satz41e)).
% 253.42/36.95 thf(satz45, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X463:$i]:((in @ X463 @ frac))) @ (^[X464:$i]:((all_of @ (^[X4:$i]:((in @ X4 @ frac))) @ (^[X4:$i]:((all_of @ (^[X13:$i]:((in @ X13 @ frac))) @ (^[X13:$i]:((((lessf @ X1 @ X464))=>((((n_eq @ X1 @ X4))=>((((n_eq @ X464 @ X13))=>((lessf @ X4 @ X13))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.BcDgwSYNpY/E---3.1_3095803.p', satz45)).
% 253.42/36.95 thf(c_0_33, plain, ((l_or)=(^[Z0:$o]:(imp @ (((imp @ (((Z0))) @ (~($true)))))))), inference(fof_simplification,[status(thm)],[def_l_or])).
% 253.42/36.95 thf(c_0_34, plain, ((d_not)=(^[Z0:$o]:((imp @ ((Z0)) @ (~($true)))))), inference(fof_simplification,[status(thm)],[def_d_not])).
% 253.42/36.95 thf(c_0_35, plain, ((lessis)=(^[Z0:$i, Z1:$i]:((imp @ (((imp @ (((((n_some @ (diffprop @ Z1 @ Z0)))))) @ (~($true))))) @ ((n_is @ Z0 @ Z1)))))), inference(fof_simplification,[status(thm)],[def_lessis])).
% 253.42/36.95 thf(c_0_36, plain, ((l_or)=(^[Z0:$o]:(imp @ (((imp @ (((Z0))) @ (~($true)))))))), inference(apply_def,[status(thm)],[c_0_33, c_0_34])).
% 253.42/36.95 thf(c_0_37, plain, ((iii)=(^[Z0:$i, Z1:$i]:((n_some @ (diffprop @ Z1 @ Z0))))), inference(fof_simplification,[status(thm)],[def_iii])).
% 253.42/36.95 thf(c_0_38, plain, ((all_of)=(^[Z0:$i > $o, Z1:$i > $o]:(![X4:$i]:(((((Z0 @ X4)))=>((Z1 @ X4))))))), inference(fof_simplification,[status(thm)],[def_all_of])).
% 253.42/36.95 thf(c_0_39, plain, ((is_of)=(^[Z0:$i, Z1:$i > $o]:((Z1 @ Z0)))), inference(fof_simplification,[status(thm)],[def_is_of])).
% 253.42/36.95 thf(c_0_40, plain, ((nat)=(d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))), inference(fof_simplification,[status(thm)],[def_nat])).
% 253.42/36.95 thf(c_0_41, plain, ![X502:$i, X503:$i]:(((epred1_2 @ X503 @ X502)<=>((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502))))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502))))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)))|(imp @ $true @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)))|(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)))|(imp @ $false @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)))|(imp @ $false @ $false))))))), introduced(definition)).
% 253.42/36.95 thf(c_0_42, plain, ((lessis)=(^[Z0:$i, Z1:$i]:((imp @ (((imp @ (((((n_some @ (diffprop @ Z1 @ Z0)))))) @ (~($true))))) @ ((n_is @ Z0 @ Z1)))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_35, c_0_36]), c_0_37])).
% 253.42/36.95 thf(c_0_43, plain, ((all_of)=(^[Z0:$i > $o, Z1:$i > $o]:(![X4:$i]:(((((Z0 @ X4)))=>((Z1 @ X4))))))), inference(apply_def,[status(thm)],[c_0_38, c_0_39])).
% 253.42/36.95 thf(c_0_44, plain, ![X609:$i, X608:$i]:(((epred7_2 @ X608 @ X609)<=>((((~(n_some @ (diffprop @ X608 @ X609))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ X608 @ X609))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ X609 @ X608)|(imp @ $true @ $true))&((n_is @ X609 @ X608)|(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ X608 @ X609))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ X608 @ X609))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ X609 @ X608)|(imp @ $false @ $true))&((n_is @ X609 @ X608)|(imp @ $false @ $false))))))), introduced(definition)).
% 253.42/36.95 thf(c_0_45, plain, ((n_ts)=(^[Z0:$i]:(ap @ (times @ Z0)))), inference(fof_simplification,[status(thm)],[def_n_ts])).
% 253.42/36.95 thf(c_0_46, plain, ((n_eq)=(^[Z0:$i, Z1:$i]:((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0)))))), inference(fof_simplification,[status(thm)],[def_n_eq])).
% 253.42/36.95 thf(c_0_47, axiom, ((num)=(first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))))), inference(apply_def,[status(thm)],[def_num, c_0_40])).
% 253.42/36.95 thf(c_0_48, axiom, ((den)=(second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))))), inference(apply_def,[status(thm)],[def_den, c_0_40])).
% 253.42/36.95 thf(c_0_49, plain, ((lessf)=(^[Z0:$i, Z1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)))))))), inference(fof_simplification,[status(thm)],[def_lessf])).
% 253.42/36.95 thf(c_0_50, plain, ![X502:$i, X503:$i]:(((epred1_2 @ X503 @ X502)=>((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502))))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502))))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)))|(imp @ $true @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)))|(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)))|(imp @ $false @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)))|(imp @ $false @ $false))))))), inference(split_equiv,[status(thm)],[c_0_41])).
% 253.42/36.95 thf(c_0_51, plain, ![X609:$i]:(((in @ X609 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))=>![X608:$i]:(((in @ X608 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))=>(((~(d_29_ii @ X609 @ X608)|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((d_29_ii @ X609 @ X608)|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))=>(epred7_2 @ X608 @ X609)))))), inference(apply_def,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz10e]), c_0_40]), c_0_34]), c_0_42]), c_0_43])]), c_0_44])).
% 253.42/36.95 thf(c_0_52, plain, ![X584:$i]:(((in @ X584 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))=>![X583:$i]:(((in @ X583 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))=>(n_is @ (ap @ (times @ X584) @ X583) @ (ap @ (times @ X583) @ X584)))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz29]), c_0_40]), c_0_45]), c_0_43])).
% 253.42/36.95 thf(c_0_53, plain, ((pair1type)=(^[Z0:$i]:(d_Pi @ (d_1to @ n_2) @ (^[Z1:$i]:(Z0))))), inference(fof_simplification,[status(thm)],[def_pair1type])).
% 253.42/36.95 thf(c_0_54, plain, ((lesseq)=(^[Z0:$i, Z1:$i]:((imp @ (((imp @ (((((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)))))))) @ (~($true))))) @ (((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0))))))))), inference(fof_simplification,[status(thm)],[def_lesseq])).
% 253.42/36.95 thf(c_0_55, plain, ((n_eq)=(^[Z0:$i, Z1:$i]:((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0)))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_46, c_0_47]), c_0_48]), c_0_45])).
% 253.42/36.95 thf(c_0_56, plain, ((lessf)=(^[Z0:$i, Z1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_49, c_0_47]), c_0_48]), c_0_45]), c_0_37])).
% 253.42/36.95 thf(c_0_57, plain, ![X523:$i]:(((in @ X523 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))=>(in @ (ordsucc @ X523) @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[suc_p]), c_0_40]), c_0_39]), c_0_43])).
% 253.42/36.95 thf(c_0_58, plain, ![X749:$i, X750:$i]:((((((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)))|(imp @ $true @ $true)|(($true)|~(imp @ $true @ $true)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)))))|~(epred1_2 @ X750 @ X749))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)))|(imp @ $true @ $false)|(($true)|~(imp @ $true @ $true)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)))))|~(epred1_2 @ X750 @ X749)))&((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)))|(imp @ $true @ $true)|(~($true)|~(imp @ $true @ $false)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)))))|~(epred1_2 @ X750 @ X749))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)))|(imp @ $true @ $false)|(~($true)|~(imp @ $true @ $false)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)))))|~(epred1_2 @ X750 @ X749))))&(((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)))|(imp @ $true @ $true)|(($true)|~(imp @ $false @ $true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)))))|~(epred1_2 @ X750 @ X749))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)))|(imp @ $true @ $false)|(($true)|~(imp @ $false @ $true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)))))|~(epred1_2 @ X750 @ X749)))&((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)))|(imp @ $true @ $true)|(~($true)|~(imp @ $false @ $false)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)))))|~(epred1_2 @ X750 @ X749))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)))|(imp @ $true @ $false)|(~($true)|~(imp @ $false @ $false)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)))))|~(epred1_2 @ X750 @ X749)))))&((((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)))|(imp @ $false @ $true)|(($true)|(imp @ $true @ $true)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)))))|~(epred1_2 @ X750 @ X749))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)))|(imp @ $false @ $false)|(($true)|(imp @ $true @ $true)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)))))|~(epred1_2 @ X750 @ X749)))&((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)))|(imp @ $false @ $true)|(~($true)|(imp @ $true @ $false)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)))))|~(epred1_2 @ X750 @ X749))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)))|(imp @ $false @ $false)|(~($true)|(imp @ $true @ $false)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)))))|~(epred1_2 @ X750 @ X749))))&(((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)))|(imp @ $false @ $true)|(($true)|(imp @ $false @ $true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)))))|~(epred1_2 @ X750 @ X749))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)))|(imp @ $false @ $false)|(($true)|(imp @ $false @ $true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)))))|~(epred1_2 @ X750 @ X749)))&((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)))|(imp @ $false @ $true)|(~($true)|(imp @ $false @ $false)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)))))|~(epred1_2 @ X750 @ X749))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)))|(imp @ $false @ $false)|(~($true)|(imp @ $false @ $false)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X749)))))|~(epred1_2 @ X750 @ X749))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])])])])).
% 253.42/36.95 thf(c_0_59, plain, ![X735:$i, X736:$i]:((((~(d_29_ii @ X735 @ X736)|(d_29_ii @ X735 @ X736)|(epred7_2 @ X736 @ X735)|~(in @ X736 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X735 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))&(((($true)|~($true)|(d_29_ii @ X735 @ X736)|(epred7_2 @ X736 @ X735)|~(in @ X736 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X735 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))&(~(imp @ $false @ $false)|~($true)|(d_29_ii @ X735 @ X736)|(epred7_2 @ X736 @ X735)|~(in @ X736 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X735 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))))&((($true)|~(imp @ $false @ $true)|(d_29_ii @ X735 @ X736)|(epred7_2 @ X736 @ X735)|~(in @ X736 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X735 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(d_29_ii @ X735 @ X736)|(epred7_2 @ X736 @ X735)|~(in @ X736 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X735 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))))))&((((~(d_29_ii @ X735 @ X736)|(($true)|~($true))|(epred7_2 @ X736 @ X735)|~(in @ X736 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X735 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))&(((($true)|~($true)|(($true)|~($true))|(epred7_2 @ X736 @ X735)|~(in @ X736 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X735 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))&(~(imp @ $false @ $false)|~($true)|(($true)|~($true))|(epred7_2 @ X736 @ X735)|~(in @ X736 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X735 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))))&((($true)|~(imp @ $false @ $true)|(($true)|~($true))|(epred7_2 @ X736 @ X735)|~(in @ X736 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X735 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(($true)|~($true))|(epred7_2 @ X736 @ X735)|~(in @ X736 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X735 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))))))&((~(d_29_ii @ X735 @ X736)|(~(imp @ $true @ $false)|~($true))|(epred7_2 @ X736 @ X735)|~(in @ X736 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X735 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))&(((($true)|~($true)|(~(imp @ $true @ $false)|~($true))|(epred7_2 @ X736 @ X735)|~(in @ X736 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X735 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))&(~(imp @ $false @ $false)|~($true)|(~(imp @ $true @ $false)|~($true))|(epred7_2 @ X736 @ X735)|~(in @ X736 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X735 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))))&((($true)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~($true))|(epred7_2 @ X736 @ X735)|~(in @ X736 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X735 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~($true))|(epred7_2 @ X736 @ X735)|~(in @ X736 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X735 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))))))&(((~(d_29_ii @ X735 @ X736)|(($true)|~(imp @ $true @ $true))|(epred7_2 @ X736 @ X735)|~(in @ X736 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X735 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))&(((($true)|~($true)|(($true)|~(imp @ $true @ $true))|(epred7_2 @ X736 @ X735)|~(in @ X736 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X735 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))&(~(imp @ $false @ $false)|~($true)|(($true)|~(imp @ $true @ $true))|(epred7_2 @ X736 @ X735)|~(in @ X736 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X735 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))))&((($true)|~(imp @ $false @ $true)|(($true)|~(imp @ $true @ $true))|(epred7_2 @ X736 @ X735)|~(in @ X736 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X735 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(($true)|~(imp @ $true @ $true))|(epred7_2 @ X736 @ X735)|~(in @ X736 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X735 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))))))&((~(d_29_ii @ X735 @ X736)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred7_2 @ X736 @ X735)|~(in @ X736 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X735 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))&(((($true)|~($true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred7_2 @ X736 @ X735)|~(in @ X736 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X735 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))&(~(imp @ $false @ $false)|~($true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred7_2 @ X736 @ X735)|~(in @ X736 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X735 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))))&((($true)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred7_2 @ X736 @ X735)|~(in @ X736 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X735 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred7_2 @ X736 @ X735)|~(in @ X736 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X735 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_51])])])])])).
% 253.42/36.95 thf(c_0_60, plain, ![X710:$i, X711:$i]:((~(in @ X710 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|(~(in @ X711 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|(n_is @ (ap @ (times @ X710) @ X711) @ (ap @ (times @ X711) @ X710))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])])])).
% 253.42/36.95 thf(c_0_61, plain, (in @ n_1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[n_1_p]), c_0_40]), c_0_39])).
% 253.42/36.95 thf(c_0_62, plain, ![X611:$i, X610:$i]:(((epred8_2 @ X610 @ X611)<=>((((((~(n_some @ (diffprop @ X610 @ X611))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ X610 @ X611))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ X611 @ X610)|~(imp @ $true @ $true))&((n_is @ X611 @ X610)|~(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ X610 @ X611))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ X610 @ X611))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ X611 @ X610)|~(imp @ $false @ $true))&((n_is @ X611 @ X610)|~(imp @ $false @ $false)))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&(((((~(n_some @ (diffprop @ X610 @ X611))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ X610 @ X611))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ X611 @ X610)|(imp @ $true @ $true))&((n_is @ X611 @ X610)|(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ X610 @ X611))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ X610 @ X611))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ X611 @ X610)|(imp @ $false @ $true))&((n_is @ X611 @ X610)|(imp @ $false @ $false)))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false))))))), introduced(definition)).
% 253.42/36.95 thf(c_0_63, axiom, ((frac)=(d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[def_frac, c_0_40]), c_0_53])).
% 253.42/36.95 thf(c_0_64, negated_conjecture, ~((all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X493:$i]:((in @ X493 @ frac))) @ (^[X494:$i]:((all_of @ (^[X4:$i]:((in @ X4 @ frac))) @ (^[X4:$i]:((((lesseq @ X1 @ X494))=>((((lessf @ X494 @ X4))=>((lessf @ X1 @ X4))))))))))))))), inference(assume_negation,[status(cth)],[satz51a])).
% 253.42/36.95 thf(c_0_65, plain, ((lesseq)=(^[Z0:$i, Z1:$i]:((imp @ (((imp @ (((((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)))))))) @ (~($true))))) @ (((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_54, c_0_36]), c_0_55]), c_0_56])).
% 253.42/36.95 thf(c_0_66, plain, ![X650:$i]:((~(in @ X650 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|(in @ (ordsucc @ X650) @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])])).
% 253.42/36.95 thf(c_0_67, plain, ![X1:$i, X4:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|(imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|~(($true))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)))))|~((epred1_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_58])).
% 253.42/36.95 thf(c_0_68, plain, ![X1:$i, X4:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|(imp @ (~($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~(($true))|~((epred1_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_58])).
% 253.42/36.95 thf(c_0_69, plain, ![X1:$i, X4:$i]:(((epred7_2 @ X1 @ X4)|~((imp @ (~($true)) @ (~($true))))|~(($true))|~((imp @ (($true)) @ (~($true))))|~(($true))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))|~((in @ X4 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))))), inference(split_conjunct,[status(thm)],[c_0_59])).
% 253.42/36.95 thf(c_0_70, plain, ![X599:$i]:(((in @ X599 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))=>![X598:$i]:(((in @ X598 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))=>![X597:$i]:(((in @ X597 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))=>((n_is @ (ap @ (times @ X599) @ X597) @ (ap @ (times @ X598) @ X597))=>(n_is @ X599 @ X598)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz33b]), c_0_40]), c_0_45]), c_0_43])).
% 253.42/36.95 thf(c_0_71, plain, ![X1:$i, X4:$i]:(((n_is @ (ap @ (times @ X1) @ X4) @ (ap @ (times @ X4) @ X1))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))|~((in @ X4 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))))), inference(split_conjunct,[status(thm)],[c_0_60])).
% 253.42/36.95 thf(c_0_72, plain, (in @ n_1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))), inference(split_conjunct,[status(thm)],[c_0_61])).
% 253.42/36.95 thf(c_0_73, plain, ((moref)=(^[Z0:$i, Z1:$i]:((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0)))))), inference(fof_simplification,[status(thm)],[def_moref])).
% 253.42/36.95 thf(c_0_74, plain, ![X611:$i]:(((in @ X611 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))=>![X610:$i]:(((in @ X610 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))=>((d_29_ii @ X611 @ X610)=>(epred8_2 @ X610 @ X611)))))), inference(apply_def,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz10g]), c_0_40]), c_0_34]), c_0_42]), c_0_43])]), c_0_62])).
% 253.42/36.95 thf(c_0_75, plain, ![X607:$i]:(((in @ X607 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))=>![X606:$i]:(((in @ X606 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))=>(((((~(n_some @ (diffprop @ X606 @ X607))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ X606 @ X607))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ X607 @ X606)|(imp @ $true @ $true))&((n_is @ X607 @ X606)|(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ X606 @ X607))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ X606 @ X607))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ X607 @ X606)|(imp @ $false @ $true))&((n_is @ X607 @ X606)|(imp @ $false @ $false)))))=>((~(d_29_ii @ X607 @ X606)|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((d_29_ii @ X607 @ X606)|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))))))), inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz10d]), c_0_40]), c_0_34]), c_0_42]), c_0_43])])).
% 253.42/36.95 thf(c_0_76, plain, ![X510:$i]:(((in @ X510 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))=>![X509:$i]:(((in @ X509 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))=>![X508:$i]:(((in @ X508 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))=>((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X509))))=>((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X508))))=>(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X508)))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz50]), c_0_63]), c_0_56]), c_0_43])).
% 253.42/36.95 thf(c_0_77, negated_conjecture, ~(![X503:$i]:(((in @ X503 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))=>![X502:$i]:(((in @ X502 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))=>![X501:$i]:(((in @ X501 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))=>((epred1_2 @ X503 @ X502)=>((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X501)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X501))))=>(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X501)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X501))))))))))))), inference(apply_def,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_64]), c_0_63]), c_0_65]), c_0_56]), c_0_43])]), c_0_41])).
% 253.42/36.95 thf(c_0_78, plain, ![X1:$i, X4:$i]:(((imp @ (~($true)) @ (($true)))|(imp @ (~($true)) @ (~($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~(($true))|~((epred1_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_58])).
% 253.42/36.95 thf(c_0_79, plain, ![X1:$i]:(((in @ (ordsucc @ X1) @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))))), inference(split_conjunct,[status(thm)],[c_0_66])).
% 253.42/36.95 thf(c_0_80, plain, ![X1:$i, X4:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|(imp @ (($true)) @ (~($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~(($true))|~((imp @ (~($true)) @ (~($true))))|~((epred1_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_58])).
% 253.42/36.95 thf(c_0_81, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|~((epred1_2 @ X1 @ X4))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4))))))), inference(cn,[status(thm)],[c_0_67])).
% 253.42/36.95 thf(c_0_82, plain, ![X1:$i, X4:$i]:(((imp @ (~($true)) @ (~($true)))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~((epred1_2 @ X1 @ X4)))), inference(cn,[status(thm)],[c_0_68])).
% 253.42/36.95 thf(c_0_83, plain, ![X609:$i, X608:$i]:(((epred7_2 @ X608 @ X609)=>((((~(n_some @ (diffprop @ X608 @ X609))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ X608 @ X609))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ X609 @ X608)|(imp @ $true @ $true))&((n_is @ X609 @ X608)|(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ X608 @ X609))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ X608 @ X609))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ X609 @ X608)|(imp @ $false @ $true))&((n_is @ X609 @ X608)|(imp @ $false @ $false))))))), inference(split_equiv,[status(thm)],[c_0_44])).
% 253.42/36.95 thf(c_0_84, plain, ![X4:$i, X1:$i]:(((epred7_2 @ X1 @ X4)|~((imp @ (($true)) @ (~($true))))|~((imp @ (~($true)) @ (~($true))))|~((in @ X4 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))))), inference(cn,[status(thm)],[c_0_69])).
% 253.42/36.95 thf(c_0_85, plain, ![X724:$i, X725:$i, X726:$i]:((~(in @ X724 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|(~(in @ X725 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|(~(in @ X726 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|(~(n_is @ (ap @ (times @ X724) @ X726) @ (ap @ (times @ X725) @ X726))|(n_is @ X724 @ X725)))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_70])])])])).
% 253.42/36.95 thf(c_0_86, plain, ![X4:$i, X1:$i]:(((n_is @ (ap @ (times @ X1) @ X4) @ (ap @ (times @ X4) @ X1))|~((in @ X4 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))))))), inference(cn,[status(thm)],[c_0_71])).
% 253.42/36.95 thf(c_0_87, plain, (in @ n_1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))), inference(cn,[status(thm)],[c_0_72])).
% 253.42/36.95 thf(c_0_88, plain, ((moref)=(^[Z0:$i, Z1:$i]:((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (second1 @ (d_Sep @ omega @ (^[Z2:$i]:(((Z2)!=(emptyset))))) @ Z0)))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_73, c_0_47]), c_0_48]), c_0_45])).
% 253.42/36.95 thf(c_0_89, plain, ![X517:$i, X518:$i]:(((epred4_2 @ X518 @ X517)<=>(((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517))))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517))))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)))|~(imp @ $true @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)))|~(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)))|~(imp @ $false @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)))|~(imp @ $false @ $false)))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false)))))), introduced(definition)).
% 253.42/36.95 thf(c_0_90, plain, ![X517:$i, X518:$i]:(((epred5_2 @ X518 @ X517)<=>(((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517))))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517))))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)))|(imp @ $true @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)))|(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)))|(imp @ $false @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)))|(imp @ $false @ $false)))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))), introduced(definition)).
% 253.42/36.95 thf(c_0_91, plain, ![X737:$i, X738:$i]:((~(in @ X737 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|(~(in @ X738 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|(~(d_29_ii @ X737 @ X738)|(epred8_2 @ X738 @ X737))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_74])])])])).
% 253.42/36.95 thf(c_0_92, plain, ![X733:$i, X734:$i]:((((((((((($true)|(imp @ $true @ $true)|~(d_29_ii @ X733 @ X734)|(~(n_some @ (diffprop @ X734 @ X733))|(n_some @ (diffprop @ X734 @ X733))|(~(n_some @ (diffprop @ X734 @ X733))|(n_some @ (diffprop @ X734 @ X733))))|~(in @ X734 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X733 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))&(~($true)|(imp @ $true @ $false)|~(d_29_ii @ X733 @ X734)|(~(n_some @ (diffprop @ X734 @ X733))|(n_some @ (diffprop @ X734 @ X733))|(~(n_some @ (diffprop @ X734 @ X733))|(n_some @ (diffprop @ X734 @ X733))))|~(in @ X734 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X733 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))))&((($true)|(imp @ $false @ $true)|(d_29_ii @ X733 @ X734)|(~(n_some @ (diffprop @ X734 @ X733))|(n_some @ (diffprop @ X734 @ X733))|(~(n_some @ (diffprop @ X734 @ X733))|(n_some @ (diffprop @ X734 @ X733))))|~(in @ X734 @ (d_Sep @ omega @ 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(^[Z0:$i]:(~(((Z0)=(emptyset)))))))))&((($true)|(imp @ $false @ $true)|(d_29_ii @ X733 @ X734)|(~(imp @ $false @ $false)|(n_is @ X733 @ X734)|(~(imp @ $true @ $false)|~(imp @ $true @ $true)))|~(in @ X734 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X733 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))&(~($true)|(imp @ $false @ $false)|(d_29_ii @ X733 @ X734)|(~(imp @ $false @ $false)|(n_is @ X733 @ X734)|(~(imp @ $true @ $false)|~(imp @ $true @ $true)))|~(in @ X734 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X733 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))))))&((((($true)|(imp @ $true @ $true)|~(d_29_ii @ X733 @ X734)|(~(n_is @ X733 @ X734)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true)))|~(in @ X734 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X733 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))&(~($true)|(imp @ $true @ $false)|~(d_29_ii @ X733 @ X734)|(~(n_is @ X733 @ X734)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true)))|~(in @ X734 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X733 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))))&((($true)|(imp @ $false @ $true)|(d_29_ii @ X733 @ X734)|(~(n_is @ X733 @ X734)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true)))|~(in @ X734 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X733 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))&(~($true)|(imp @ $false @ $false)|(d_29_ii @ X733 @ X734)|(~(n_is @ X733 @ X734)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true)))|~(in @ X734 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X733 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))))&(((($true)|(imp @ $true @ $true)|~(d_29_ii @ X733 @ X734)|(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true)))|~(in @ X734 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X733 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))&(~($true)|(imp @ $true @ $false)|~(d_29_ii @ X733 @ X734)|(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true)))|~(in @ X734 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X733 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))))&((($true)|(imp @ $false @ $true)|(d_29_ii @ X733 @ X734)|(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true)))|~(in @ X734 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X733 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))&(~($true)|(imp @ $false @ $false)|(d_29_ii @ X733 @ X734)|(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true)))|~(in @ X734 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))|~(in @ X733 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_75])])])])])).
% 253.42/36.96 thf(c_0_93, plain, ![X629:$i, X630:$i, X631:$i]:((~(in @ X629 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X630 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X631 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X630)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X629)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X629)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X630))))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X631)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X630)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X630)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X631))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X631)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X629)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X629)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X631)))))))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_76])])])])).
% 253.42/36.96 thf(c_0_94, negated_conjecture, ((in @ esk1_0 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))&((in @ esk2_0 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))&((in @ esk3_0 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))&((epred1_2 @ esk1_0 @ esk2_0)&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ esk2_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ esk3_0))))&~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ esk1_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ esk3_0))))))))), inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_77])])])])).
% 253.42/36.96 thf(c_0_95, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (($true)))|(imp @ (~($true)) @ (~($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~((epred1_2 @ X1 @ X4))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(cn,[status(thm)],[c_0_78])).
% 253.42/36.96 thf(c_0_96, plain, ![X1:$i]:(((in @ (ordsucc @ X1) @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))))))), inference(cn,[status(thm)],[c_0_79])).
% 253.42/36.96 thf(c_0_97, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~(($true))|~((imp @ (~($true)) @ (~($true))))|~((epred1_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_58])).
% 253.42/36.96 thf(c_0_98, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~((epred1_2 @ X1 @ X4))|~((imp @ (~($true)) @ (~($true)))))), inference(cn,[status(thm)],[c_0_80])).
% 253.42/36.96 thf(c_0_99, plain, ![X1:$i, X4:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)))|(imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)))))|~((epred1_2 @ X1 @ X4)))), inference(cn,[status(thm)],[c_0_81])).
% 253.42/36.96 thf(c_0_100, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1))))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)))|(imp @ (~($true)) @ (~($true)))|~((epred1_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_82])).
% 253.42/36.96 thf(c_0_101, plain, ![X761:$i, X762:$i]:((((((~(n_is @ X761 @ X762)|(imp @ $true @ $true)|(($true)|~(imp @ $true @ $true)|~(n_some @ (diffprop @ X762 @ X761)))|~(epred7_2 @ X762 @ X761))&((n_is @ X761 @ X762)|(imp @ $true @ $false)|(($true)|~(imp @ $true @ $true)|~(n_some @ (diffprop @ X762 @ X761)))|~(epred7_2 @ X762 @ X761)))&((~(n_is @ X761 @ X762)|(imp @ $true @ $true)|(~($true)|~(imp @ $true @ $false)|~(n_some @ (diffprop @ X762 @ X761)))|~(epred7_2 @ X762 @ X761))&((n_is @ X761 @ X762)|(imp @ $true @ $false)|(~($true)|~(imp @ $true @ $false)|~(n_some @ (diffprop @ X762 @ X761)))|~(epred7_2 @ X762 @ X761))))&(((~(n_is @ X761 @ X762)|(imp @ $true @ $true)|(($true)|~(imp @ $false @ $true)|(n_some @ (diffprop @ X762 @ X761)))|~(epred7_2 @ X762 @ X761))&((n_is @ X761 @ X762)|(imp @ $true @ $false)|(($true)|~(imp @ $false @ $true)|(n_some @ (diffprop @ X762 @ X761)))|~(epred7_2 @ X762 @ X761)))&((~(n_is @ X761 @ X762)|(imp @ $true @ $true)|(~($true)|~(imp @ $false @ $false)|(n_some @ (diffprop @ X762 @ X761)))|~(epred7_2 @ X762 @ X761))&((n_is @ X761 @ X762)|(imp @ $true @ $false)|(~($true)|~(imp @ $false @ $false)|(n_some @ (diffprop @ X762 @ X761)))|~(epred7_2 @ X762 @ X761)))))&((((~(n_is @ X761 @ X762)|(imp @ $false @ $true)|(($true)|(imp @ $true @ $true)|~(n_some @ (diffprop @ X762 @ X761)))|~(epred7_2 @ X762 @ X761))&((n_is @ X761 @ X762)|(imp @ $false @ $false)|(($true)|(imp @ $true @ $true)|~(n_some @ (diffprop @ X762 @ X761)))|~(epred7_2 @ X762 @ X761)))&((~(n_is @ X761 @ X762)|(imp @ $false @ $true)|(~($true)|(imp @ $true @ $false)|~(n_some @ (diffprop @ X762 @ X761)))|~(epred7_2 @ X762 @ X761))&((n_is @ X761 @ X762)|(imp @ $false @ $false)|(~($true)|(imp @ $true @ $false)|~(n_some @ (diffprop @ X762 @ X761)))|~(epred7_2 @ X762 @ X761))))&(((~(n_is @ X761 @ X762)|(imp @ $false @ $true)|(($true)|(imp @ $false @ $true)|(n_some @ (diffprop @ X762 @ X761)))|~(epred7_2 @ X762 @ X761))&((n_is @ X761 @ X762)|(imp @ $false @ $false)|(($true)|(imp @ $false @ $true)|(n_some @ (diffprop @ X762 @ X761)))|~(epred7_2 @ X762 @ X761)))&((~(n_is @ X761 @ X762)|(imp @ $false @ $true)|(~($true)|(imp @ $false @ $false)|(n_some @ (diffprop @ X762 @ X761)))|~(epred7_2 @ X762 @ X761))&((n_is @ X761 @ X762)|(imp @ $false @ $false)|(~($true)|(imp @ $false @ $false)|(n_some @ (diffprop @ X762 @ X761)))|~(epred7_2 @ X762 @ X761))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_83])])])])).
% 253.42/36.96 thf(c_0_102, plain, ![X4:$i, X1:$i]:(((epred7_2 @ X1 @ X4)|~((in @ X4 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((imp @ (($true)) @ (~($true))))|~((imp @ (~($true)) @ (~($true)))))), inference(cn,[status(thm)],[c_0_84])).
% 253.42/36.96 thf(c_0_103, plain, ![X1:$i, X4:$i, X5:$i]:(((n_is @ X1 @ X4)|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))|~((in @ X4 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))|~((in @ X5 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))|~((n_is @ (ap @ (times @ X1) @ X5) @ (ap @ (times @ X4) @ X5))))), inference(split_conjunct,[status(thm)],[c_0_85])).
% 253.42/36.96 thf(c_0_104, plain, ![X1:$i]:(((n_is @ (ap @ (times @ X1) @ n_1) @ (ap @ (times @ n_1) @ X1))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))))))), inference(spm,[status(thm)],[c_0_86, c_0_87])).
% 253.42/36.96 thf(c_0_105, plain, ![X518:$i]:(((in @ X518 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))=>![X517:$i]:(((in @ X517 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))=>(((epred4_2 @ X518 @ X517)&(epred5_2 @ X518 @ X517))=>(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz41k]), c_0_34]), c_0_88]), c_0_63]), c_0_65]), c_0_43])]), c_0_89]), c_0_90])).
% 253.42/36.96 thf(c_0_106, plain, ![X512:$i]:(((in @ X512 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))=>![X511:$i]:(((in @ X511 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))=>(((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X512)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X512)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X511))))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X512)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X512)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X511))))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X512)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X512)))|(imp @ $true @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X512)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X512)))|(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X512)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X512)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X511))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X512)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X512)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X511))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X512)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X512)))|(imp @ $false @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X512)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X512)))|(imp @ $false @ $false)))))=>((~(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X512)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X512)))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X512)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X512)))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))))))), inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz41d]), c_0_34]), c_0_88]), c_0_63]), c_0_65]), c_0_43])])).
% 253.42/36.96 thf(c_0_107, plain, ![X611:$i, X610:$i]:(((epred8_2 @ X610 @ X611)=>((((((~(n_some @ (diffprop @ X610 @ X611))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ X610 @ X611))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ X611 @ X610)|~(imp @ $true @ $true))&((n_is @ X611 @ X610)|~(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ X610 @ X611))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ X610 @ X611))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ X611 @ X610)|~(imp @ $false @ $true))&((n_is @ X611 @ X610)|~(imp @ $false @ $false)))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&(((((~(n_some @ (diffprop @ X610 @ X611))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ X610 @ X611))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ X611 @ X610)|(imp @ $true @ $true))&((n_is @ X611 @ X610)|(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ X610 @ X611))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ X610 @ X611))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ X611 @ X610)|(imp @ $false @ $true))&((n_is @ X611 @ X610)|(imp @ $false @ $false)))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false))))))), inference(split_equiv,[status(thm)],[c_0_62])).
% 253.42/36.96 thf(c_0_108, plain, ![X1:$i, X4:$i]:(((epred8_2 @ X4 @ X1)|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))|~((in @ X4 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))|~((d_29_ii @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_91])).
% 253.42/36.96 thf(c_0_109, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (~($true)))|(d_29_ii @ X1 @ X4)|(imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|~(($true))|~((n_is @ X1 @ X4))|~((imp @ (~($true)) @ (($true))))|~(($true))|~(($true))|~((in @ X4 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))))), inference(split_conjunct,[status(thm)],[c_0_92])).
% 253.42/36.96 thf(c_0_110, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|~(($true))|~((d_29_ii @ X1 @ X4))|~((n_is @ X1 @ X4))|~((imp @ (~($true)) @ (($true))))|~(($true))|~(($true))|~((in @ X4 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))))), inference(split_conjunct,[status(thm)],[c_0_92])).
% 253.42/36.96 thf(c_0_111, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (~($true)))|(d_29_ii @ X1 @ X4)|~(($true))|~((n_is @ X1 @ X4))|~((imp @ (~($true)) @ (($true))))|~((n_is @ X1 @ X4))|~((imp @ (($true)) @ (($true))))|~((in @ X4 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))))), inference(split_conjunct,[status(thm)],[c_0_92])).
% 253.42/36.96 thf(c_0_112, plain, ![X1:$i, X4:$i, X5:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X5)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X5))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X5 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X5)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X5))))))), inference(split_conjunct,[status(thm)],[c_0_93])).
% 253.42/36.96 thf(c_0_113, negated_conjecture, (n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ esk2_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ esk3_0)))), inference(split_conjunct,[status(thm)],[c_0_94])).
% 253.42/36.96 thf(c_0_114, negated_conjecture, (in @ esk3_0 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))), inference(split_conjunct,[status(thm)],[c_0_94])).
% 253.42/36.96 thf(c_0_115, negated_conjecture, (in @ esk2_0 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))), inference(split_conjunct,[status(thm)],[c_0_94])).
% 253.42/36.96 thf(c_0_116, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1))))|(imp @ (~($true)) @ (~($true)))|(imp @ (~($true)) @ (($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((epred1_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_95])).
% 253.42/36.96 thf(c_0_117, plain, ![X1:$i, X4:$i]:(((n_is @ (ap @ (times @ X1) @ (ordsucc @ X4)) @ (ap @ (times @ (ordsucc @ X4)) @ X1))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((in @ X4 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))))))), inference(spm,[status(thm)],[c_0_86, c_0_96])).
% 253.42/36.96 thf(c_0_118, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~((epred1_2 @ X1 @ X4))|~((imp @ (~($true)) @ (~($true))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(cn,[status(thm)],[c_0_97])).
% 253.42/36.96 thf(c_0_119, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1))))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)))|(imp @ (($true)) @ (~($true)))|~((imp @ (~($true)) @ (~($true))))|~((epred1_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_98])).
% 253.42/36.96 thf(c_0_120, plain, ![X1:$i, X4:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)))|(imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))|~((epred1_2 @ X1 @ X4)))), inference(csr,[status(thm)],[c_0_99, c_0_100])).
% 253.42/36.96 thf(c_0_121, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (($true)))|(n_some @ (diffprop @ X4 @ X1))|~((n_is @ X1 @ X4))|~(($true))|~((imp @ (~($true)) @ (~($true))))|~((epred7_2 @ X4 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_101])).
% 253.42/36.96 thf(c_0_122, plain, ![X1:$i]:(((epred7_2 @ X1 @ n_1)|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((imp @ (($true)) @ (~($true))))|~((imp @ (~($true)) @ (~($true)))))), inference(spm,[status(thm)],[c_0_102, c_0_87])).
% 253.42/36.96 thf(c_0_123, plain, ![X5:$i, X4:$i, X1:$i]:(((n_is @ X1 @ X4)|~((n_is @ (ap @ (times @ X1) @ X5) @ (ap @ (times @ X4) @ X5)))|~((in @ X5 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((in @ X4 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))))))), inference(cn,[status(thm)],[c_0_103])).
% 253.42/36.96 thf(c_0_124, plain, (n_is @ (ap @ (times @ n_1) @ n_1) @ (ap @ (times @ n_1) @ n_1)), inference(spm,[status(thm)],[c_0_104, c_0_87])).
% 253.42/36.96 thf(c_0_125, plain, ![X638:$i, X639:$i]:((~(in @ X638 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X639 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|(~(epred4_2 @ X638 @ X639)|~(epred5_2 @ X638 @ X639)|(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X638)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X639)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X639)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X638))))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_105])])])])).
% 253.42/36.96 thf(c_0_126, plain, ![X632:$i, X633:$i]:((((((((((($true)|(imp @ $true @ $true)|~(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X632)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X633)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X633)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X632)))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X633)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X632)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X632)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X633))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X633)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X632)) @ (ap @ (times @ (first1 @ (d_Sep @ 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X633)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X632)))|(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true)))|~(in @ X633 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X632 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_106])])])])])).
% 253.42/36.99 thf(c_0_127, plain, ![X602:$i]:(((in @ X602 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))=>![X601:$i]:(((in @ X601 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))=>((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X602)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X601)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X601)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X602)))=>(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X601)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X602)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X602)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X601)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz38]), c_0_55]), c_0_63]), c_0_43])).
% 253.42/36.99 thf(c_0_128, plain, ![X617:$i]:(((in @ X617 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))=>![X616:$i]:(((in @ X616 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))=>((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X616)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X617)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X617)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X616))))=>(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X616)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X617)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X617)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X616)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz43]), c_0_88]), c_0_63]), c_0_56]), c_0_43])).
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X764)|~(imp @ $true @ $true)|(~($true)|~(imp @ $true @ $false)|~(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763)))&((($true)|(imp @ $true @ $true)|((n_is @ X763 @ X764)|~(imp @ $true @ $false)|(~($true)|~(imp @ $true @ $false)|~(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $true @ $false)|((n_is @ X763 @ X764)|~(imp @ $true @ $false)|(~($true)|~(imp @ $true @ $false)|~(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763)))))&((((($true)|(imp @ $true @ $true)|(~(n_is @ X763 @ X764)|~(imp @ $true @ $true)|(($true)|~(imp @ $false @ $true)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $true @ $false)|(~(n_is @ X763 @ X764)|~(imp @ $true @ $true)|(($true)|~(imp @ $false @ $true)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763)))&((($true)|(imp @ $true @ $true)|((n_is @ X763 @ X764)|~(imp @ $true @ $false)|(($true)|~(imp @ $false @ $true)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $true @ $false)|((n_is @ X763 @ X764)|~(imp @ $true @ $false)|(($true)|~(imp @ $false @ $true)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))))&(((($true)|(imp @ $true @ $true)|(~(n_is @ X763 @ X764)|~(imp @ $true @ $true)|(~($true)|~(imp @ $false @ $false)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $true @ $false)|(~(n_is @ X763 @ X764)|~(imp @ $true @ $true)|(~($true)|~(imp @ $false @ $false)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763)))&((($true)|(imp @ $true @ $true)|((n_is @ X763 @ X764)|~(imp @ $true @ $false)|(~($true)|~(imp @ $false @ $false)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $true @ $false)|((n_is @ X763 @ X764)|~(imp @ $true @ $false)|(~($true)|~(imp @ $false @ $false)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))))))&(((((($true)|(imp @ $true @ $true)|(~(n_is @ X763 @ X764)|~(imp @ $false @ $true)|(($true)|(imp @ $true @ $true)|~(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $true @ $false)|(~(n_is @ X763 @ X764)|~(imp @ $false @ $true)|(($true)|(imp @ $true @ $true)|~(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763)))&((($true)|(imp @ $true @ $true)|((n_is @ X763 @ X764)|~(imp @ $false @ $false)|(($true)|(imp @ $true @ $true)|~(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $true @ $false)|((n_is @ X763 @ X764)|~(imp @ $false @ $false)|(($true)|(imp @ $true @ $true)|~(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))))&(((($true)|(imp @ $true @ $true)|(~(n_is @ X763 @ X764)|~(imp @ $false @ $true)|(~($true)|(imp @ $true @ $false)|~(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $true @ $false)|(~(n_is @ X763 @ X764)|~(imp @ $false @ $true)|(~($true)|(imp @ $true @ $false)|~(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763)))&((($true)|(imp @ $true @ $true)|((n_is @ X763 @ X764)|~(imp @ $false @ $false)|(~($true)|(imp @ $true @ $false)|~(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $true @ $false)|((n_is @ X763 @ X764)|~(imp @ $false @ $false)|(~($true)|(imp @ $true @ $false)|~(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763)))))&((((($true)|(imp @ $true @ $true)|(~(n_is @ X763 @ X764)|~(imp @ $false @ $true)|(($true)|(imp @ $false @ $true)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $true @ $false)|(~(n_is @ X763 @ X764)|~(imp @ $false @ $true)|(($true)|(imp @ $false @ $true)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763)))&((($true)|(imp @ $true @ $true)|((n_is @ X763 @ X764)|~(imp @ $false @ $false)|(($true)|(imp @ $false @ $true)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $true @ $false)|((n_is @ X763 @ X764)|~(imp @ $false @ $false)|(($true)|(imp @ $false @ $true)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))))&(((($true)|(imp @ $true @ $true)|(~(n_is @ X763 @ X764)|~(imp @ $false @ $true)|(~($true)|(imp @ $false @ $false)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $true @ $false)|(~(n_is @ X763 @ X764)|~(imp @ $false @ $true)|(~($true)|(imp @ $false @ $false)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763)))&((($true)|(imp @ $true @ $true)|((n_is @ X763 @ X764)|~(imp @ $false @ $false)|(~($true)|(imp @ $false @ $false)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $true @ $false)|((n_is @ X763 @ X764)|~(imp @ $false @ $false)|(~($true)|(imp @ $false @ $false)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763)))))))&((((((($true)|(imp @ $false @ $true)|(~(n_is @ X763 @ X764)|(imp @ $true @ $true)|(($true)|~(imp @ $true @ $true)|~(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $false @ $false)|(~(n_is @ X763 @ X764)|(imp @ $true @ $true)|(($true)|~(imp @ $true @ $true)|~(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763)))&((($true)|(imp @ $false @ $true)|((n_is @ X763 @ X764)|(imp @ $true @ $false)|(($true)|~(imp @ $true @ $true)|~(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $false @ $false)|((n_is @ X763 @ X764)|(imp @ $true @ $false)|(($true)|~(imp @ $true @ $true)|~(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))))&(((($true)|(imp @ $false @ $true)|(~(n_is @ X763 @ X764)|(imp @ $true @ $true)|(~($true)|~(imp @ $true @ $false)|~(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $false @ $false)|(~(n_is @ X763 @ X764)|(imp @ $true @ $true)|(~($true)|~(imp @ $true @ $false)|~(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763)))&((($true)|(imp @ $false @ $true)|((n_is @ X763 @ X764)|(imp @ $true @ $false)|(~($true)|~(imp @ $true @ $false)|~(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $false @ $false)|((n_is @ X763 @ X764)|(imp @ $true @ $false)|(~($true)|~(imp @ $true @ $false)|~(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763)))))&((((($true)|(imp @ $false @ $true)|(~(n_is @ X763 @ X764)|(imp @ $true @ $true)|(($true)|~(imp @ $false @ $true)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $false @ $false)|(~(n_is @ X763 @ X764)|(imp @ $true @ $true)|(($true)|~(imp @ $false @ $true)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763)))&((($true)|(imp @ $false @ $true)|((n_is @ X763 @ X764)|(imp @ $true @ $false)|(($true)|~(imp @ $false @ $true)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $false @ $false)|((n_is @ X763 @ X764)|(imp @ $true @ $false)|(($true)|~(imp @ $false @ $true)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))))&(((($true)|(imp @ $false @ $true)|(~(n_is @ X763 @ X764)|(imp @ $true @ $true)|(~($true)|~(imp @ $false @ $false)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $false @ $false)|(~(n_is @ X763 @ X764)|(imp @ $true @ $true)|(~($true)|~(imp @ $false @ $false)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763)))&((($true)|(imp @ $false @ $true)|((n_is @ X763 @ X764)|(imp @ $true @ $false)|(~($true)|~(imp @ $false @ $false)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $false @ $false)|((n_is @ X763 @ X764)|(imp @ $true @ $false)|(~($true)|~(imp @ $false @ $false)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))))))&(((((($true)|(imp @ $false @ $true)|(~(n_is @ X763 @ X764)|(imp @ $false @ $true)|(($true)|(imp @ $true @ $true)|~(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $false @ $false)|(~(n_is @ X763 @ X764)|(imp @ $false @ $true)|(($true)|(imp @ $true @ $true)|~(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763)))&((($true)|(imp @ $false @ $true)|((n_is @ X763 @ X764)|(imp @ $false @ $false)|(($true)|(imp @ $true @ $true)|~(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $false @ $false)|((n_is @ X763 @ X764)|(imp @ $false @ $false)|(($true)|(imp @ $true @ $true)|~(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))))&(((($true)|(imp @ $false @ $true)|(~(n_is @ X763 @ X764)|(imp @ $false @ $true)|(~($true)|(imp @ $true @ $false)|~(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $false @ $false)|(~(n_is @ X763 @ X764)|(imp @ $false @ $true)|(~($true)|(imp @ $true @ $false)|~(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763)))&((($true)|(imp @ $false @ $true)|((n_is @ X763 @ X764)|(imp @ $false @ $false)|(~($true)|(imp @ $true @ $false)|~(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $false @ $false)|((n_is @ X763 @ X764)|(imp @ $false @ $false)|(~($true)|(imp @ $true @ $false)|~(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763)))))&((((($true)|(imp @ $false @ $true)|(~(n_is @ X763 @ X764)|(imp @ $false @ $true)|(($true)|(imp @ $false @ $true)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $false @ $false)|(~(n_is @ X763 @ X764)|(imp @ $false @ $true)|(($true)|(imp @ $false @ $true)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763)))&((($true)|(imp @ $false @ $true)|((n_is @ X763 @ X764)|(imp @ $false @ $false)|(($true)|(imp @ $false @ $true)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $false @ $false)|((n_is @ X763 @ X764)|(imp @ $false @ $false)|(($true)|(imp @ $false @ $true)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))))&(((($true)|(imp @ $false @ $true)|(~(n_is @ X763 @ X764)|(imp @ $false @ $true)|(~($true)|(imp @ $false @ $false)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $false @ $false)|(~(n_is @ X763 @ X764)|(imp @ $false @ $true)|(~($true)|(imp @ $false @ $false)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763)))&((($true)|(imp @ $false @ $true)|((n_is @ X763 @ X764)|(imp @ $false @ $false)|(~($true)|(imp @ $false @ $false)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))&(~($true)|(imp @ $false @ $false)|((n_is @ X763 @ X764)|(imp @ $false @ $false)|(~($true)|(imp @ $false @ $false)|(n_some @ (diffprop @ X764 @ X763))))|~(epred8_2 @ X764 @ X763))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_107])])])])).
% 253.42/36.99 thf(c_0_130, plain, ![X4:$i, X1:$i]:(((epred8_2 @ X1 @ X4)|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((in @ X4 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((d_29_ii @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_108])).
% 253.42/36.99 thf(c_0_131, plain, ![X4:$i, X1:$i]:(((d_29_ii @ X1 @ X4)|(imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))|~((n_is @ X1 @ X4))|~((imp @ (~($true)) @ (($true))))|~((in @ X4 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))))), inference(cn,[status(thm)],[c_0_109])).
% 253.42/36.99 thf(c_0_132, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))|~((n_is @ X1 @ X4))|~((d_29_ii @ X1 @ X4))|~((imp @ (~($true)) @ (($true))))|~((in @ X4 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))))), inference(cn,[status(thm)],[c_0_110])).
% 253.42/36.99 thf(c_0_133, plain, ![X4:$i, X1:$i]:(((d_29_ii @ X1 @ X4)|(imp @ (~($true)) @ (~($true)))|~((n_is @ X1 @ X4))|~((imp @ (($true)) @ (($true))))|~((imp @ (~($true)) @ (($true))))|~((in @ X4 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset))))))))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))))))), inference(cn,[status(thm)],[c_0_111])).
% 253.42/36.99 thf(c_0_134, plain, ![X1:$i, X5:$i, X4:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X5)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X5)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X5)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X5)))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X5 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[c_0_112])).
% 253.42/36.99 thf(c_0_135, negated_conjecture, (n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)))), inference(cn,[status(thm)],[c_0_113])).
% 253.42/36.99 thf(c_0_136, negated_conjecture, (in @ esk3_0 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset)))))))), inference(cn,[status(thm)],[c_0_114])).
% 253.42/36.99 thf(c_0_137, negated_conjecture, (in @ esk2_0 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset)))))))), inference(cn,[status(thm)],[c_0_115])).
% 253.42/36.99 thf(c_0_138, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1))))|(imp @ (~($true)) @ (($true)))|(imp @ (~($true)) @ (~($true)))|~((epred1_2 @ X4 @ X1)))), inference(csr,[status(thm)],[c_0_116, c_0_100])).
% 253.42/36.99 thf(c_0_139, negated_conjecture, (epred1_2 @ esk1_0 @ esk2_0), inference(split_conjunct,[status(thm)],[c_0_94])).
% 253.42/36.99 thf(c_0_140, negated_conjecture, (in @ esk1_0 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))), inference(split_conjunct,[status(thm)],[c_0_94])).
% 253.42/36.99 thf(c_0_141, negated_conjecture, ~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ esk1_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ esk3_0))))), inference(split_conjunct,[status(thm)],[c_0_94])).
% 253.42/36.99 thf(c_0_142, plain, ![X4:$i, X1:$i]:(((n_is @ (ap @ (times @ (ordsucc @ X1)) @ (ordsucc @ X4)) @ (ap @ (times @ (ordsucc @ X4)) @ (ordsucc @ X1)))|~((in @ X4 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))))))), inference(spm,[status(thm)],[c_0_117, c_0_96])).
% 253.42/36.99 thf(c_0_143, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1))))|(imp @ (($true)) @ (($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((imp @ (~($true)) @ (~($true))))|~((epred1_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_118])).
% 253.42/36.99 thf(c_0_144, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1))))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)))|(imp @ (($true)) @ (~($true)))|~((epred1_2 @ X4 @ X1)))), inference(csr,[status(thm)],[c_0_119, c_0_120])).
% 253.42/36.99 thf(c_0_145, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (($true)))|~((n_is @ X1 @ X4))|~(($true))|~((imp @ (($true)) @ (~($true))))|~((n_some @ (diffprop @ X4 @ X1)))|~((epred7_2 @ X4 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_101])).
% 253.42/36.99 thf(c_0_146, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ X4 @ X1))|(imp @ (($true)) @ (($true)))|~((n_is @ X1 @ X4))|~((epred7_2 @ X4 @ X1))|~((imp @ (~($true)) @ (~($true)))))), inference(cn,[status(thm)],[c_0_121])).
% 253.42/36.99 thf(c_0_147, plain, ((epred7_2 @ n_1 @ n_1)|~((imp @ (($true)) @ (~($true))))|~((imp @ (~($true)) @ (~($true))))), inference(spm,[status(thm)],[c_0_122, c_0_87])).
% 253.42/36.99 thf(c_0_148, plain, (n_is @ n_1 @ n_1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123, c_0_124]), c_0_87])])).
% 253.42/36.99 thf(c_0_149, plain, ![X615:$i]:(((in @ X615 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))=>![X614:$i]:(((in @ X614 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))=>((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X615)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X614)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X614)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X615)))=>(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X615)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X614)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X614)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X615))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz42]), c_0_88]), c_0_63]), c_0_56]), c_0_43])).
% 253.42/36.99 thf(c_0_150, plain, ![X1:$i, X4:$i]:(((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))|~((epred4_2 @ X1 @ X4))|~((epred5_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_125])).
% 253.42/36.99 thf(c_0_151, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (~($true)))|(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|~(($true))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((imp @ (~($true)) @ (($true))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((imp @ (($true)) @ (($true))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))))), inference(split_conjunct,[status(thm)],[c_0_126])).
% 253.42/36.99 thf(c_0_152, plain, ![X728:$i, X729:$i]:((~(in @ X728 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X729 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|(~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X728)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X729)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X729)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X728)))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X729)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X728)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X728)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X729))))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_127])])])])).
% 253.42/36.99 thf(c_0_153, plain, ![X600:$i]:(((in @ X600 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))=>(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X600)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X600)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X600)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X600))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz37]), c_0_55]), c_0_63]), c_0_43])).
% 253.42/36.99 thf(c_0_154, plain, ![X743:$i, X744:$i]:((~(in @ X743 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X744 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X744)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X743)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X743)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X744))))|(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X744)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X743)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X743)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X744))))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_128])])])])).
% 253.42/36.99 thf(c_0_155, plain, ![X513:$i, X514:$i]:(((epred2_2 @ X514 @ X513)<=>((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513))))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513))))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)))|(imp @ $true @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)))|(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)))|(imp @ $false @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)))|(imp @ $false @ $false))))))), introduced(definition)).
% 253.42/36.99 thf(c_0_156, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (~($true)))|(n_is @ X1 @ X4)|(imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|~(($true))|~(($true))|~((n_some @ (diffprop @ X4 @ X1)))|~((epred8_2 @ X4 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_129])).
% 253.42/36.99 thf(c_0_157, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (~($true)))|(n_is @ X1 @ X4)|(imp @ (~($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))|(n_some @ (diffprop @ X4 @ X1))|~(($true))|~(($true))|~((epred8_2 @ X4 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_129])).
% 253.42/36.99 thf(c_0_158, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (~($true)))|(imp @ (~($true)) @ (($true)))|(imp @ (~($true)) @ (~($true)))|(n_some @ (diffprop @ X4 @ X1))|~(($true))|~((n_is @ X1 @ X4))|~(($true))|~((epred8_2 @ X4 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_129])).
% 253.42/36.99 thf(c_0_159, plain, ![X4:$i, X1:$i]:(((epred8_2 @ (ordsucc @ X1) @ X4)|~((in @ X4 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((d_29_ii @ X4 @ (ordsucc @ X1))))), inference(spm,[status(thm)],[c_0_130, c_0_96])).
% 253.42/36.99 thf(c_0_160, plain, ![X1:$i, X4:$i]:(((imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|(d_29_ii @ X1 @ X4)|~((in @ X4 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((imp @ (~($true)) @ (($true))))|~((n_is @ X1 @ X4)))), inference(cn,[status(thm)],[c_0_131])).
% 253.42/36.99 thf(c_0_161, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((in @ X4 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((imp @ (~($true)) @ (($true))))|~((n_is @ X4 @ X1))|~((d_29_ii @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_132])).
% 253.42/36.99 thf(c_0_162, plain, ![X1:$i, X4:$i]:(((imp @ (~($true)) @ (~($true)))|(d_29_ii @ X1 @ X4)|~((in @ X4 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((imp @ (($true)) @ (($true))))|~((imp @ (~($true)) @ (($true))))|~((n_is @ X1 @ X4)))), inference(cn,[status(thm)],[c_0_133])).
% 253.42/36.99 thf(c_0_163, negated_conjecture, ![X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134, c_0_135]), c_0_136]), c_0_137])])).
% 253.42/36.99 thf(c_0_164, negated_conjecture, ((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0))))|(imp @ (~($true)) @ (~($true)))|(imp @ (~($true)) @ (($true)))), inference(spm,[status(thm)],[c_0_138, c_0_139])).
% 253.42/36.99 thf(c_0_165, negated_conjecture, (in @ esk1_0 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset)))))))), inference(cn,[status(thm)],[c_0_140])).
% 253.42/36.99 thf(c_0_166, negated_conjecture, ~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0))))), inference(cn,[status(thm)],[c_0_141])).
% 253.42/36.99 thf(c_0_167, plain, ![X1:$i]:(((n_is @ (ap @ (times @ (ordsucc @ X1)) @ (ordsucc @ n_1)) @ (ap @ (times @ (ordsucc @ n_1)) @ (ordsucc @ X1)))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))))))), inference(spm,[status(thm)],[c_0_142, c_0_87])).
% 253.42/36.99 thf(c_0_168, negated_conjecture, ((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0))))|(imp @ (($true)) @ (($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0))))|~((imp @ (~($true)) @ (~($true))))), inference(spm,[status(thm)],[c_0_143, c_0_139])).
% 253.42/36.99 thf(c_0_169, negated_conjecture, ((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0))))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)))|(imp @ (($true)) @ (~($true)))), inference(spm,[status(thm)],[c_0_144, c_0_139])).
% 253.42/36.99 thf(c_0_170, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (($true)))|~((n_is @ X1 @ X4))|~((epred7_2 @ X4 @ X1))|~((n_some @ (diffprop @ X4 @ X1)))|~((imp @ (($true)) @ (~($true)))))), inference(cn,[status(thm)],[c_0_145])).
% 253.42/36.99 thf(c_0_171, plain, ((n_some @ (diffprop @ n_1 @ n_1))|(imp @ (($true)) @ (($true)))|~((imp @ (~($true)) @ (~($true))))|~((imp @ (($true)) @ (~($true))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146, c_0_147]), c_0_148])])).
% 253.42/36.99 thf(c_0_172, plain, ![X741:$i, X742:$i]:((~(in @ X741 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X742 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|(~(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X741)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X742)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X742)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X741)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X741)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X742)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X742)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X741)))))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_149])])])])).
% 253.42/36.99 thf(c_0_173, plain, ![X1:$i, X4:$i]:(((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset)))))))))|~((epred4_2 @ X1 @ X4))|~((epred5_2 @ X1 @ X4)))), inference(cn,[status(thm)],[c_0_150])).
% 253.42/36.99 thf(c_0_174, plain, ![X517:$i, X518:$i]:(((((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517))))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517))))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)))|(imp @ $true @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)))|(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)))|(imp @ $false @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)))|(imp @ $false @ $false)))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false))))=>(epred5_2 @ X518 @ X517))), inference(split_equiv,[status(thm)],[c_0_90])).
% 253.42/36.99 thf(c_0_175, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (~($true)))|(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|~((imp @ (($true)) @ (($true))))|~((imp @ (~($true)) @ (($true))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(cn,[status(thm)],[c_0_151])).
% 253.42/36.99 thf(c_0_176, plain, ![X4:$i, X1:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(split_conjunct,[status(thm)],[c_0_152])).
% 253.42/36.99 thf(c_0_177, negated_conjecture, ((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0))))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)))|(imp @ (~($true)) @ (~($true)))), inference(spm,[status(thm)],[c_0_100, c_0_139])).
% 253.42/36.99 thf(c_0_178, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (~($true)))|(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|(imp @ (~($true)) @ (~($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~(($true))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((imp @ (~($true)) @ (($true))))|~(($true))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))))), inference(split_conjunct,[status(thm)],[c_0_126])).
% 253.42/36.99 thf(c_0_179, plain, ![X727:$i]:((~(in @ X727 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X727)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X727)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X727)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X727))))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_153])])])).
% 253.42/36.99 thf(c_0_180, plain, ![X1:$i, X4:$i]:(((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4))))))), inference(split_conjunct,[status(thm)],[c_0_154])).
% 253.42/36.99 thf(c_0_181, plain, ![X514:$i]:(((in @ X514 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))=>![X513:$i]:(((in @ X513 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))=>(((~(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))=>(epred2_2 @ X514 @ X513)))))), inference(apply_def,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz41e]), c_0_34]), c_0_88]), c_0_63]), c_0_65]), c_0_43])]), c_0_155])).
% 253.42/36.99 thf(c_0_182, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (~($true)))|(imp @ (~($true)) @ (($true)))|(imp @ (($true)) @ (~($true)))|~(($true))|~((n_is @ X1 @ X4))|~(($true))|~((n_some @ (diffprop @ X4 @ X1)))|~((epred8_2 @ X4 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_129])).
% 253.42/36.99 thf(c_0_183, plain, ![X4:$i, X1:$i]:(((n_is @ X1 @ X4)|(imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))|~((epred8_2 @ X4 @ X1))|~((n_some @ (diffprop @ X4 @ X1))))), inference(cn,[status(thm)],[c_0_156])).
% 253.42/36.99 thf(c_0_184, plain, ![X4:$i, X1:$i]:(((n_is @ X1 @ X4)|(n_some @ (diffprop @ X4 @ X1))|(imp @ (~($true)) @ (~($true)))|~((epred8_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_157])).
% 253.42/36.99 thf(c_0_185, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ X4 @ X1))|(imp @ (~($true)) @ (($true)))|(imp @ (~($true)) @ (~($true)))|~((n_is @ X1 @ X4))|~((epred8_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_158])).
% 253.42/36.99 thf(c_0_186, plain, ![X4:$i, X1:$i]:(((epred8_2 @ (ordsucc @ X1) @ (ordsucc @ X4))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((in @ X4 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((d_29_ii @ (ordsucc @ X4) @ (ordsucc @ X1))))), inference(spm,[status(thm)],[c_0_159, c_0_96])).
% 253.42/36.99 thf(c_0_187, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((in @ X4 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((imp @ (~($true)) @ (($true))))|~((n_is @ X4 @ X1)))), inference(csr,[status(thm)],[c_0_160, c_0_161])).
% 253.42/36.99 thf(c_0_188, plain, ![X1:$i, X4:$i]:(((d_29_ii @ X1 @ (ordsucc @ X4))|(imp @ (~($true)) @ (~($true)))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((in @ X4 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((imp @ (($true)) @ (($true))))|~((imp @ (~($true)) @ (($true))))|~((n_is @ X1 @ (ordsucc @ X4))))), inference(spm,[status(thm)],[c_0_162, c_0_96])).
% 253.42/36.99 thf(c_0_189, negated_conjecture, ((imp @ (~($true)) @ (($true)))|(imp @ (~($true)) @ (~($true)))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163, c_0_164]), c_0_165])]), c_0_166])).
% 253.42/36.99 thf(c_0_190, plain, (n_is @ (ap @ (times @ (ordsucc @ n_1)) @ (ordsucc @ n_1)) @ (ap @ (times @ (ordsucc @ n_1)) @ (ordsucc @ n_1))), inference(spm,[status(thm)],[c_0_167, c_0_87])).
% 253.42/36.99 thf(c_0_191, negated_conjecture, ((imp @ (($true)) @ (($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0))))|~((imp @ (~($true)) @ (~($true))))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163, c_0_168]), c_0_165])]), c_0_166])).
% 253.42/36.99 thf(c_0_192, negated_conjecture, ((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)))|(imp @ (($true)) @ (~($true)))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163, c_0_169]), c_0_165])]), c_0_166])).
% 253.42/36.99 thf(c_0_193, plain, ((imp @ (($true)) @ (($true)))|~((imp @ (($true)) @ (~($true))))|~((imp @ (~($true)) @ (~($true))))), inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170, c_0_147]), c_0_148])]), c_0_171])).
% 253.42/36.99 thf(c_0_194, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(split_conjunct,[status(thm)],[c_0_172])).
% 253.42/36.99 thf(c_0_195, negated_conjecture, ![X1:$i]:(((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset)))))))))|~((epred4_2 @ X1 @ esk1_0))|~((epred5_2 @ X1 @ esk1_0)))), inference(spm,[status(thm)],[c_0_173, c_0_165])).
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(^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X757))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X757)))))|(epred5_2 @ X758 @ X757))&(((($true)|~($true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X757))))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ 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$true)|(($true)|~($true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred5_2 @ X758 @ X757)))))&((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X757))))|(~(imp @ $true @ $false)|~($true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))&(((($true)|~($true)|(~(imp @ $true @ $false)|~($true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))&(~(imp @ $false @ $false)|~($true)|(~(imp @ $true @ $false)|~($true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred5_2 @ X758 @ X757)))&((($true)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~($true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~($true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X757))))|(($true)|~(imp @ $true @ $true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))&(((($true)|~($true)|(($true)|~(imp @ $true @ $true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))&(~(imp @ $false @ $false)|~($true)|(($true)|~(imp @ $true @ $true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred5_2 @ X758 @ X757)))&((($true)|~(imp @ $false @ $true)|(($true)|~(imp @ $true @ $true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(($true)|~(imp @ $true @ $true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred5_2 @ X758 @ X757)))))&((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X757))))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))&(((($true)|~($true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))&(~(imp @ $false @ $false)|~($true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred5_2 @ X758 @ X757)))&((($true)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))))))))&(((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X758)))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X758)))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))&(~(imp @ $false @ $false)|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X758)))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred5_2 @ X758 @ X757)))&((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X758)))|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))))))))&(((($true)|~($true)|(epred5_2 @ X758 @ X757))&(~(imp @ $false @ $false)|~($true)|(epred5_2 @ X758 @ X757)))&((($true)|~(imp @ $false @ $true)|(epred5_2 @ X758 @ X757))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(epred5_2 @ X758 @ X757)))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_174])])])])).
% 253.42/37.00 thf(c_0_197, plain, ![X517:$i, X518:$i]:(((((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517))))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517))))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)))|~(imp @ $true @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)))|~(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)))|~(imp @ $false @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X518)))|~(imp @ $false @ $false)))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))=>(epred4_2 @ X518 @ X517))), inference(split_equiv,[status(thm)],[c_0_89])).
% 253.42/37.00 thf(c_0_198, plain, ![X4:$i, X1:$i]:(((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)))|(imp @ (~($true)) @ (~($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (($true)) @ (($true))))|~((imp @ (~($true)) @ (($true)))))), inference(cn,[status(thm)],[c_0_175])).
% 253.42/37.00 thf(c_0_199, plain, ![X1:$i, X4:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[c_0_176])).
% 253.42/37.00 thf(c_0_200, negated_conjecture, ((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)))|(imp @ (~($true)) @ (~($true)))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163, c_0_177]), c_0_165])]), c_0_166])).
% 253.42/37.00 thf(c_0_201, plain, ![X513:$i, X514:$i]:(((epred2_2 @ X514 @ X513)=>((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513))))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513))))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)))|(imp @ $true @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)))|(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)))|(imp @ $false @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X513)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X514)))|(imp @ $false @ $false))))))), inference(split_equiv,[status(thm)],[c_0_155])).
% 253.42/37.00 thf(c_0_202, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (~($true)))|(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~((imp @ (~($true)) @ (($true))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(cn,[status(thm)],[c_0_178])).
% 253.42/37.00 thf(c_0_203, plain, ![X1:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))))), inference(split_conjunct,[status(thm)],[c_0_179])).
% 253.42/37.00 thf(c_0_204, plain, ![X1:$i, X4:$i]:(((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[c_0_180])).
% 253.42/37.00 thf(c_0_205, plain, ![X634:$i, X635:$i]:((((~(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X634)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X635)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X635)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X634)))|(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X634)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X635)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X635)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X634)))|(epred2_2 @ X634 @ X635)|~(in @ X635 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X634 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))&(((($true)|~($true)|(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X634)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X635)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X635)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X634)))|(epred2_2 @ X634 @ X635)|~(in @ X635 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X634 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))&(~(imp @ $false @ $false)|~($true)|(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X634)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X635)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X635)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X634)))|(epred2_2 @ X634 @ X635)|~(in @ X635 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X634 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))))&((($true)|~(imp @ $false @ $true)|(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X634)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X635)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X635)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X634)))|(epred2_2 @ X634 @ X635)|~(in @ X635 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X634 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X634)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X635)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X635)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X634)))|(epred2_2 @ X634 @ X635)|~(in @ X635 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X634 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))))))&((((~(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X634)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X635)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X635)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X634)))|(($true)|~($true))|(epred2_2 @ X634 @ X635)|~(in @ X635 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X634 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))&(((($true)|~($true)|(($true)|~($true))|(epred2_2 @ X634 @ X635)|~(in @ X635 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X634 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))&(~(imp @ $false @ $false)|~($true)|(($true)|~($true))|(epred2_2 @ X634 @ X635)|~(in @ X635 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X634 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))))&((($true)|~(imp @ $false @ $true)|(($true)|~($true))|(epred2_2 @ X634 @ X635)|~(in @ X635 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X634 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(($true)|~($true))|(epred2_2 @ X634 @ X635)|~(in @ X635 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X634 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))))))&((~(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X634)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X635)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X635)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X634)))|(~(imp @ $true @ $false)|~($true))|(epred2_2 @ X634 @ X635)|~(in @ X635 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X634 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))&(((($true)|~($true)|(~(imp @ $true @ $false)|~($true))|(epred2_2 @ X634 @ X635)|~(in @ X635 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X634 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))&(~(imp @ $false @ $false)|~($true)|(~(imp @ $true @ $false)|~($true))|(epred2_2 @ X634 @ X635)|~(in @ X635 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X634 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))))&((($true)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~($true))|(epred2_2 @ X634 @ X635)|~(in @ X635 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X634 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~($true))|(epred2_2 @ X634 @ X635)|~(in @ X635 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X634 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))))))&(((~(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X634)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X635)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X635)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X634)))|(($true)|~(imp @ $true @ $true))|(epred2_2 @ X634 @ X635)|~(in @ X635 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X634 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))&(((($true)|~($true)|(($true)|~(imp @ $true @ $true))|(epred2_2 @ X634 @ X635)|~(in @ X635 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X634 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))&(~(imp @ $false @ $false)|~($true)|(($true)|~(imp @ $true @ $true))|(epred2_2 @ X634 @ X635)|~(in @ X635 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X634 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))))&((($true)|~(imp @ $false @ $true)|(($true)|~(imp @ $true @ $true))|(epred2_2 @ X634 @ X635)|~(in @ X635 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X634 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(($true)|~(imp @ $true @ $true))|(epred2_2 @ X634 @ X635)|~(in @ X635 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X634 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))))))&((~(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X634)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X635)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X635)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X634)))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred2_2 @ X634 @ X635)|~(in @ X635 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X634 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))&(((($true)|~($true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred2_2 @ X634 @ X635)|~(in @ X635 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X634 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))&(~(imp @ $false @ $false)|~($true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred2_2 @ X634 @ X635)|~(in @ X635 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X634 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))))&((($true)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred2_2 @ X634 @ X635)|~(in @ X635 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X634 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred2_2 @ X634 @ X635)|~(in @ X635 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X634 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_181])])])])])).
% 253.42/37.00 thf(c_0_206, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (($true)))|(imp @ (~($true)) @ (~($true)))|~((n_is @ X1 @ X4))|~((epred8_2 @ X4 @ X1))|~((n_some @ (diffprop @ X4 @ X1))))), inference(cn,[status(thm)],[c_0_182])).
% 253.42/37.00 thf(c_0_207, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|(n_is @ X1 @ X4)|~((epred8_2 @ X4 @ X1)))), inference(csr,[status(thm)],[c_0_183, c_0_184])).
% 253.42/37.00 thf(c_0_208, plain, ![X1:$i, X4:$i]:(((imp @ (~($true)) @ (~($true)))|(imp @ (~($true)) @ (($true)))|(n_some @ (diffprop @ X1 @ X4))|~((epred8_2 @ X1 @ X4)))), inference(csr,[status(thm)],[c_0_185, c_0_184])).
% 253.42/37.00 thf(c_0_209, plain, ![X1:$i]:(((epred8_2 @ (ordsucc @ n_1) @ (ordsucc @ X1))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((d_29_ii @ (ordsucc @ X1) @ (ordsucc @ n_1))))), inference(spm,[status(thm)],[c_0_186, c_0_87])).
% 253.42/37.00 thf(c_0_210, plain, ![X1:$i]:(((imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((imp @ (~($true)) @ (($true))))|~((n_is @ X1 @ n_1)))), inference(spm,[status(thm)],[c_0_187, c_0_87])).
% 253.42/37.00 thf(c_0_211, plain, ![X1:$i, X4:$i]:(((d_29_ii @ (ordsucc @ X1) @ (ordsucc @ X4))|(imp @ (~($true)) @ (~($true)))|~((in @ X4 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((n_is @ (ordsucc @ X1) @ (ordsucc @ X4)))|~((imp @ (($true)) @ (($true)))))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_188, c_0_96]), c_0_189])).
% 253.42/37.00 thf(c_0_212, plain, ((n_is @ (ordsucc @ n_1) @ (ordsucc @ n_1))|~((in @ (ordsucc @ n_1) @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))), inference(spm,[status(thm)],[c_0_123, c_0_190])).
% 253.42/37.00 thf(c_0_213, negated_conjecture, ((imp @ (($true)) @ (($true)))|~((imp @ (~($true)) @ (~($true))))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_191, c_0_192]), c_0_193])).
% 253.42/37.00 thf(c_0_214, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[c_0_194])).
% 253.42/37.00 thf(c_0_215, negated_conjecture, ((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)))|~((epred4_2 @ esk3_0 @ esk1_0))|~((epred5_2 @ esk3_0 @ esk1_0))), inference(spm,[status(thm)],[c_0_195, c_0_136])).
% 253.42/37.00 thf(c_0_216, plain, ![X1:$i, X4:$i]:(((epred5_2 @ X1 @ X4)|~((imp @ (~($true)) @ (~($true))))|~(($true)))), inference(split_conjunct,[status(thm)],[c_0_196])).
% 253.42/37.00 thf(c_0_217, plain, ![X755:$i, X756:$i]:(((((((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X755))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X755))))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X755))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X755)))))|(epred4_2 @ X756 @ X755))&(((($true)|~($true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X755))))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ 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$true @ $true))|(epred4_2 @ X756 @ X755))))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X755))))|(($true)|~(imp @ $true @ $true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred4_2 @ X756 @ X755))&(((($true)|~($true)|(($true)|~(imp @ $true @ $true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred4_2 @ X756 @ X755))&(~(imp @ $false @ $false)|~($true)|(($true)|~(imp @ $true @ $true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred4_2 @ X756 @ X755)))&((($true)|~(imp @ $false @ $true)|(($true)|~(imp @ $true @ $true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred4_2 @ X756 @ X755))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(($true)|~(imp @ $true @ $true))|((imp @ 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X755))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred4_2 @ X756 @ X755))))))))&(((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X756)))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X756)))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred4_2 @ X756 @ X755))&((imp @ $false @ $false)|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X756)))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred4_2 @ X756 @ X755)))&((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X756)))|(imp @ $false @ $true)|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred4_2 @ X756 @ X755))&((imp @ $false @ $false)|(imp @ $false @ $true)|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred4_2 @ X756 @ X755))))))))&(((($true)|~($true)|(epred4_2 @ X756 @ X755))&(~(imp @ $true @ $false)|~($true)|(epred4_2 @ X756 @ X755)))&((($true)|~(imp @ $true @ $true)|(epred4_2 @ X756 @ X755))&(~(imp @ $true @ $false)|~(imp @ $true @ $true)|(epred4_2 @ X756 @ X755)))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_197])])])])).
% 253.42/37.00 thf(c_0_218, negated_conjecture, ![X1:$i]:(((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)))|(imp @ (~($true)) @ (~($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (($true)) @ (($true))))|~((imp @ (~($true)) @ (($true)))))), inference(spm,[status(thm)],[c_0_198, c_0_165])).
% 253.42/37.00 thf(c_0_219, negated_conjecture, ((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)))|(imp @ (~($true)) @ (~($true)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199, c_0_200]), c_0_137]), c_0_165])])).
% 253.42/37.00 thf(c_0_220, plain, ![X751:$i, X752:$i]:((((((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $true @ $true)|(($true)|~(imp @ $true @ $true)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $true @ $false)|(($true)|~(imp @ $true @ $true)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751)))&((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $true @ $true)|(~($true)|~(imp @ $true @ $false)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $true @ $false)|(~($true)|~(imp @ $true @ $false)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751))))&(((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $true @ $true)|(($true)|~(imp @ $false @ $true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $true @ $false)|(($true)|~(imp @ $false @ $true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751)))&((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $true @ $true)|(~($true)|~(imp @ $false @ $false)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $true @ $false)|(~($true)|~(imp @ $false @ $false)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751)))))&((((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $false @ $true)|(($true)|(imp @ $true @ $true)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $false @ $false)|(($true)|(imp @ $true @ $true)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751)))&((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $false @ $true)|(~($true)|(imp @ $true @ $false)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $false @ $false)|(~($true)|(imp @ $true @ $false)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751))))&(((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $false @ $true)|(($true)|(imp @ $false @ $true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $false @ $false)|(($true)|(imp @ $false @ $true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751)))&((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $false @ $true)|(~($true)|(imp @ $false @ $false)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $false @ $false)|(~($true)|(imp @ $false @ $false)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_201])])])])).
% 253.42/37.00 thf(c_0_221, plain, ![X1:$i, X4:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1))))|(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)))|(imp @ (~($true)) @ (~($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (($true)))))), inference(cn,[status(thm)],[c_0_202])).
% 253.42/37.00 thf(c_0_222, plain, ![X1:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[c_0_203])).
% 253.42/37.00 thf(c_0_223, negated_conjecture, ![X1:$i]:(((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset))))))))))), inference(spm,[status(thm)],[c_0_204, c_0_136])).
% 253.42/37.00 thf(c_0_224, plain, ![X4:$i, X1:$i]:(((epred2_2 @ X1 @ X4)|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((imp @ (($true)) @ (~($true))))|~(($true))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))))), inference(split_conjunct,[status(thm)],[c_0_205])).
% 253.42/37.00 thf(c_0_225, plain, ![X1:$i, X4:$i]:(((imp @ (~($true)) @ (~($true)))|(imp @ (~($true)) @ (($true)))|(imp @ (($true)) @ (~($true)))|~((epred8_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_206, c_0_207]), c_0_208])).
% 253.42/37.00 thf(c_0_226, plain, ((epred8_2 @ (ordsucc @ n_1) @ (ordsucc @ n_1))|~((d_29_ii @ (ordsucc @ n_1) @ (ordsucc @ n_1)))), inference(spm,[status(thm)],[c_0_209, c_0_87])).
% 253.42/37.00 thf(c_0_227, plain, ((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))|~((imp @ (~($true)) @ (($true))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_210, c_0_87]), c_0_148])])).
% 253.42/37.00 thf(c_0_228, plain, ![X1:$i]:(((d_29_ii @ (ordsucc @ X1) @ (ordsucc @ n_1))|(imp @ (~($true)) @ (~($true)))|~((in @ X1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset)))))))|~((n_is @ (ordsucc @ X1) @ (ordsucc @ n_1)))|~((imp @ (($true)) @ (($true)))))), inference(spm,[status(thm)],[c_0_211, c_0_87])).
% 253.42/37.00 thf(c_0_229, plain, (n_is @ (ordsucc @ n_1) @ (ordsucc @ n_1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212, c_0_96]), c_0_87])])).
% 253.42/37.00 thf(c_0_230, negated_conjecture, ((imp @ (~($true)) @ (($true)))|(imp @ (($true)) @ (($true)))), inference(spm,[status(thm)],[c_0_213, c_0_189])).
% 253.42/37.00 thf(c_0_231, plain, ![X507:$i]:(((in @ X507 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))=>![X506:$i]:(((in @ X506 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))=>![X505:$i]:(((in @ X505 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))=>![X504:$i]:(((in @ X504 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))=>((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X506))))=>((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X505)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X505)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X507)))=>((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X504)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X504)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X506)))=>(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X504)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X505)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X505)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X504))))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz45]), c_0_55]), c_0_63]), c_0_56]), c_0_43])).
% 253.42/37.00 thf(c_0_232, negated_conjecture, (~((epred4_2 @ esk3_0 @ esk1_0))|~((epred5_2 @ esk3_0 @ esk1_0))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214, c_0_215]), c_0_165]), c_0_136])]), c_0_166])).
% 253.42/37.00 thf(c_0_233, plain, ![X1:$i, X4:$i]:(((epred5_2 @ X1 @ X4)|~((imp @ (~($true)) @ (~($true)))))), inference(cn,[status(thm)],[c_0_216])).
% 253.42/37.00 thf(c_0_234, plain, ![X1:$i, X4:$i]:(((epred4_2 @ X1 @ X4)|~((imp @ (($true)) @ (~($true))))|~(($true)))), inference(split_conjunct,[status(thm)],[c_0_217])).
% 253.42/37.00 thf(c_0_235, negated_conjecture, ((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)))|(imp @ (~($true)) @ (~($true)))|~((imp @ (($true)) @ (($true))))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_218, c_0_137]), c_0_189]), c_0_219])).
% 253.42/37.00 thf(c_0_236, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~(($true))|~((imp @ (($true)) @ (~($true))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)))))|~((epred2_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_220])).
% 253.42/37.00 thf(c_0_237, negated_conjecture, ![X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0))))|(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)))|(imp @ (~($true)) @ (~($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (($true)))))), inference(spm,[status(thm)],[c_0_221, c_0_136])).
% 253.42/37.00 thf(c_0_238, negated_conjecture, (n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0))), inference(spm,[status(thm)],[c_0_222, c_0_136])).
% 253.42/37.00 thf(c_0_239, negated_conjecture, ((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)))))), inference(spm,[status(thm)],[c_0_223, c_0_136])).
% 253.42/37.00 thf(c_0_240, plain, ![X4:$i, X1:$i]:(((epred2_2 @ X1 @ X4)|~((imp @ (($true)) @ (~($true))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(cn,[status(thm)],[c_0_224])).
% 253.42/37.00 thf(c_0_241, plain, ((imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|~((d_29_ii @ (ordsucc @ n_1) @ (ordsucc @ n_1)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_225, c_0_226]), c_0_227])).
% 253.42/37.00 thf(c_0_242, plain, ((d_29_ii @ (ordsucc @ n_1) @ (ordsucc @ n_1))|(imp @ (~($true)) @ (~($true)))|~((imp @ (($true)) @ (($true))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_228, c_0_87]), c_0_229])])).
% 253.42/37.00 thf(c_0_243, negated_conjecture, ((imp @ (($true)) @ (~($true)))|(imp @ (($true)) @ (($true)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_213, c_0_227]), c_0_230])).
% 253.42/37.00 thf(c_0_244, plain, ![X625:$i, X626:$i, X627:$i, X628:$i]:((~(in @ X625 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X626 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset)))))))))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X626)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X625)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X625)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X626))))|(~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X625)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X627)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X627)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X625)))|(~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X626)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X628)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X628)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X626)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X628)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X627)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X627)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X628)))))))))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_231])])])])).
% 253.42/37.00 thf(c_0_245, plain, (~((epred4_2 @ esk3_0 @ esk1_0))|~((imp @ (~($true)) @ (~($true))))), inference(spm,[status(thm)],[c_0_232, c_0_233])).
% 253.42/37.00 thf(c_0_246, plain, ![X1:$i, X4:$i]:(((epred4_2 @ X1 @ X4)|~((imp @ (($true)) @ (~($true)))))), inference(cn,[status(thm)],[c_0_234])).
% 253.42/37.00 thf(c_0_247, negated_conjecture, ((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0))))|(imp @ (~($true)) @ (~($true)))|~((imp @ (($true)) @ (($true))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214, c_0_235]), c_0_165]), c_0_137])])).
% 253.42/37.00 thf(c_0_248, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (($true)))|~((epred2_2 @ X1 @ X4))|~((imp @ (($true)) @ (~($true))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4))))))), inference(cn,[status(thm)],[c_0_236])).
% 253.42/37.00 thf(c_0_249, negated_conjecture, ((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)))|(imp @ (~($true)) @ (~($true)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_237, c_0_136]), c_0_238])]), c_0_189]), c_0_239])).
% 253.42/37.00 thf(c_0_250, plain, ![X4:$i, X1:$i]:(((epred2_2 @ X1 @ X4)|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (($true)) @ (~($true)))))), inference(cn,[status(thm)],[c_0_240])).
% 253.42/37.00 thf(c_0_251, plain, ((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_241, c_0_242]), c_0_243])).
% 253.42/37.00 thf(c_0_252, plain, ![X1:$i, X6:$i, X5:$i, X4:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X6)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X5)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X5)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X6))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X5 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X6 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(~(((Z1)=(emptyset))))))))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X5)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X5)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X6)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X6)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(~(((Z0)=(emptyset)))))) @ X4)))))), inference(split_conjunct,[status(thm)],[c_0_244])).
% 253.42/37.00 thf(c_0_253, plain, (~((imp @ (~($true)) @ (~($true))))|~((imp @ (($true)) @ (~($true))))), inference(spm,[status(thm)],[c_0_245, c_0_246])).
% 253.42/37.00 thf(c_0_254, negated_conjecture, ((imp @ (~($true)) @ (~($true)))|~((imp @ (($true)) @ (($true))))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163, c_0_247]), c_0_165])]), c_0_166])).
% 253.42/37.00 thf(c_0_255, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (($true)))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((imp @ (($true)) @ (~($true))))|~((epred2_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_248])).
% 253.42/37.00 thf(c_0_256, negated_conjecture, ((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0))))|(imp @ (~($true)) @ (~($true)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214, c_0_249]), c_0_136])])).
% 253.42/37.00 thf(c_0_257, negated_conjecture, ((imp @ (~($true)) @ (~($true)))|(epred2_2 @ esk3_0 @ esk3_0)), inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_250, c_0_249]), c_0_136])]), c_0_251])).
% 253.42/37.00 thf(c_0_258, plain, ![X1:$i, X4:$i, X5:$i, X6:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X5)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X6)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X6)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X5)))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X5)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X5))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X6)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X6))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X5 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X6 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[c_0_252])).
% 253.42/37.00 thf(c_0_259, plain, (~((imp @ (($true)) @ (~($true))))|~((imp @ (($true)) @ (($true))))), inference(spm,[status(thm)],[c_0_253, c_0_254])).
% 253.42/37.00 thf(c_0_260, plain, (imp @ (($true)) @ (($true))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_255, c_0_256]), c_0_238])]), c_0_257]), c_0_251]), c_0_213])).
% 253.42/37.00 thf(c_0_261, negated_conjecture, ![X1:$i, X4:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_258, c_0_135]), c_0_136]), c_0_137])])).
% 253.42/37.00 thf(c_0_262, negated_conjecture, ((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)))|(imp @ (($true)) @ (~($true)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199, c_0_192]), c_0_137]), c_0_165])])).
% 253.42/37.00 thf(c_0_263, plain, ~((imp @ (($true)) @ (~($true)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_259, c_0_260])])).
% 253.42/37.00 thf(c_0_264, negated_conjecture, ![X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk3_0))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0:$i]:(d_Sep @ omega @ (^[Z1:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_261, c_0_136]), c_0_238])])).
% 253.42/37.00 thf(c_0_265, negated_conjecture, (n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0:$i]:(((Z0)!=(emptyset))))) @ esk2_0))), inference(sr,[status(thm)],[c_0_262, c_0_263])).
% 253.42/37.00 thf(c_0_266, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_264, c_0_165]), c_0_265])]), c_0_166]), ['proof']).
% 253.42/37.00 % SZS output end CNFRefutation
% 253.42/37.00 % Parsed axioms : 565
% 253.42/37.00 % Removed by relevancy pruning/SinE : 499
% 253.42/37.00 % Initial clauses : 11240
% 253.42/37.00 % Removed in clause preprocessing : 10869
% 253.42/37.00 % Initial clauses in saturation : 371
% 253.42/37.00 % Processed clauses : 10115
% 253.42/37.00 % ...of these trivial : 118
% 253.42/37.00 % ...subsumed : 3880
% 253.42/37.00 % ...remaining for further processing : 6117
% 253.42/37.00 % Other redundant clauses eliminated : 13
% 253.42/37.00 % Clauses deleted for lack of memory : 0
% 253.42/37.00 % Backward-subsumed : 2494
% 253.42/37.00 % Backward-rewritten : 859
% 253.42/37.00 % Generated clauses : 58523
% 253.42/37.00 % ...of the previous two non-redundant : 15184
% 253.42/37.00 % ...aggressively subsumed : 0
% 253.42/37.00 % Contextual simplify-reflections : 988
% 253.42/37.00 % Paramodulations : 17546
% 253.42/37.00 % Factorizations : 2
% 253.42/37.00 % NegExts : 219
% 253.42/37.00 % Equation resolutions : 14
% 253.42/37.00 % Disequality decompositions : 0
% 253.42/37.00 % Total rewrite steps : 7929
% 253.42/37.00 % ...of those cached : 7778
% 253.42/37.00 % Propositional unsat checks : 0
% 253.42/37.00 % Propositional check models : 0
% 253.42/37.00 % Propositional check unsatisfiable : 0
% 253.42/37.00 % Propositional clauses : 0
% 253.42/37.00 % Propositional clauses after purity: 0
% 253.42/37.00 % Propositional unsat core size : 0
% 253.42/37.00 % Propositional preprocessing time : 0.000
% 253.42/37.00 % Propositional encoding time : 0.000
% 253.42/37.00 % Propositional solver time : 0.000
% 253.42/37.00 % Success case prop preproc time : 0.000
% 253.42/37.00 % Success case prop encoding time : 0.000
% 253.42/37.00 % Success case prop solver time : 0.000
% 253.42/37.00 % Current number of processed clauses : 2290
% 253.42/37.00 % Positive orientable unit clauses : 259
% 253.42/37.00 % Positive unorientable unit clauses: 0
% 253.42/37.00 % Negative unit clauses : 12
% 253.42/37.00 % Non-unit-clauses : 2019
% 253.42/37.00 % Current number of unprocessed clauses: 4400
% 253.42/37.00 % ...number of literals in the above : 27265
% 253.42/37.00 % Current number of archived formulas : 0
% 253.42/37.00 % Current number of archived clauses : 3827
% 253.42/37.00 % Clause-clause subsumption calls (NU) : 4995633
% 253.42/37.00 % Rec. Clause-clause subsumption calls : 812379
% 253.42/37.00 % Non-unit clause-clause subsumptions : 7090
% 253.42/37.00 % Unit Clause-clause subsumption calls : 73227
% 253.42/37.00 % Rewrite failures with RHS unbound : 0
% 253.42/37.00 % BW rewrite match attempts : 18770
% 253.42/37.00 % BW rewrite match successes : 72
% 253.42/37.00 % Condensation attempts : 0
% 253.42/37.00 % Condensation successes : 0
% 253.42/37.00 % Termbank termtop insertions : 4231972
% 253.42/37.00 % Search garbage collected termcells : 89078
% 253.42/37.00
% 253.42/37.00 % -------------------------------------------------
% 253.42/37.00 % User time : 35.861 s
% 253.42/37.00 % System time : 0.242 s
% 253.42/37.00 % Total time : 36.103 s
% 253.42/37.00 % Maximum resident set size: 32308 pages
% 253.42/37.00
% 253.42/37.00 % -------------------------------------------------
% 253.42/37.00 % User time : 35.902 s
% 253.42/37.00 % System time : 0.305 s
% 253.42/37.00 % Total time : 36.206 s
% 253.42/37.00 % Maximum resident set size: 11264 pages
% 253.42/37.00 % E exiting
%------------------------------------------------------------------------------