0.07/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.12	% Command    : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 240 THM
0.11/0.32	% Computer : n017.cluster.edu
0.11/0.32	% Model    : x86_64 x86_64
0.11/0.32	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.32	% Memory   : 8042.1875MB
0.11/0.32	% OS       : Linux 3.10.0-693.el7.x86_64
0.11/0.32	% CPULimit   : 1920
0.11/0.32	% WCLimit    : 240
0.11/0.32	% DateTime   : Wed Jul 30 09:04:49 EDT 2025
0.11/0.33	% CPUTime    : 
0.19/0.47	Running higher-order theorem proving
0.34/0.52	Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=240 /export/starexec/sandbox/tmp/tmp.sdvj496mc6/E---3.1_3482.p
74.98/9.01	# Version: 3.0.0-ho
74.98/9.01	# Preprocessing class: HSLMSMSMLLLCHSA.
74.98/9.01	# Scheduled 5 strats onto 8 cores with 240 seconds (1920 total)
74.98/9.01	# Starting pre_casc_4 with 960s (4) cores
74.98/9.01	# Starting full_lambda_6 with 240s (1) cores
74.98/9.01	# Starting sh10 with 240s (1) cores
74.98/9.01	# Starting post_as_ho9 with 240s (1) cores
74.98/9.01	# Starting post_as_ho8 with 240s (1) cores
74.98/9.01	# post_as_ho9 with pid 3563 completed with status 0
74.98/9.01	# Result found by post_as_ho9
74.98/9.01	# Preprocessing class: HSLMSMSMLLLCHSA.
74.98/9.01	# Scheduled 5 strats onto 8 cores with 240 seconds (1920 total)
74.98/9.01	# Starting pre_casc_4 with 960s (4) cores
74.98/9.01	# Starting full_lambda_6 with 240s (1) cores
74.98/9.01	# Starting sh10 with 240s (1) cores
74.98/9.01	# Starting post_as_ho9 with 240s (1) cores
74.98/9.01	# SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true)
74.98/9.01	# Search class: HGUNF-FSLM21-DHSMMFBN
74.98/9.01	# partial match(5): HGUSM-FSLM31-DHSFFFBN
74.98/9.01	# Scheduled 6 strats onto 1 cores with 240 seconds (240 total)
74.98/9.01	# Starting new_bool_5 with 108s (1) cores
74.98/9.01	# new_bool_5 with pid 3572 completed with status 0
74.98/9.01	# Result found by new_bool_5
74.98/9.01	# Preprocessing class: HSLMSMSMLLLCHSA.
74.98/9.01	# Scheduled 5 strats onto 8 cores with 240 seconds (1920 total)
74.98/9.01	# Starting pre_casc_4 with 960s (4) cores
74.98/9.01	# Starting full_lambda_6 with 240s (1) cores
74.98/9.01	# Starting sh10 with 240s (1) cores
74.98/9.01	# Starting post_as_ho9 with 240s (1) cores
74.98/9.01	# SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true)
74.98/9.01	# Search class: HGUNF-FSLM21-DHSMMFBN
74.98/9.01	# partial match(5): HGUSM-FSLM31-DHSFFFBN
74.98/9.01	# Scheduled 6 strats onto 1 cores with 240 seconds (240 total)
74.98/9.01	# Starting new_bool_5 with 108s (1) cores
74.98/9.01	# Preprocessing time       : 0.010 s
74.98/9.01	# Presaturation interreduction done
74.98/9.01	
74.98/9.01	# Proof found!
74.98/9.01	# SZS status Theorem
74.98/9.01	# SZS output start CNFRefutation
74.98/9.01	thf(decl_23, type, is_of: $i > ($i > $o) > $o).
74.98/9.01	thf(decl_24, type, all_of: ($i > $o) > ($i > $o) > $o).
74.98/9.01	thf(decl_26, type, in: $i > $i > $o).
74.98/9.01	thf(decl_28, type, emptyset: $i).
74.98/9.01	thf(decl_43, type, d_Sep: $i > ($i > $o) > $i).
74.98/9.01	thf(decl_50, type, omega: $i).
74.98/9.01	thf(decl_59, type, ap: $i > $i > $i).
74.98/9.01	thf(decl_61, type, d_Pi: $i > ($i > $i) > $i).
74.98/9.01	thf(decl_62, type, imp: $o > $o > $o).
74.98/9.01	thf(decl_63, type, d_not: $o > $o).
74.98/9.01	thf(decl_68, type, l_or: $o > $o > $o).
74.98/9.01	thf(decl_124, type, nat: $i).
74.98/9.01	thf(decl_125, type, n_is: $i > $i > $o).
74.98/9.01	thf(decl_128, type, n_some: ($i > $o) > $o).
74.98/9.01	thf(decl_148, type, diffprop: $i > $i > $i > $o).
74.98/9.01	thf(decl_149, type, d_29_ii: $i > $i > $o).
74.98/9.01	thf(decl_150, type, iii: $i > $i > $o).
74.98/9.01	thf(decl_162, type, times: $i > $i).
74.98/9.01	thf(decl_163, type, n_ts: $i > $i > $i).
74.98/9.01	thf(decl_168, type, d_1to: $i > $i).
74.98/9.01	thf(decl_173, type, n_2: $i).
74.98/9.01	thf(decl_177, type, pair1type: $i > $i).
74.98/9.01	thf(decl_179, type, first1: $i > $i > $i).
74.98/9.01	thf(decl_180, type, second1: $i > $i > $i).
74.98/9.01	thf(decl_190, type, frac: $i).
74.98/9.01	thf(decl_192, type, num: $i > $i).
74.98/9.01	thf(decl_193, type, den: $i > $i).
74.98/9.01	thf(decl_194, type, n_eq: $i > $i > $o).
74.98/9.01	thf(decl_195, type, moref: $i > $i > $o).
74.98/9.01	thf(decl_196, type, lessf: $i > $i > $o).
74.98/9.01	thf(decl_198, type, lesseq: $i > $i > $o).
74.98/9.01	thf(decl_199, type, epred1_2: $i > $i > $o).
74.98/9.01	thf(decl_200, type, epred2_2: $i > $i > $o).
74.98/9.01	thf(decl_201, type, epred3_2: $i > $i > $o).
74.98/9.01	thf(decl_202, type, epred4_2: $i > $i > $o).
74.98/9.01	thf(decl_203, type, epred5_2: $i > $i > $o).
74.98/9.01	thf(decl_209, type, esk1_0: $i).
74.98/9.01	thf(decl_210, type, esk2_0: $i).
74.98/9.01	thf(decl_211, type, esk3_0: $i).
74.98/9.01	thf(def_nat, axiom, ((nat)=(d_Sep @ omega @ (^[X1:$i]:(((X1)!=(emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.sdvj496mc6/E---3.1_3482.p', def_nat)).
74.98/9.01	thf(def_n_eq, axiom, ((n_eq)=(^[X1:$i, X218:$i]:((n_is @ (n_ts @ (num @ X1) @ (den @ X218)) @ (n_ts @ (num @ X218) @ (den @ X1)))))), file('/export/starexec/sandbox/tmp/tmp.sdvj496mc6/E---3.1_3482.p', def_n_eq)).
74.98/9.01	thf(def_num, axiom, ((num)=(first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))))), file('/export/starexec/sandbox/tmp/tmp.sdvj496mc6/E---3.1_3482.p', def_num)).
74.98/9.01	thf(def_den, axiom, ((den)=(second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))))), file('/export/starexec/sandbox/tmp/tmp.sdvj496mc6/E---3.1_3482.p', def_den)).
74.98/9.01	thf(def_n_ts, axiom, ((n_ts)=(^[X1:$i]:(ap @ (times @ X1)))), file('/export/starexec/sandbox/tmp/tmp.sdvj496mc6/E---3.1_3482.p', def_n_ts)).
74.98/9.01	thf(def_l_or, axiom, ((l_or)=(^[X42:$o]:(imp @ ((d_not @ ((X42))))))), file('/export/starexec/sandbox/tmp/tmp.sdvj496mc6/E---3.1_3482.p', def_l_or)).
74.98/9.01	thf(def_d_not, axiom, ((d_not)=(^[X36:$o]:((imp @ ((X36)) @ (~($true)))))), file('/export/starexec/sandbox/tmp/tmp.sdvj496mc6/E---3.1_3482.p', def_d_not)).
74.98/9.01	thf(def_lessf, axiom, ((lessf)=(^[X1:$i, X220:$i]:((iii @ (n_ts @ (num @ X1) @ (den @ X220)) @ (n_ts @ (num @ X220) @ (den @ X1)))))), file('/export/starexec/sandbox/tmp/tmp.sdvj496mc6/E---3.1_3482.p', def_lessf)).
74.98/9.01	thf(def_iii, axiom, ((iii)=(^[X1:$i, X185:$i]:((n_some @ (diffprop @ X185 @ X1))))), file('/export/starexec/sandbox/tmp/tmp.sdvj496mc6/E---3.1_3482.p', def_iii)).
74.98/9.01	thf(def_all_of, axiom, ((all_of)=(^[X3:$i > $o, X2:$i > $o]:(![X4:$i]:(((is_of @ X4 @ X3)=>(X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.sdvj496mc6/E---3.1_3482.p', def_all_of)).
74.98/9.01	thf(def_is_of, axiom, ((is_of)=(^[X1:$i, X2:$i > $o]:((X2 @ X1)))), file('/export/starexec/sandbox/tmp/tmp.sdvj496mc6/E---3.1_3482.p', def_is_of)).
74.98/9.01	thf(def_moref, axiom, ((moref)=(^[X1:$i, X219:$i]:((d_29_ii @ (n_ts @ (num @ X1) @ (den @ X219)) @ (n_ts @ (num @ X219) @ (den @ X1)))))), file('/export/starexec/sandbox/tmp/tmp.sdvj496mc6/E---3.1_3482.p', def_moref)).
74.98/9.01	thf(def_pair1type, axiom, ((pair1type)=(^[X1:$i]:(d_Pi @ (d_1to @ n_2) @ (^[X207:$i]:(X1))))), file('/export/starexec/sandbox/tmp/tmp.sdvj496mc6/E---3.1_3482.p', def_pair1type)).
74.98/9.01	thf(def_lesseq, axiom, ((lesseq)=(^[X1:$i, X222:$i]:((l_or @ ((lessf @ X1 @ X222)) @ ((n_eq @ X1 @ X222)))))), file('/export/starexec/sandbox/tmp/tmp.sdvj496mc6/E---3.1_3482.p', def_lesseq)).
74.98/9.01	thf(def_frac, axiom, ((frac)=(d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.sdvj496mc6/E---3.1_3482.p', def_frac)).
74.98/9.01	thf(satz41d, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X235:$i]:((in @ X235 @ frac))) @ (^[X236:$i]:(((lesseq @ X1 @ X236)=>(d_not @ ((moref @ X1 @ X236)))))))))), file('/export/starexec/sandbox/tmp/tmp.sdvj496mc6/E---3.1_3482.p', satz41d)).
74.98/9.01	thf(satz37, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((n_eq @ X1 @ X1)))), file('/export/starexec/sandbox/tmp/tmp.sdvj496mc6/E---3.1_3482.p', satz37)).
74.98/9.01	thf(satz51a, conjecture, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X404:$i]:((in @ X404 @ frac))) @ (^[X405:$i]:((all_of @ (^[X4:$i]:((in @ X4 @ frac))) @ (^[X4:$i]:((((lessf @ X405 @ X4)=>(lessf @ X1 @ X4))<=(lesseq @ X1 @ X405))))))))))), file('/export/starexec/sandbox/tmp/tmp.sdvj496mc6/E---3.1_3482.p', satz51a)).
74.98/9.01	thf(satz41g, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X452:$i]:((in @ X452 @ frac))) @ (^[X453:$i]:(((moref @ X1 @ X453)=>(d_not @ ((lesseq @ X1 @ X453)))))))))), file('/export/starexec/sandbox/tmp/tmp.sdvj496mc6/E---3.1_3482.p', satz41g)).
74.98/9.01	thf(satz41k, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X446:$i]:((in @ X446 @ frac))) @ (^[X447:$i]:(((moref @ X1 @ X447)<=(d_not @ ((lesseq @ X1 @ X447)))))))))), file('/export/starexec/sandbox/tmp/tmp.sdvj496mc6/E---3.1_3482.p', satz41k)).
74.98/9.01	thf(satz50, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X256:$i]:((in @ X256 @ frac))) @ (^[X257:$i]:((all_of @ (^[X4:$i]:((in @ X4 @ frac))) @ (^[X4:$i]:((((lessf @ X257 @ X4)=>(lessf @ X1 @ X4))<=(lessf @ X1 @ X257))))))))))), file('/export/starexec/sandbox/tmp/tmp.sdvj496mc6/E---3.1_3482.p', satz50)).
74.98/9.01	thf(satz42, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X239:$i]:((in @ X239 @ frac))) @ (^[X240:$i]:(((moref @ X1 @ X240)=>(lessf @ X240 @ X1)))))))), file('/export/starexec/sandbox/tmp/tmp.sdvj496mc6/E---3.1_3482.p', satz42)).
74.98/9.01	thf(satz41e, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X310:$i]:((in @ X310 @ frac))) @ (^[X311:$i]:(((lesseq @ X1 @ X311)<=(d_not @ ((moref @ X1 @ X311)))))))))), file('/export/starexec/sandbox/tmp/tmp.sdvj496mc6/E---3.1_3482.p', satz41e)).
74.98/9.01	thf(satz43, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X482:$i]:((in @ X482 @ frac))) @ (^[X483:$i]:(((moref @ X483 @ X1)<=(lessf @ X1 @ X483)))))))), file('/export/starexec/sandbox/tmp/tmp.sdvj496mc6/E---3.1_3482.p', satz43)).
74.98/9.01	thf(satz45, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X298:$i]:((in @ X298 @ frac))) @ (^[X299:$i]:((all_of @ (^[X4:$i]:((in @ X4 @ frac))) @ (^[X4:$i]:((all_of @ (^[X10:$i]:((in @ X10 @ frac))) @ (^[X10:$i]:(((lessf @ X1 @ X299)=>((n_eq @ X1 @ X4)=>((n_eq @ X299 @ X10)=>(lessf @ X4 @ X10)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.sdvj496mc6/E---3.1_3482.p', satz45)).
74.98/9.01	thf(c_0_25, plain, ((nat)=(d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset)))))), inference(fof_simplification,[status(thm)],[def_nat])).
74.98/9.01	thf(c_0_26, plain, ((n_eq)=(^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (second1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (second1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z0)))))), inference(fof_simplification,[status(thm)],[def_n_eq])).
74.98/9.01	thf(c_0_27, axiom, ((num)=(first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))))), inference(apply_def,[status(thm)],[def_num, c_0_25])).
74.98/9.01	thf(c_0_28, axiom, ((den)=(second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))))), inference(apply_def,[status(thm)],[def_den, c_0_25])).
74.98/9.01	thf(c_0_29, plain, ((n_ts)=(^[Z0/* 59 */:$i]:(ap @ (times @ Z0)))), inference(fof_simplification,[status(thm)],[def_n_ts])).
74.98/9.01	thf(c_0_30, plain, ((l_or)=(^[Z0/* 62 */:$o]:(imp @ (((imp @ (((Z0))) @ (~($true)))))))), inference(fof_simplification,[status(thm)],[def_l_or])).
74.98/9.01	thf(c_0_31, plain, ((d_not)=(^[Z0/* 3 */:$o]:((imp @ ((Z0)) @ (~($true)))))), inference(fof_simplification,[status(thm)],[def_d_not])).
74.98/9.01	thf(c_0_32, plain, ((lessf)=(^[Z0/* 19 */:$i, Z1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (second1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (second1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z1)))))))), inference(fof_simplification,[status(thm)],[def_lessf])).
74.98/9.01	thf(c_0_33, plain, ((iii)=(^[Z0/* 19 */:$i, Z1:$i]:((n_some @ (diffprop @ Z1 @ Z0))))), inference(fof_simplification,[status(thm)],[def_iii])).
74.98/9.01	thf(c_0_34, plain, ((all_of)=(^[Z0/* 19 */:$i > $o, Z1:$i > $o]:(![X4:$i]:((((Z0 @ X4))=>(Z1 @ X4)))))), inference(fof_simplification,[status(thm)],[def_all_of])).
74.98/9.01	thf(c_0_35, plain, ((is_of)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((Z1 @ Z0)))), inference(fof_simplification,[status(thm)],[def_is_of])).
74.98/9.01	thf(c_0_36, plain, ((moref)=(^[Z0/* 19 */:$i, Z1:$i]:((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (second1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (second1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z0)))))), inference(fof_simplification,[status(thm)],[def_moref])).
74.98/9.01	thf(c_0_37, plain, ((pair1type)=(^[Z0/* 61 */:$i]:(d_Pi @ (d_1to @ n_2) @ (^[Z1/* 1 */:$i]:(Z0))))), inference(fof_simplification,[status(thm)],[def_pair1type])).
74.98/9.01	thf(c_0_38, plain, ((lesseq)=(^[Z0/* 19 */:$i, Z1:$i]:((imp @ (((imp @ (((((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (second1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (second1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z1)))))))) @ (~($true))))) @ (((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (second1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (second1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z0))))))))), inference(fof_simplification,[status(thm)],[def_lesseq])).
74.98/9.01	thf(c_0_39, plain, ((n_eq)=(^[Z0/* 19 */:$i, Z1:$i]:((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (second1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (second1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z0)))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_26, c_0_27]), c_0_28]), c_0_29])).
74.98/9.01	thf(c_0_40, plain, ((l_or)=(^[Z0/* 62 */:$o]:(imp @ (((imp @ (((Z0))) @ (~($true)))))))), inference(apply_def,[status(thm)],[c_0_30, c_0_31])).
74.98/9.01	thf(c_0_41, plain, ((lessf)=(^[Z0/* 19 */:$i, Z1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (second1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (second1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$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_32, c_0_27]), c_0_28]), c_0_29]), c_0_33])).
74.98/9.01	thf(c_0_42, plain, ((all_of)=(^[Z0/* 19 */:$i > $o, Z1:$i > $o]:(![X4:$i]:((((Z0 @ X4))=>(Z1 @ X4)))))), inference(apply_def,[status(thm)],[c_0_34, c_0_35])).
74.98/9.01	thf(c_0_43, plain, ((moref)=(^[Z0/* 19 */:$i, Z1:$i]:((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (second1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (second1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z0)))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_36, c_0_27]), c_0_28]), c_0_29])).
74.98/9.01	thf(c_0_44, axiom, ((frac)=(d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[def_frac, c_0_25]), c_0_37])).
74.98/9.01	thf(c_0_45, plain, ((lesseq)=(^[Z0/* 19 */:$i, Z1:$i]:((imp @ (((imp @ (((((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (second1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (second1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z1)))))))) @ (~($true))))) @ (((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z0)) @ (second1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z1)) @ (second1 @ (d_Sep @ omega @ (^[Z2/* 4 */:$i]:(((Z2)!=(emptyset))))) @ Z0))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_38, c_0_39]), c_0_40]), c_0_41])).
74.98/9.01	thf(c_0_46, plain, ![X505:$i]:(((in @ X505 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>![X504:$i]:(((in @ X504 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>(((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X504)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X505)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X505)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X504))))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X504)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X505)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X505)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X504))))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X505)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X504)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X504)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X505)))|(imp @ $true @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X505)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X504)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X504)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X505)))|(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X504)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X505)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X505)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X504))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X504)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X505)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X505)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X504))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X505)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X504)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X504)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X505)))|(imp @ $false @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X505)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X504)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X504)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X505)))|(imp @ $false @ $false)))))=>((~(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X505)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X504)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X504)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X505)))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X505)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X504)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X504)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X505)))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))))))), inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz41d]), c_0_42]), c_0_43]), c_0_31]), c_0_44]), c_0_45])])).
74.98/9.01	thf(c_0_47, plain, ![X502:$i, X503:$i]:(((epred1_2 @ X503 @ X502)<=>((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502))))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502))))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)))|(imp @ $true @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)))|(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)))|(imp @ $false @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)))|(imp @ $false @ $false))))))), introduced(definition)).
74.98/9.01	thf(c_0_48, plain, ![X625:$i, X626:$i]:((((((((((($true)|(imp @ $true @ $true)|~(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X625)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X626)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X626)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X625)))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X626)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X625)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X625)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X626))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X626)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 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@ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X625 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))&(~($true)|(imp @ $true @ $false)|~(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X625)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X626)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X626)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X625)))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X626)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X625)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X625)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X626))))|(n_some @ (diffprop 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*/:$i]:(~(((Z0)=(emptyset)))))) @ X626)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X626)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X625)))|(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true)))|~(in @ X626 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X625 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])])])])])).
75.37/9.02	thf(c_0_49, plain, ![X502:$i, X503:$i]:(((epred1_2 @ X503 @ X502)=>((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502))))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502))))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)))|(imp @ $true @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)))|(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)))|(imp @ $false @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)))|(imp @ $false @ $false))))))), inference(split_equiv,[status(thm)],[c_0_47])).
75.37/9.02	thf(c_0_50, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (~($true)))|(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|(imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|~(($true))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((imp @ (~($true)) @ (($true))))|~(($true))|~(($true))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))), inference(split_conjunct,[status(thm)],[c_0_48])).
75.37/9.02	thf(c_0_51, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|~(($true))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((imp @ (~($true)) @ (($true))))|~(($true))|~(($true))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))), inference(split_conjunct,[status(thm)],[c_0_48])).
75.37/9.02	thf(c_0_52, plain, ![X524:$i]:(((in @ X524 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X524)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X524)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X524)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X524))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz37]), c_0_42]), c_0_39]), c_0_44])).
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@ $false @ $true)|(($true)|(imp @ $true @ $true)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X749)))))|~(epred1_2 @ X750 @ X749))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X750)))|(imp @ $false @ $false)|(($true)|(imp @ $true @ $true)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ 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(d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X749)))))|~(epred1_2 @ X750 @ X749))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X750)))|(imp @ $false @ $false)|(~($true)|(imp @ $true @ $false)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X749)))))|~(epred1_2 @ X750 @ X749))))&(((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X750)))|(imp @ $false @ $true)|(($true)|(imp @ $false @ $true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X749)))))|~(epred1_2 @ X750 @ X749))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X750)))|(imp @ $false @ $false)|(($true)|(imp @ $false @ $true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X749)))))|~(epred1_2 @ X750 @ X749)))&((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X750)))|(imp @ $false @ $true)|(~($true)|(imp @ $false @ $false)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X749)))))|~(epred1_2 @ X750 @ X749))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X750)))|(imp @ $false @ $false)|(~($true)|(imp @ $false @ $false)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X749)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X750)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X749)))))|~(epred1_2 @ X750 @ X749))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])])])).
75.37/9.02	thf(c_0_54, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))|(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|~((imp @ (~($true)) @ (($true))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(cn,[status(thm)],[c_0_50])).
75.37/9.02	thf(c_0_55, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))|~((imp @ (~($true)) @ (($true))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(cn,[status(thm)],[c_0_51])).
75.37/9.02	thf(c_0_56, plain, ![X651:$i]:((~(in @ X651 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X651)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X651)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X651)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X651))))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])])).
75.37/9.02	thf(c_0_57, negated_conjecture, ~(![X503:$i]:(((in @ X503 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>![X502:$i]:(((in @ X502 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>![X501:$i]:(((in @ X501 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>((epred1_2 @ X503 @ X502)=>((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X501)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X502)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X501))))=>(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X501)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X503)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X501))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz51a])]), c_0_42]), c_0_44]), c_0_41]), c_0_45])])]), c_0_47])).
75.37/9.02	thf(c_0_58, plain, ![X510:$i, X511:$i]:(((epred5_2 @ X511 @ X510)<=>((((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510))))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510))))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)))|~(imp @ $true @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)))|~(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)))|~(imp @ $false @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)))|~(imp @ $false @ $false)))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&(((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510))))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510))))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)))|(imp @ $true @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)))|(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)))|(imp @ $false @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)))|(imp @ $false @ $false)))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false))))))), introduced(definition)).
75.37/9.02	thf(c_0_59, plain, ![X1:$i, X4:$i]:(((imp @ (~($true)) @ (($true)))|(imp @ (~($true)) @ (~($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~(($true))|~((epred1_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_53])).
75.37/9.02	thf(c_0_60, plain, ![X1:$i, X4:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|(imp @ (~($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~(($true))|~((epred1_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_53])).
75.37/9.02	thf(c_0_61, plain, ![X4:$i, X1:$i]:(((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))|(imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (($true)))))), inference(cn,[status(thm)],[c_0_54])).
75.37/9.02	thf(c_0_62, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (($true)))))), inference(cn,[status(thm)],[c_0_55])).
75.37/9.02	thf(c_0_63, plain, ![X1:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))), inference(split_conjunct,[status(thm)],[c_0_56])).
75.37/9.02	thf(c_0_64, negated_conjecture, ((in @ esk1_0 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))&((in @ esk2_0 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))&((in @ esk3_0 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))&((epred1_2 @ esk1_0 @ esk2_0)&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ esk2_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ esk3_0))))&~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ esk1_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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_57])])])])).
75.37/9.02	thf(c_0_65, plain, ![X510:$i, X511:$i]:(((epred5_2 @ X511 @ X510)=>((((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510))))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510))))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)))|~(imp @ $true @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)))|~(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)))|~(imp @ $false @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)))|~(imp @ $false @ $false)))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&(((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510))))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510))))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)))|(imp @ $true @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)))|(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)))|(imp @ $false @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)))|(imp @ $false @ $false)))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false))))))), inference(split_equiv,[status(thm)],[c_0_58])).
75.37/9.02	thf(c_0_66, plain, ![X1:$i, X4:$i]:(((imp @ (~($true)) @ (($true)))|(imp @ (($true)) @ (~($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~(($true))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)))))|~((epred1_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_53])).
75.37/9.02	thf(c_0_67, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (($true)))|(imp @ (~($true)) @ (~($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~((epred1_2 @ X1 @ X4))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(cn,[status(thm)],[c_0_59])).
75.37/9.02	thf(c_0_68, plain, ![X1:$i, X4:$i]:(((imp @ (~($true)) @ (~($true)))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~((epred1_2 @ X1 @ X4)))), inference(cn,[status(thm)],[c_0_60])).
75.37/9.02	thf(c_0_69, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (($true)))))), inference(csr,[status(thm)],[c_0_61, c_0_62])).
75.37/9.02	thf(c_0_70, plain, ![X1:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[c_0_63])).
75.37/9.02	thf(c_0_71, negated_conjecture, (in @ esk3_0 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))), inference(split_conjunct,[status(thm)],[c_0_64])).
75.37/9.02	thf(c_0_72, plain, ![X757:$i, X758:$i]:((((((((($true)|(imp @ $true @ $true)|(~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)))|~(imp @ $true @ $true)|(($true)|~(imp @ $true @ $true)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757))))))|~(epred5_2 @ X758 @ X757))&(~($true)|(imp @ $true @ $false)|(~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 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X758)))|~(imp @ $true @ $false)|(($true)|~(imp @ $true @ $true)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757))))))|~(epred5_2 @ X758 @ X757))))&(((($true)|(imp @ $true @ $true)|(~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)))|~(imp @ $true @ $true)|(~($true)|~(imp @ $true @ $false)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 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*/:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757))))))|~(epred5_2 @ X758 @ X757))&(~($true)|(imp @ $false @ $false)|((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)))|(imp @ $false @ $false)|(~($true)|(imp @ $true @ $false)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757))))))|~(epred5_2 @ X758 @ X757)))))&((((($true)|(imp @ $false @ $true)|(~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)))|(imp @ $false @ $true)|(($true)|(imp @ $false @ $true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757))))))|~(epred5_2 @ X758 @ X757))&(~($true)|(imp @ $false @ $false)|(~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)))|(imp @ $false @ $true)|(($true)|(imp @ $false @ $true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757))))))|~(epred5_2 @ X758 @ X757)))&((($true)|(imp @ $false @ $true)|((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)))|(imp @ $false @ $false)|(($true)|(imp @ $false @ $true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757))))))|~(epred5_2 @ X758 @ X757))&(~($true)|(imp @ $false @ $false)|((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)))|(imp @ $false @ $false)|(($true)|(imp @ $false @ $true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757))))))|~(epred5_2 @ X758 @ X757))))&(((($true)|(imp @ $false @ $true)|(~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)))|(imp @ $false @ $true)|(~($true)|(imp @ $false @ $false)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757))))))|~(epred5_2 @ X758 @ X757))&(~($true)|(imp @ $false @ $false)|(~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)))|(imp @ $false @ $true)|(~($true)|(imp @ $false @ $false)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757))))))|~(epred5_2 @ X758 @ X757)))&((($true)|(imp @ $false @ $true)|((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)))|(imp @ $false @ $false)|(~($true)|(imp @ $false @ $false)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757))))))|~(epred5_2 @ X758 @ X757))&(~($true)|(imp @ $false @ $false)|((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)))|(imp @ $false @ $false)|(~($true)|(imp @ $false @ $false)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X757))))))|~(epred5_2 @ X758 @ X757))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_65])])])])).
75.37/9.02	thf(c_0_73, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~(($true))|~((imp @ (~($true)) @ (~($true))))|~((epred1_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_53])).
75.37/9.02	thf(c_0_74, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (($true)))|~((epred1_2 @ X1 @ X4))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))))), inference(cn,[status(thm)],[c_0_66])).
75.37/9.02	thf(c_0_75, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|(imp @ (~($true)) @ (~($true)))|(imp @ (~($true)) @ (($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((epred1_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_67])).
75.37/9.02	thf(c_0_76, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)))|(imp @ (~($true)) @ (~($true)))|~((epred1_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_68])).
75.37/9.02	thf(c_0_77, plain, ![X1:$i]:(((imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (($true)))))), inference(spm,[status(thm)],[c_0_69, c_0_70])).
75.37/9.02	thf(c_0_78, negated_conjecture, (in @ esk3_0 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))), inference(cn,[status(thm)],[c_0_71])).
75.37/9.02	thf(c_0_79, plain, ![X1:$i, X4:$i]:(((imp @ (~($true)) @ (~($true)))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|(imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|~(($true))|~(($true))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)))))|~((epred5_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_72])).
75.37/9.02	thf(c_0_80, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|(imp @ (($true)) @ (~($true)))|~(($true))|~((imp @ (~($true)) @ (~($true))))|~(($true))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)))))|~((epred5_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_72])).
75.37/9.02	thf(c_0_81, plain, ![X1:$i, X4:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|(imp @ (($true)) @ (~($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~(($true))|~((imp @ (~($true)) @ (~($true))))|~((epred1_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_53])).
75.37/9.02	thf(c_0_82, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|~(($true))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((imp @ (~($true)) @ (($true))))|~(($true))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)))))|~((epred5_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_72])).
75.37/9.02	thf(c_0_83, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~((epred1_2 @ X1 @ X4))|~((imp @ (~($true)) @ (~($true))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(cn,[status(thm)],[c_0_73])).
75.37/9.02	thf(c_0_84, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (($true)))|(imp @ (($true)) @ (~($true)))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((epred1_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_74])).
75.37/9.02	thf(c_0_85, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|(imp @ (~($true)) @ (($true)))|(imp @ (~($true)) @ (~($true)))|~((epred1_2 @ X4 @ X1)))), inference(csr,[status(thm)],[c_0_75, c_0_76])).
75.37/9.02	thf(c_0_86, negated_conjecture, ((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))|~((imp @ (~($true)) @ (($true))))), inference(spm,[status(thm)],[c_0_77, c_0_78])).
75.37/9.02	thf(c_0_87, plain, ![X508:$i, X509:$i]:(((epred3_2 @ X509 @ X508)<=>(((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508))))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508))))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)))|~(imp @ $true @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)))|~(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)))|~(imp @ $false @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)))|~(imp @ $false @ $false)))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false)))))), introduced(definition)).
75.37/9.02	thf(c_0_88, plain, ![X508:$i, X509:$i]:(((epred4_2 @ X509 @ X508)<=>(((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508))))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508))))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)))|(imp @ $true @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)))|(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)))|(imp @ $false @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)))|(imp @ $false @ $false)))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))), introduced(definition)).
75.37/9.02	thf(c_0_89, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|~((epred5_2 @ X1 @ X4))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))))), inference(cn,[status(thm)],[c_0_79])).
75.37/9.02	thf(c_0_90, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|~((epred5_2 @ X1 @ X4))|~((imp @ (~($true)) @ (~($true))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))))), inference(cn,[status(thm)],[c_0_80])).
75.37/9.02	thf(c_0_91, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~((epred1_2 @ X1 @ X4))|~((imp @ (~($true)) @ (~($true)))))), inference(cn,[status(thm)],[c_0_81])).
75.37/9.02	thf(c_0_92, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~(($true))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((imp @ (($true)) @ (($true))))|~(($true))|~((imp @ (~($true)) @ (~($true))))|~((epred5_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_72])).
75.37/9.02	thf(c_0_93, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|~((epred5_2 @ X1 @ X4))|~((imp @ (~($true)) @ (($true))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))))), inference(cn,[status(thm)],[c_0_82])).
75.37/9.02	thf(c_0_94, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|(imp @ (($true)) @ (($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((imp @ (~($true)) @ (~($true))))|~((epred1_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_83])).
75.37/9.02	thf(c_0_95, plain, ![X1:$i, X4:$i]:(((imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((epred1_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_85]), c_0_86])).
75.37/9.02	thf(c_0_96, plain, ![X511:$i]:(((in @ X511 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>![X510:$i]:(((in @ X510 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X510)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X511)))=>(epred5_2 @ X511 @ X510)))))), inference(apply_def,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz41g]), c_0_42]), c_0_43]), c_0_31]), c_0_44]), c_0_45])]), c_0_58])).
75.37/9.02	thf(c_0_97, plain, ![X509:$i]:(((in @ X509 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>![X508:$i]:(((in @ X508 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>(((epred3_2 @ X509 @ X508)&(epred4_2 @ X509 @ X508))=>(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz41k]), c_0_42]), c_0_43]), c_0_31]), c_0_44]), c_0_45])])]), c_0_87]), c_0_88])).
75.37/9.02	thf(c_0_98, plain, ![X508:$i, X509:$i]:(((((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508))))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508))))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)))|~(imp @ $true @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)))|~(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)))|~(imp @ $false @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)))|~(imp @ $false @ $false)))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))=>(epred3_2 @ X509 @ X508))), inference(split_equiv,[status(thm)],[c_0_87])).
75.37/9.02	thf(c_0_99, plain, ![X1:$i, X4:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))|(imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)))))|~((epred5_2 @ X1 @ X4)))), inference(cn,[status(thm)],[c_0_89])).
75.37/9.02	thf(c_0_100, plain, ![X1:$i, X4:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))|(imp @ (($true)) @ (~($true)))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)))))|~((imp @ (~($true)) @ (~($true))))|~((epred5_2 @ X1 @ X4)))), inference(cn,[status(thm)],[c_0_90])).
75.37/9.02	thf(c_0_101, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)))|(imp @ (($true)) @ (~($true)))|~((imp @ (~($true)) @ (~($true))))|~((epred1_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_91])).
75.37/9.02	thf(c_0_102, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (~($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~((epred5_2 @ X1 @ X4))|~((imp @ (($true)) @ (($true))))|~((imp @ (~($true)) @ (~($true))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(cn,[status(thm)],[c_0_92])).
75.37/9.02	thf(c_0_103, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (~($true)))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((imp @ (~($true)) @ (($true))))|~((epred5_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_93])).
75.37/9.02	thf(c_0_104, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (($true)))|(imp @ (~($true)) @ (($true)))|(imp @ (($true)) @ (~($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((epred1_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_94]), c_0_95])).
75.37/9.02	thf(c_0_105, plain, ![X631:$i, X632:$i]:((~(in @ X631 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X632 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X631)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X632)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X632)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X631)))|(epred5_2 @ X631 @ X632))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_96])])])])).
75.37/9.02	thf(c_0_106, plain, ![X629:$i, X630:$i]:((~(in @ X629 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X630 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(epred3_2 @ X629 @ X630)|~(epred4_2 @ X629 @ X630)|(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X629)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X630)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X630)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X629))))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_97])])])])).
75.37/9.02	thf(c_0_107, plain, ![X753:$i, X754:$i]:(((((((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753))))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753)))))|(epred3_2 @ X754 @ X753))&(((($true)|~($true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753))))|(~(n_some @ 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X753))))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred3_2 @ X754 @ X753))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753))))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred3_2 @ X754 @ X753)))))&((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753))))|(($true)|~($true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred3_2 @ X754 @ X753))&(((($true)|~($true)|(($true)|~($true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred3_2 @ X754 @ X753))&(~(imp @ $false @ $false)|~($true)|(($true)|~($true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred3_2 @ X754 @ X753)))&((($true)|~(imp @ $false @ $true)|(($true)|~($true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred3_2 @ X754 @ X753))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(($true)|~($true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred3_2 @ X754 @ X753)))))&((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753))))|(~(imp @ $true @ $false)|~($true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred3_2 @ X754 @ X753))&(((($true)|~($true)|(~(imp @ $true @ $false)|~($true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred3_2 @ X754 @ X753))&(~(imp @ $false @ $false)|~($true)|(~(imp @ $true @ $false)|~($true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred3_2 @ X754 @ X753)))&((($true)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~($true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred3_2 @ X754 @ X753))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~($true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred3_2 @ X754 @ X753))))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753))))|(($true)|~(imp @ $true @ $true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred3_2 @ X754 @ X753))&(((($true)|~($true)|(($true)|~(imp @ $true @ $true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred3_2 @ X754 @ X753))&(~(imp @ $false @ $false)|~($true)|(($true)|~(imp @ $true @ $true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred3_2 @ X754 @ X753)))&((($true)|~(imp @ $false @ $true)|(($true)|~(imp @ $true @ $true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred3_2 @ X754 @ X753))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(($true)|~(imp @ $true @ $true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred3_2 @ X754 @ X753)))))&((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753))))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred3_2 @ X754 @ X753))&(((($true)|~($true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred3_2 @ X754 @ X753))&(~(imp @ $false @ $false)|~($true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred3_2 @ X754 @ X753)))&((($true)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred3_2 @ X754 @ X753))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred3_2 @ X754 @ X753))))))))&(((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred3_2 @ X754 @ X753))&((imp @ $false @ $false)|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred3_2 @ X754 @ X753)))&((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X753)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X754)))|(imp @ $false @ $true)|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred3_2 @ X754 @ X753))&((imp @ $false @ $false)|(imp @ $false @ $true)|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred3_2 @ X754 @ X753))))))))&(((($true)|~($true)|(epred3_2 @ X754 @ X753))&(~(imp @ $true @ $false)|~($true)|(epred3_2 @ X754 @ X753)))&((($true)|~(imp @ $true @ $true)|(epred3_2 @ X754 @ X753))&(~(imp @ $true @ $false)|~(imp @ $true @ $true)|(epred3_2 @ X754 @ X753)))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_98])])])])).
75.37/9.03	thf(c_0_108, plain, ![X506:$i, X507:$i]:(((epred2_2 @ X507 @ X506)<=>((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506))))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506))))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)))|(imp @ $true @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)))|(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)))|(imp @ $false @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)))|(imp @ $false @ $false))))))), introduced(definition)).
75.37/9.03	thf(c_0_109, plain, ![X1:$i, X4:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))|(imp @ (($true)) @ (~($true)))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)))))|~((epred5_2 @ X1 @ X4)))), inference(csr,[status(thm)],[c_0_99, c_0_100])).
75.37/9.03	thf(c_0_110, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)))|(imp @ (($true)) @ (~($true)))|~((epred1_2 @ X4 @ X1)))), inference(csr,[status(thm)],[c_0_101, c_0_76])).
75.37/9.03	thf(c_0_111, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|(imp @ (($true)) @ (~($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((imp @ (($true)) @ (($true))))|~((imp @ (~($true)) @ (~($true))))|~((epred5_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_102])).
75.37/9.03	thf(c_0_112, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (($true)))|(imp @ (($true)) @ (~($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((epred5_2 @ X1 @ X4))|~((epred1_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_103, c_0_94]), c_0_86]), c_0_104])).
75.37/9.03	thf(c_0_113, plain, ![X4:$i, X1:$i]:(((epred5_2 @ X1 @ X4)|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(split_conjunct,[status(thm)],[c_0_105])).
75.37/9.03	thf(c_0_114, plain, ![X1:$i, X4:$i]:(((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((epred3_2 @ X1 @ X4))|~((epred4_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_106])).
75.37/9.03	thf(c_0_115, plain, ![X518:$i]:(((in @ X518 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>![X517:$i]:(((in @ X517 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>![X516:$i]:(((in @ X516 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X517))))=>((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X516)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X517)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X516))))=>(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X516)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X516)))))))))))), inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz50]), c_0_42]), c_0_44]), c_0_41])])).
75.37/9.03	thf(c_0_116, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|(imp @ (($true)) @ (~($true)))|(imp @ (($true)) @ (($true)))|(epred3_2 @ X4 @ X1)|~((imp @ (~($true)) @ (~($true))))|~(($true)))), inference(split_conjunct,[status(thm)],[c_0_107])).
75.37/9.03	thf(c_0_117, plain, ![X1:$i, X4:$i]:(((epred3_2 @ X1 @ X4)|~((imp @ (($true)) @ (~($true))))|~(($true)))), inference(split_conjunct,[status(thm)],[c_0_107])).
75.37/9.03	thf(c_0_118, plain, ![X506:$i, X507:$i]:(((epred2_2 @ X507 @ X506)=>((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506))))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506))))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)))|(imp @ $true @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)))|(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)))|(imp @ $false @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)))|(imp @ $false @ $false))))))), inference(split_equiv,[status(thm)],[c_0_108])).
75.37/9.03	thf(c_0_119, plain, ![X1:$i, X4:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))|(imp @ (($true)) @ (~($true)))|~((epred5_2 @ X1 @ X4))|~((epred1_2 @ X1 @ X4)))), inference(spm,[status(thm)],[c_0_109, c_0_110])).
75.37/9.03	thf(c_0_120, plain, ![X1:$i, X4:$i]:(((imp @ (~($true)) @ (($true)))|(imp @ (($true)) @ (~($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((epred1_2 @ X1 @ X4))|~((epred5_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_111]), c_0_95]), c_0_112])).
75.37/9.03	thf(c_0_121, plain, ![X4:$i, X1:$i]:(((epred5_2 @ X1 @ X4)|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[c_0_113])).
75.37/9.03	thf(c_0_122, plain, ![X1:$i, X4:$i]:(((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((epred3_2 @ X1 @ X4))|~((epred4_2 @ X1 @ X4)))), inference(cn,[status(thm)],[c_0_114])).
75.37/9.03	thf(c_0_123, negated_conjecture, (in @ esk2_0 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))), inference(split_conjunct,[status(thm)],[c_0_64])).
75.37/9.03	thf(c_0_124, plain, ![X1:$i, X4:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|(imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|~(($true))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)))))|~((epred1_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_53])).
75.37/9.03	thf(c_0_125, plain, ![X637:$i, X638:$i, X639:$i]:((~(in @ X637 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X638 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X639 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X638)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X637)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X637)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X638))))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X639)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X638)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X638)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X639))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X639)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X637)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X637)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X639)))))))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_115])])])])).
75.37/9.03	thf(c_0_126, plain, ![X4:$i, X1:$i]:(((epred3_2 @ X4 @ X1)|(imp @ (($true)) @ (($true)))|(imp @ (($true)) @ (~($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((imp @ (~($true)) @ (~($true)))))), inference(cn,[status(thm)],[c_0_116])).
75.37/9.03	thf(c_0_127, plain, ![X1:$i, X4:$i]:(((epred3_2 @ X1 @ X4)|~((imp @ (($true)) @ (~($true)))))), inference(cn,[status(thm)],[c_0_117])).
75.37/9.03	thf(c_0_128, plain, ![X751:$i, X752:$i]:((((((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $true @ $true)|(($true)|~(imp @ $true @ $true)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $true @ $false)|(($true)|~(imp @ $true @ $true)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751)))&((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $true @ $true)|(~($true)|~(imp @ $true @ $false)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $true @ $false)|(~($true)|~(imp @ $true @ $false)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751))))&(((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $true @ $true)|(($true)|~(imp @ $false @ $true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $true @ $false)|(($true)|~(imp @ $false @ $true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751)))&((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $true @ $true)|(~($true)|~(imp @ $false @ $false)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $true @ $false)|(~($true)|~(imp @ $false @ $false)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751)))))&((((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $false @ $true)|(($true)|(imp @ $true @ $true)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $false @ $false)|(($true)|(imp @ $true @ $true)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751)))&((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $false @ $true)|(~($true)|(imp @ $true @ $false)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $false @ $false)|(~($true)|(imp @ $true @ $false)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751))))&(((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $false @ $true)|(($true)|(imp @ $false @ $true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $false @ $false)|(($true)|(imp @ $false @ $true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751)))&((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $false @ $true)|(~($true)|(imp @ $false @ $false)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)))|(imp @ $false @ $false)|(~($true)|(imp @ $false @ $false)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X752)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X751)))))|~(epred2_2 @ X752 @ X751))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_118])])])])).
75.37/9.03	thf(c_0_129, plain, ![X508:$i, X509:$i]:(((((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508))))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508))))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)))|(imp @ $true @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)))|(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)))|(imp @ $false @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X508)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)))|(imp @ $false @ $false)))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false))))=>(epred4_2 @ X509 @ X508))), inference(split_equiv,[status(thm)],[c_0_88])).
75.37/9.03	thf(c_0_130, plain, ![X1:$i, X4:$i]:(((imp @ (~($true)) @ (~($true)))|(imp @ (~($true)) @ (($true)))|(imp @ (~($true)) @ (~($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~(($true))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~(($true))|~((epred5_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_72])).
75.37/9.03	thf(c_0_131, plain, ![X1:$i, X4:$i]:(((imp @ (~($true)) @ (~($true)))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|(imp @ (~($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~(($true))|~(($true))|~((epred5_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_72])).
75.37/9.03	thf(c_0_132, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((imp @ (~($true)) @ (($true))))|~((imp @ (($true)) @ (($true))))|~((epred5_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_103, c_0_111]), c_0_86])).
75.37/9.03	thf(c_0_133, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|(imp @ (($true)) @ (($true)))|~((epred5_2 @ X1 @ X4))|~((epred1_2 @ X1 @ X4)))), inference(spm,[status(thm)],[c_0_112, c_0_119])).
75.37/9.03	thf(c_0_134, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (($true)))|~((epred1_2 @ X1 @ X4))|~((epred5_2 @ X1 @ X4)))), inference(spm,[status(thm)],[c_0_120, c_0_119])).
75.37/9.03	thf(c_0_135, plain, ![X1:$i, X4:$i]:(((epred5_2 @ X1 @ X4)|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((epred3_2 @ X1 @ X4))|~((epred4_2 @ X1 @ X4)))), inference(spm,[status(thm)],[c_0_121, c_0_122])).
75.37/9.03	thf(c_0_136, negated_conjecture, (in @ esk2_0 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))), inference(cn,[status(thm)],[c_0_123])).
75.37/9.03	thf(c_0_137, negated_conjecture, (in @ esk1_0 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))), inference(split_conjunct,[status(thm)],[c_0_64])).
75.37/9.03	thf(c_0_138, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|~((epred1_2 @ X1 @ X4))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))))), inference(cn,[status(thm)],[c_0_124])).
75.37/9.03	thf(c_0_139, plain, ![X1:$i, X4:$i, X5:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X5)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X5))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X5 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X5)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X5))))))), inference(split_conjunct,[status(thm)],[c_0_125])).
75.37/9.03	thf(c_0_140, negated_conjecture, (n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ esk2_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ esk3_0)))), inference(split_conjunct,[status(thm)],[c_0_64])).
75.37/9.03	thf(c_0_141, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|(imp @ (($true)) @ (($true)))|(epred3_2 @ X4 @ X1)|~((imp @ (~($true)) @ (~($true)))))), inference(csr,[status(thm)],[inference(cn,[status(thm)],[c_0_126]), c_0_127])).
75.37/9.03	thf(c_0_142, plain, ![X1:$i, X4:$i]:(((imp @ (~($true)) @ (($true)))|(imp @ (~($true)) @ (~($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~(($true))|~((epred2_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_128])).
75.37/9.03	thf(c_0_143, plain, ![X1:$i, X4:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|(imp @ (~($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~(($true))|~((epred2_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_128])).
75.37/9.03	thf(c_0_144, plain, ![X755:$i, X756:$i]:(((((((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755))))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)))))|(epred4_2 @ X756 @ X755))&(((($true)|~($true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755))))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)))))|(epred4_2 @ X756 @ X755))&(~(imp @ $false @ $false)|~($true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755))))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)))))|(epred4_2 @ X756 @ X755)))&((($true)|~(imp @ $false @ $true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755))))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)))))|(epred4_2 @ X756 @ X755))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755))))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)))))|(epred4_2 @ X756 @ X755)))))&((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755))))|(($true)|~($true))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)))))|(epred4_2 @ X756 @ X755))&(((($true)|~($true)|(($true)|~($true))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)))))|(epred4_2 @ X756 @ X755))&(~(imp @ $false @ $false)|~($true)|(($true)|~($true))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)))))|(epred4_2 @ X756 @ X755)))&((($true)|~(imp @ $false @ $true)|(($true)|~($true))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ 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(times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred4_2 @ X756 @ X755)))&((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X756)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X755)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 @ $false @ $false)|~($true)|(epred4_2 @ X756 @ X755)))&((($true)|~(imp @ $false @ $true)|(epred4_2 @ X756 @ X755))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(epred4_2 @ X756 @ X755)))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_129])])])])).
75.37/9.03	thf(c_0_145, plain, ![X1:$i, X4:$i]:(((imp @ (~($true)) @ (~($true)))|(imp @ (~($true)) @ (($true)))|(imp @ (($true)) @ (~($true)))|~(($true))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~(($true))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)))))|~((epred5_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_72])).
75.37/9.03	thf(c_0_146, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~(($true))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((imp @ (~($true)) @ (($true))))|~(($true))|~((epred5_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_72])).
75.37/9.03	thf(c_0_147, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (($true)))|(imp @ (~($true)) @ (~($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~((epred5_2 @ X1 @ X4))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(cn,[status(thm)],[c_0_130])).
75.37/9.03	thf(c_0_148, plain, ![X1:$i, X4:$i]:(((imp @ (~($true)) @ (~($true)))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~((epred5_2 @ X1 @ X4)))), inference(cn,[status(thm)],[c_0_131])).
75.37/9.03	thf(c_0_149, plain, ![X539:$i]:(((in @ X539 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>![X538:$i]:(((in @ X538 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X539)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X538)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X538)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X539)))=>(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X539)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X538)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X538)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X539))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz42]), c_0_42]), c_0_43]), c_0_44]), c_0_41])).
75.37/9.03	thf(c_0_150, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|~((epred5_2 @ X1 @ X4))|~((epred1_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_132, c_0_119]), c_0_133]), c_0_134])).
75.37/9.03	thf(c_0_151, negated_conjecture, (epred1_2 @ esk1_0 @ esk2_0), inference(split_conjunct,[status(thm)],[c_0_64])).
75.37/9.03	thf(c_0_152, negated_conjecture, ![X1:$i]:(((epred5_2 @ X1 @ esk2_0)|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((epred3_2 @ X1 @ esk2_0))|~((epred4_2 @ X1 @ esk2_0)))), inference(spm,[status(thm)],[c_0_135, c_0_136])).
75.37/9.03	thf(c_0_153, negated_conjecture, (in @ esk1_0 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))), inference(cn,[status(thm)],[c_0_137])).
75.37/9.03	thf(c_0_154, plain, ![X1:$i, X4:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))|(imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)))))|~((epred1_2 @ X1 @ X4)))), inference(cn,[status(thm)],[c_0_138])).
75.37/9.03	thf(c_0_155, plain, ![X1:$i, X5:$i, X4:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X5)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X5)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X5)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X5)))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X5 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[c_0_139])).
75.37/9.03	thf(c_0_156, negated_conjecture, (n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk3_0)))), inference(cn,[status(thm)],[c_0_140])).
75.37/9.03	thf(c_0_157, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (($true)))|(epred3_2 @ X4 @ X1)|((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))<~>(imp @ (($true)) @ (($true))))|~((imp @ (~($true)) @ (~($true)))))), inference(ext_eqfact,[status(thm)],[c_0_141])).
75.37/9.03	thf(c_0_158, plain, ![X1:$i, X4:$i]:(((imp @ (~($true)) @ (($true)))|(imp @ (($true)) @ (~($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~(($true))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)))))|~((epred2_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_128])).
75.37/9.03	thf(c_0_159, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (($true)))|(imp @ (~($true)) @ (~($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~((epred2_2 @ X1 @ X4))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(cn,[status(thm)],[c_0_142])).
75.37/9.03	thf(c_0_160, plain, ![X1:$i, X4:$i]:(((imp @ (~($true)) @ (~($true)))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~((epred2_2 @ X1 @ X4)))), inference(cn,[status(thm)],[c_0_143])).
75.37/9.03	thf(c_0_161, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~(($true))|~((imp @ (($true)) @ (~($true))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)))))|~((epred2_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_128])).
75.37/9.03	thf(c_0_162, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (~($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|(epred4_2 @ X1 @ X4)|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((imp @ (~($true)) @ (($true))))|~(($true)))), inference(split_conjunct,[status(thm)],[c_0_144])).
75.37/9.03	thf(c_0_163, plain, ![X1:$i, X4:$i]:(((epred4_2 @ X1 @ X4)|~((imp @ (~($true)) @ (~($true))))|~(($true)))), inference(split_conjunct,[status(thm)],[c_0_144])).
75.37/9.03	thf(c_0_164, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|(epred4_2 @ X1 @ X4)|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((imp @ (~($true)) @ (($true))))|~(($true))|~(($true)))), inference(split_conjunct,[status(thm)],[c_0_144])).
75.37/9.03	thf(c_0_165, plain, ![X4:$i, X1:$i]:(((epred4_2 @ X1 @ X4)|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((imp @ (~($true)) @ (($true))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((imp @ (($true)) @ (($true)))))), inference(split_conjunct,[status(thm)],[c_0_144])).
75.37/9.03	thf(c_0_166, plain, ![X4:$i, X1:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)))|(epred4_2 @ X4 @ X1)|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))|~((imp @ (($true)) @ (~($true))))|~(($true))|~((imp @ (($true)) @ (~($true)))))), inference(split_conjunct,[status(thm)],[c_0_144])).
75.37/9.03	thf(c_0_167, plain, ![X507:$i]:(((in @ X507 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>![X506:$i]:(((in @ X506 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>(((~(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X506)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X507)))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))=>(epred2_2 @ X507 @ X506)))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz41e]), c_0_42]), c_0_43]), c_0_31]), c_0_44]), c_0_45])])]), c_0_108])).
75.37/9.03	thf(c_0_168, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (($true)))|(imp @ (~($true)) @ (~($true)))|~((epred5_2 @ X1 @ X4))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))))), inference(cn,[status(thm)],[c_0_145])).
75.37/9.03	thf(c_0_169, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~((epred5_2 @ X1 @ X4))|~((imp @ (~($true)) @ (($true))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(cn,[status(thm)],[c_0_146])).
75.37/9.03	thf(c_0_170, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|(imp @ (~($true)) @ (~($true)))|(imp @ (~($true)) @ (($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((epred5_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_147])).
75.37/9.03	thf(c_0_171, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)))|(imp @ (~($true)) @ (~($true)))|~((epred5_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_148])).
75.37/9.03	thf(c_0_172, plain, ![X665:$i, X666:$i]:((~(in @ X665 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X666 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X665)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X666)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X666)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X665)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X665)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X666)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X666)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X665)))))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_149])])])])).
75.37/9.03	thf(c_0_173, negated_conjecture, ((imp @ (($true)) @ (~($true)))|~((epred5_2 @ esk1_0 @ esk2_0))), inference(spm,[status(thm)],[c_0_150, c_0_151])).
75.37/9.03	thf(c_0_174, negated_conjecture, ((epred5_2 @ esk1_0 @ esk2_0)|~((epred3_2 @ esk1_0 @ esk2_0))|~((epred4_2 @ esk1_0 @ esk2_0))), inference(spm,[status(thm)],[c_0_152, c_0_153])).
75.37/9.03	thf(c_0_175, plain, ![X1:$i, X4:$i]:(((imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|~((epred1_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_154, c_0_76]), c_0_95])).
75.37/9.03	thf(c_0_176, negated_conjecture, ~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ esk1_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ esk3_0))))), inference(split_conjunct,[status(thm)],[c_0_64])).
75.37/9.03	thf(c_0_177, negated_conjecture, ![X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk3_0))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk2_0)))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155, c_0_156]), c_0_78]), c_0_136])])).
75.37/9.03	thf(c_0_178, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|(imp @ (($true)) @ (($true)))|(epred3_2 @ X4 @ X1)|~((imp @ (~($true)) @ (~($true)))))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_157])])])).
75.37/9.03	thf(c_0_179, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (($true)))|~((epred2_2 @ X1 @ X4))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))))), inference(cn,[status(thm)],[c_0_158])).
75.37/9.03	thf(c_0_180, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|(imp @ (~($true)) @ (~($true)))|(imp @ (~($true)) @ (($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((epred2_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_159])).
75.37/9.03	thf(c_0_181, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)))|(imp @ (~($true)) @ (~($true)))|~((epred2_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_160])).
75.37/9.03	thf(c_0_182, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (($true)))|~((epred2_2 @ X1 @ X4))|~((imp @ (($true)) @ (~($true))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))))), inference(cn,[status(thm)],[c_0_161])).
75.37/9.03	thf(c_0_183, plain, ![X4:$i, X1:$i]:(((epred4_2 @ X1 @ X4)|(imp @ (~($true)) @ (~($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~((imp @ (~($true)) @ (($true))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(cn,[status(thm)],[c_0_162])).
75.37/9.03	thf(c_0_184, plain, ![X1:$i, X4:$i]:(((epred4_2 @ X1 @ X4)|~((imp @ (~($true)) @ (~($true)))))), inference(cn,[status(thm)],[c_0_163])).
75.37/9.03	thf(c_0_185, plain, ![X4:$i, X1:$i]:(((epred4_2 @ X1 @ X4)|(imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))|~((imp @ (~($true)) @ (($true))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(cn,[status(thm)],[c_0_164])).
75.37/9.03	thf(c_0_186, plain, ![X4:$i, X1:$i]:(((epred4_2 @ X1 @ X4)|~((imp @ (($true)) @ (($true))))|~((imp @ (~($true)) @ (($true))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(cn,[status(thm)],[c_0_165])).
75.37/9.03	thf(c_0_187, plain, ![X4:$i, X1:$i]:(((epred4_2 @ X4 @ X1)|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)))|~((imp @ (($true)) @ (~($true))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))))), inference(cn,[status(thm)],[c_0_166])).
75.37/9.03	thf(c_0_188, plain, ![X627:$i, X628:$i]:((((~(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X627)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X628)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X628)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X627)))|(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X627)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X628)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X628)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X627)))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))&(((($true)|~($true)|(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X627)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X628)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X628)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X627)))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))&(~(imp @ $false @ $false)|~($true)|(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X627)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X628)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X628)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X627)))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))&((($true)|~(imp @ $false @ $true)|(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X627)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X628)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X628)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X627)))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X627)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X628)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X628)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X627)))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))))&((((~(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X627)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X628)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X628)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X627)))|(($true)|~($true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))&(((($true)|~($true)|(($true)|~($true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))&(~(imp @ $false @ $false)|~($true)|(($true)|~($true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))&((($true)|~(imp @ $false @ $true)|(($true)|~($true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(($true)|~($true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))))&((~(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X627)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X628)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X628)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X627)))|(~(imp @ $true @ $false)|~($true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))&(((($true)|~($true)|(~(imp @ $true @ $false)|~($true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))&(~(imp @ $false @ $false)|~($true)|(~(imp @ $true @ $false)|~($true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))&((($true)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~($true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~($true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))))))&(((~(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X627)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X628)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X628)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X627)))|(($true)|~(imp @ $true @ $true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))&(((($true)|~($true)|(($true)|~(imp @ $true @ $true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))&(~(imp @ $false @ $false)|~($true)|(($true)|~(imp @ $true @ $true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))&((($true)|~(imp @ $false @ $true)|(($true)|~(imp @ $true @ $true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(($true)|~(imp @ $true @ $true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))))&((~(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X627)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X628)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X628)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X627)))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))&(((($true)|~($true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))&(~(imp @ $false @ $false)|~($true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))&((($true)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_167])])])])])).
75.37/9.03	thf(c_0_189, plain, ![X1:$i, X4:$i]:(((imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (($true)))|~(($true))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~(($true))|~((imp @ (($true)) @ (~($true))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)))))|~((epred5_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_72])).
75.37/9.03	thf(c_0_190, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (~($true)))|(imp @ (~($true)) @ (($true)))|(imp @ (($true)) @ (~($true)))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((epred5_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_168])).
75.37/9.03	thf(c_0_191, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|(imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((imp @ (~($true)) @ (($true))))|~((epred5_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_169])).
75.37/9.03	thf(c_0_192, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|(imp @ (~($true)) @ (($true)))|(imp @ (~($true)) @ (~($true)))|~((epred5_2 @ X4 @ X1)))), inference(csr,[status(thm)],[c_0_170, c_0_171])).
75.37/9.03	thf(c_0_193, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(split_conjunct,[status(thm)],[c_0_172])).
75.37/9.03	thf(c_0_194, negated_conjecture, ((imp @ (($true)) @ (~($true)))|~((epred3_2 @ esk1_0 @ esk2_0))|~((epred4_2 @ esk1_0 @ esk2_0))), inference(spm,[status(thm)],[c_0_173, c_0_174])).
75.37/9.03	thf(c_0_195, negated_conjecture, ((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))), inference(spm,[status(thm)],[c_0_175, c_0_151])).
75.37/9.03	thf(c_0_196, negated_conjecture, ~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk3_0))))), inference(cn,[status(thm)],[c_0_176])).
75.37/9.03	thf(c_0_197, plain, ![X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk3_0))))|(imp @ (($true)) @ (($true)))|(epred3_2 @ X1 @ esk2_0)|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (~($true)))))), inference(spm,[status(thm)],[c_0_177, c_0_178])).
75.37/9.03	thf(c_0_198, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (($true)))|(imp @ (($true)) @ (~($true)))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((epred2_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_179])).
75.37/9.03	thf(c_0_199, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|(imp @ (~($true)) @ (($true)))|(imp @ (~($true)) @ (~($true)))|~((epred2_2 @ X4 @ X1)))), inference(csr,[status(thm)],[c_0_180, c_0_181])).
75.37/9.03	thf(c_0_200, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (($true)))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((imp @ (($true)) @ (~($true))))|~((epred2_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_182])).
75.37/9.03	thf(c_0_201, plain, ![X1:$i, X4:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|(epred4_2 @ X4 @ X1)|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((imp @ (~($true)) @ (($true)))))), inference(csr,[status(thm)],[inference(cn,[status(thm)],[c_0_183]), c_0_184])).
75.37/9.03	thf(c_0_202, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (~($true)))|(epred4_2 @ X1 @ X4)|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((imp @ (~($true)) @ (($true)))))), inference(csr,[status(thm)],[inference(cn,[status(thm)],[c_0_185]), c_0_184])).
75.37/9.03	thf(c_0_203, plain, ![X4:$i, X1:$i]:(((epred4_2 @ X1 @ X4)|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((imp @ (($true)) @ (($true))))|~((imp @ (~($true)) @ (($true)))))), inference(cn,[status(thm)],[c_0_186])).
75.37/9.03	thf(c_0_204, plain, ![X1:$i, X4:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))|(epred4_2 @ X1 @ X4)|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)))))|~((imp @ (($true)) @ (~($true)))))), inference(cn,[status(thm)],[c_0_187])).
75.37/9.03	thf(c_0_205, plain, ![X4:$i, X1:$i]:(((epred2_2 @ X1 @ X4)|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((imp @ (($true)) @ (~($true))))|~(($true))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))), inference(split_conjunct,[status(thm)],[c_0_188])).
75.37/9.03	thf(c_0_206, plain, ![X545:$i]:(((in @ X545 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>![X544:$i]:(((in @ X544 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X544)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X545)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X545)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X544))))=>(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X544)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X545)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X545)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X544)))))))), inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz43]), c_0_42]), c_0_43]), c_0_44]), c_0_41])])).
75.37/9.03	thf(c_0_207, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (($true)))|(imp @ (~($true)) @ (~($true)))|~((epred5_2 @ X1 @ X4))|~((imp @ (($true)) @ (~($true))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))))), inference(cn,[status(thm)],[c_0_189])).
75.37/9.03	thf(c_0_208, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((epred5_2 @ X4 @ X1)))), inference(csr,[status(thm)],[c_0_190, c_0_103])).
75.37/9.03	thf(c_0_209, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|(imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))|~((epred5_2 @ X4 @ X1)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_191, c_0_192]), c_0_171])).
75.37/9.03	thf(c_0_210, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[c_0_193])).
75.37/9.03	thf(c_0_211, plain, ((imp @ (($true)) @ (~($true)))|~((epred3_2 @ esk1_0 @ esk2_0))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_194, c_0_184]), c_0_195])).
75.37/9.03	thf(c_0_212, negated_conjecture, ((epred3_2 @ esk1_0 @ esk2_0)|(imp @ (($true)) @ (($true)))|~((imp @ (~($true)) @ (~($true))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196, c_0_197]), c_0_153])])).
75.37/9.03	thf(c_0_213, plain, ![X1:$i, X4:$i]:(((imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((epred2_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_198, c_0_199]), c_0_86])).
75.37/9.03	thf(c_0_214, plain, ![X1:$i, X4:$i]:(((epred4_2 @ X1 @ X4)|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((imp @ (~($true)) @ (($true))))|~((epred2_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_200, c_0_201]), c_0_202]), c_0_203])).
75.37/9.03	thf(c_0_215, plain, ![X1:$i, X4:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))|(epred4_2 @ X1 @ X4)|~((epred2_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_204, c_0_181]), c_0_195]), c_0_184])).
75.37/9.03	thf(c_0_216, plain, ![X4:$i, X1:$i]:(((epred2_2 @ X1 @ X4)|~((imp @ (($true)) @ (~($true))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(cn,[status(thm)],[c_0_205])).
75.37/9.03	thf(c_0_217, plain, ![X671:$i, X672:$i]:((~(in @ X671 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X672 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X672)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X671)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X671)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X672))))|(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X672)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X671)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X671)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X672))))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_206])])])])).
75.37/9.03	thf(c_0_218, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (($true)))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((imp @ (($true)) @ (~($true))))|~((epred5_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_207])).
75.37/9.03	thf(c_0_219, plain, ![X1:$i, X4:$i]:(((imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((epred5_2 @ X1 @ X4)))), inference(spm,[status(thm)],[c_0_208, c_0_209])).
75.37/9.03	thf(c_0_220, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (($true)) @ (~($true))))|~((epred2_2 @ X1 @ X4)))), inference(spm,[status(thm)],[c_0_200, c_0_210])).
75.37/9.03	thf(c_0_221, plain, ((imp @ (($true)) @ (($true)))|(imp @ (($true)) @ (~($true)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_211, c_0_212]), c_0_195])).
75.37/9.03	thf(c_0_222, plain, ![X1:$i, X4:$i]:(((imp @ (~($true)) @ (~($true)))|(imp @ (~($true)) @ (($true)))|(imp @ (($true)) @ (($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((epred2_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_200, c_0_199]), c_0_213])).
75.37/9.03	thf(c_0_223, plain, ![X1:$i, X4:$i]:(((epred4_2 @ X1 @ X4)|~((imp @ (~($true)) @ (($true))))|~((epred2_2 @ X1 @ X4)))), inference(spm,[status(thm)],[c_0_214, c_0_215])).
75.37/9.03	thf(c_0_224, plain, ![X4:$i, X1:$i]:(((epred2_2 @ X1 @ X4)|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (($true)) @ (~($true)))))), inference(cn,[status(thm)],[c_0_216])).
75.37/9.03	thf(c_0_225, plain, ![X1:$i, X4:$i]:(((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))))), inference(split_conjunct,[status(thm)],[c_0_217])).
75.37/9.03	thf(c_0_226, plain, ![X1:$i, X4:$i]:(((imp @ (~($true)) @ (($true)))|(imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((epred5_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_218, c_0_192]), c_0_219])).
75.37/9.03	thf(c_0_227, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((epred2_2 @ X1 @ X4))|~((epred4_2 @ X4 @ X1)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_220, c_0_122]), c_0_127]), c_0_221])).
75.37/9.03	thf(c_0_228, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (($true)))|(epred4_2 @ X1 @ X4)|~((epred2_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_222, c_0_215]), c_0_223]), c_0_184])).
75.37/9.03	thf(c_0_229, plain, ![X1:$i, X4:$i]:(((epred2_2 @ X1 @ X4)|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (($true)) @ (~($true))))|~((epred4_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_224, c_0_122]), c_0_127])).
75.37/9.03	thf(c_0_230, plain, ![X1:$i, X4:$i]:(((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[c_0_225])).
75.37/9.03	thf(c_0_231, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (($true)))|(epred4_2 @ X1 @ X4)|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((epred5_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_218, c_0_201]), c_0_226]), c_0_219]), c_0_184])).
75.37/9.03	thf(c_0_232, plain, ![X1:$i, X4:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))|(epred4_2 @ X1 @ X4)|~((epred5_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_204, c_0_171]), c_0_195]), c_0_184])).
75.37/9.03	thf(c_0_233, plain, ![X1:$i]:(((imp @ (($true)) @ (($true)))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((epred2_2 @ X1 @ X1)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_227, c_0_70]), c_0_228])).
75.37/9.03	thf(c_0_234, negated_conjecture, ![X1:$i]:(((epred2_2 @ X1 @ esk3_0)|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (($true)) @ (~($true))))|~((epred4_2 @ X1 @ esk3_0)))), inference(spm,[status(thm)],[c_0_229, c_0_78])).
75.37/9.03	thf(c_0_235, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (~($true)))|(imp @ (~($true)) @ (($true)))|((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))<~>(imp @ (~($true)) @ (~($true))))|~((epred1_2 @ X4 @ X1)))), inference(ext_eqfact,[status(thm)],[c_0_85])).
75.37/9.03	thf(c_0_236, plain, ![X4:$i, X1:$i]:(((epred4_2 @ X4 @ X1)|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))|~((imp @ (($true)) @ (~($true))))|~(($true))|~((imp @ (($true)) @ (~($true))))|~((imp @ (($true)) @ (($true)))))), inference(split_conjunct,[status(thm)],[c_0_144])).
75.37/9.03	thf(c_0_237, plain, ![X1:$i, X4:$i]:(((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))|(epred4_2 @ X4 @ X1)|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (($true)))))), inference(spm,[status(thm)],[c_0_230, c_0_201])).
75.37/9.03	thf(c_0_238, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (($true)))|(epred4_2 @ X1 @ X4)|~((epred5_2 @ X1 @ X4)))), inference(spm,[status(thm)],[c_0_231, c_0_232])).
75.37/9.03	thf(c_0_239, negated_conjecture, ((imp @ (($true)) @ (($true)))|~((epred2_2 @ esk3_0 @ esk3_0))), inference(spm,[status(thm)],[c_0_233, c_0_78])).
75.37/9.03	thf(c_0_240, negated_conjecture, ((epred2_2 @ esk3_0 @ esk3_0)|~((imp @ (($true)) @ (~($true))))|~((epred4_2 @ esk3_0 @ esk3_0))), inference(spm,[status(thm)],[c_0_234, c_0_78])).
75.37/9.03	thf(c_0_241, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|(imp @ (~($true)) @ (($true)))|(imp @ (~($true)) @ (~($true)))|~((epred1_2 @ X4 @ X1)))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_235])])])).
75.37/9.03	thf(c_0_242, plain, ![X4:$i, X1:$i]:(((epred4_2 @ X4 @ X1)|~((imp @ (($true)) @ (($true))))|~((imp @ (($true)) @ (~($true))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))))), inference(cn,[status(thm)],[c_0_236])).
75.37/9.03	thf(c_0_243, plain, ![X1:$i, X4:$i]:(((epred4_2 @ X1 @ X4)|(epred5_2 @ X4 @ X1)|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (($true)))))), inference(spm,[status(thm)],[c_0_121, c_0_237])).
75.37/9.03	thf(c_0_244, plain, ![X1:$i, X4:$i]:(((epred4_2 @ X1 @ X4)|~((imp @ (~($true)) @ (($true))))|~((epred5_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_203, c_0_232]), c_0_238])).
75.37/9.03	thf(c_0_245, negated_conjecture, ((imp @ (($true)) @ (($true)))|~((epred4_2 @ esk3_0 @ esk3_0))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_239, c_0_240]), c_0_221])).
75.37/9.03	thf(c_0_246, plain, ![X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk3_0))))|(imp @ (~($true)) @ (~($true)))|(imp @ (~($true)) @ (($true)))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((epred1_2 @ X1 @ esk2_0)))), inference(spm,[status(thm)],[c_0_177, c_0_241])).
75.37/9.03	thf(c_0_247, plain, ![X1:$i, X4:$i]:(((epred4_2 @ X1 @ X4)|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)))))|~((imp @ (($true)) @ (($true))))|~((imp @ (($true)) @ (~($true)))))), inference(cn,[status(thm)],[c_0_242])).
75.37/9.03	thf(c_0_248, plain, ![X1:$i]:(((epred4_2 @ X1 @ X1)|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (($true)))))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_243, c_0_70]), c_0_244])).
75.37/9.03	thf(c_0_249, plain, ((imp @ (($true)) @ (($true)))|~((imp @ (~($true)) @ (~($true))))), inference(spm,[status(thm)],[c_0_245, c_0_184])).
75.37/9.03	thf(c_0_250, negated_conjecture, ((imp @ (~($true)) @ (($true)))|(imp @ (~($true)) @ (~($true)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196, c_0_246]), c_0_153]), c_0_151])])).
75.37/9.03	thf(c_0_251, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~(($true))|~((imp @ (($true)) @ (~($true))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)))))|~((epred1_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_53])).
75.37/9.03	thf(c_0_252, plain, ![X1:$i, X4:$i]:(((epred4_2 @ X1 @ X4)|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (($true)) @ (($true))))|~((imp @ (($true)) @ (~($true)))))), inference(spm,[status(thm)],[c_0_247, c_0_210])).
75.37/9.03	thf(c_0_253, negated_conjecture, ((epred4_2 @ esk3_0 @ esk3_0)|~((imp @ (~($true)) @ (($true))))), inference(spm,[status(thm)],[c_0_248, c_0_78])).
75.37/9.03	thf(c_0_254, negated_conjecture, ((imp @ (~($true)) @ (($true)))|(imp @ (($true)) @ (($true)))), inference(spm,[status(thm)],[c_0_249, c_0_250])).
75.37/9.03	thf(c_0_255, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (($true)))|~((epred1_2 @ X1 @ X4))|~((imp @ (($true)) @ (~($true))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))))), inference(cn,[status(thm)],[c_0_251])).
75.37/9.03	thf(c_0_256, negated_conjecture, ~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk3_0)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196, c_0_210]), c_0_153]), c_0_78])])).
75.37/9.03	thf(c_0_257, plain, ![X4:$i, X1:$i]:(((epred4_2 @ X1 @ X4)|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (($true)) @ (($true))))|~((imp @ (($true)) @ (~($true))))|~((epred4_2 @ X4 @ X1)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_252, c_0_122]), c_0_127])).
75.37/9.03	thf(c_0_258, negated_conjecture, (imp @ (($true)) @ (($true))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_245, c_0_253]), c_0_254])).
75.37/9.03	thf(c_0_259, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (($true)))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((imp @ (($true)) @ (~($true))))|~((epred1_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_255])).
75.37/9.03	thf(c_0_260, negated_conjecture, (~((epred3_2 @ esk3_0 @ esk1_0))|~((epred4_2 @ esk3_0 @ esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_256, c_0_122]), c_0_153]), c_0_78])])).
75.37/9.03	thf(c_0_261, plain, ![X4:$i, X1:$i]:(((epred4_2 @ X1 @ X4)|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (($true)) @ (~($true))))|~((epred4_2 @ X4 @ X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_257, c_0_258])])).
75.37/9.03	thf(c_0_262, plain, ![X1:$i, X4:$i]:(((epred4_2 @ X1 @ X4)|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((imp @ (~($true)) @ (($true))))|~((epred1_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_259, c_0_201]), c_0_202]), c_0_203])).
75.37/9.03	thf(c_0_263, plain, ![X1:$i, X4:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))|(epred4_2 @ X1 @ X4)|~((epred1_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_204, c_0_76]), c_0_195]), c_0_184])).
75.37/9.03	thf(c_0_264, plain, (~((epred3_2 @ esk3_0 @ esk1_0))|~((imp @ (~($true)) @ (~($true))))), inference(spm,[status(thm)],[c_0_260, c_0_184])).
75.37/9.03	thf(c_0_265, negated_conjecture, ![X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk3_0))))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk2_0))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177, c_0_210]), c_0_136])])).
75.37/9.03	thf(c_0_266, negated_conjecture, ![X1:$i]:(((epred4_2 @ esk2_0 @ X1)|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (($true)) @ (~($true))))|~((epred4_2 @ X1 @ esk2_0)))), inference(spm,[status(thm)],[c_0_261, c_0_136])).
75.37/9.03	thf(c_0_267, plain, ![X1:$i, X4:$i]:(((epred4_2 @ X1 @ X4)|~((imp @ (~($true)) @ (($true))))|~((epred1_2 @ X1 @ X4)))), inference(spm,[status(thm)],[c_0_262, c_0_263])).
75.37/9.03	thf(c_0_268, plain, (~((imp @ (~($true)) @ (~($true))))|~((imp @ (($true)) @ (~($true))))), inference(spm,[status(thm)],[c_0_264, c_0_127])).
75.37/9.03	thf(c_0_269, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (~($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~(($true))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((imp @ (~($true)) @ (~($true))))|~(($true))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((imp @ (($true)) @ (($true))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))), inference(split_conjunct,[status(thm)],[c_0_48])).
75.37/9.03	thf(c_0_270, negated_conjecture, ~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk2_0)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196, c_0_265]), c_0_153])])).
75.37/9.03	thf(c_0_271, negated_conjecture, ((epred4_2 @ esk2_0 @ esk1_0)|~((imp @ (($true)) @ (~($true))))|~((epred4_2 @ esk1_0 @ esk2_0))), inference(spm,[status(thm)],[c_0_266, c_0_153])).
75.37/9.03	thf(c_0_272, negated_conjecture, ((epred4_2 @ esk1_0 @ esk2_0)|~((imp @ (~($true)) @ (($true))))), inference(spm,[status(thm)],[c_0_267, c_0_151])).
75.37/9.03	thf(c_0_273, plain, ((imp @ (~($true)) @ (($true)))|~((imp @ (($true)) @ (~($true))))), inference(spm,[status(thm)],[c_0_268, c_0_250])).
75.37/9.03	thf(c_0_274, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (~($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~((imp @ (($true)) @ (($true))))|~((imp @ (~($true)) @ (~($true))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(cn,[status(thm)],[c_0_269])).
75.37/9.03	thf(c_0_275, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|~(($true))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((imp @ (~($true)) @ (~($true))))|~((imp @ (~($true)) @ (($true))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)))))|~(($true))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))), inference(split_conjunct,[status(thm)],[c_0_48])).
75.37/9.03	thf(c_0_276, negated_conjecture, (~((epred3_2 @ esk2_0 @ esk1_0))|~((epred4_2 @ esk2_0 @ esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_270, c_0_122]), c_0_153]), c_0_136])])).
75.37/9.03	thf(c_0_277, negated_conjecture, ((epred4_2 @ esk2_0 @ esk1_0)|~((imp @ (($true)) @ (~($true))))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_271, c_0_272]), c_0_273])).
75.37/9.03	thf(c_0_278, plain, ![X1:$i, X4:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|(imp @ (($true)) @ (~($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (($true)) @ (($true))))|~((imp @ (~($true)) @ (~($true)))))), inference(cn,[status(thm)],[c_0_274])).
75.37/9.03	thf(c_0_279, plain, ![X1:$i, X4:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|(imp @ (($true)) @ (~($true)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~(($true))|~((imp @ (~($true)) @ (~($true))))|~((epred2_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_128])).
75.37/9.03	thf(c_0_280, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (~($true)))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|(imp @ (($true)) @ (~($true)))|~(($true))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((imp @ (~($true)) @ (~($true))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)))))|~(($true))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))), inference(split_conjunct,[status(thm)],[c_0_48])).
75.37/9.03	thf(c_0_281, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|~((imp @ (~($true)) @ (($true))))|~((imp @ (~($true)) @ (~($true))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))))), inference(cn,[status(thm)],[c_0_275])).
75.37/9.03	thf(c_0_282, negated_conjecture, ~((imp @ (($true)) @ (~($true)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_276, c_0_277]), c_0_127])).
75.37/9.03	thf(c_0_283, plain, ![X1:$i, X4:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (($true)) @ (($true))))|~((imp @ (~($true)) @ (~($true)))))), inference(csr,[status(thm)],[c_0_278, c_0_268])).
75.37/9.03	thf(c_0_284, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~((epred2_2 @ X1 @ X4))|~((imp @ (~($true)) @ (~($true)))))), inference(cn,[status(thm)],[c_0_279])).
75.37/9.03	thf(c_0_285, plain, ![X522:$i]:(((in @ X522 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>![X521:$i]:(((in @ X521 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>![X520:$i]:(((in @ X520 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>![X519:$i]:(((in @ X519 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X521)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X522)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X522)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X521))))=>((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X522)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X520)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X520)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X522)))=>((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X521)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X519)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X519)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X521)))=>(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X519)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X520)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X520)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X519))))))))))))))), 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_42]), c_0_39]), c_0_44]), c_0_41])).
75.37/9.03	thf(c_0_286, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|~((imp @ (~($true)) @ (~($true))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))))), inference(cn,[status(thm)],[c_0_280])).
75.37/9.03	thf(c_0_287, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (($true))))|~((imp @ (~($true)) @ (~($true)))))), inference(cn,[status(thm)],[c_0_281])).
75.37/9.03	thf(c_0_288, negated_conjecture, (imp @ (~($true)) @ (~($true))), inference(sr,[status(thm)],[c_0_195, c_0_282])).
75.37/9.03	thf(c_0_289, plain, ![X1:$i, X4:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (~($true)))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_283, c_0_258])])).
75.37/9.03	thf(c_0_290, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)))|(imp @ (($true)) @ (~($true)))|~((imp @ (~($true)) @ (~($true))))|~((epred2_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_284])).
75.37/9.03	thf(c_0_291, plain, ![X640:$i, X641:$i, X642:$i, X643:$i]:((~(in @ X640 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X641 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X642 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X643 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X641)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X640)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X640)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X641))))|(~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X640)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X642)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X642)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X640)))|(~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X641)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X643)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X643)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X641)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X643)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X642)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X642)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X643)))))))))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_285])])])])).
75.37/9.03	thf(c_0_292, plain, ![X4:$i, X1:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))|(imp @ (($true)) @ (~($true)))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)))))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (~($true)))))), inference(cn,[status(thm)],[c_0_286])).
75.37/9.03	thf(c_0_293, plain, ![X1:$i, X4:$i]:((~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (($true)))))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_287, c_0_288])]), c_0_282])).
75.37/9.03	thf(c_0_294, plain, ![X1:$i, X4:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_289, c_0_288])])).
75.37/9.03	thf(c_0_295, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)))|(imp @ (($true)) @ (~($true)))|~((epred2_2 @ X4 @ X1)))), inference(csr,[status(thm)],[c_0_290, c_0_181])).
75.37/9.03	thf(c_0_296, plain, ![X4:$i, X1:$i]:(((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|(epred2_2 @ X1 @ X4)|~((imp @ (~($true)) @ (~($true))))|~(($true))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))), inference(split_conjunct,[status(thm)],[c_0_188])).
75.37/9.03	thf(c_0_297, plain, ![X1:$i, X6:$i, X5:$i, X4:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X6)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X5)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X5)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X6))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X5 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X6 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X5)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X5)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X6)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X6)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)))))), inference(split_conjunct,[status(thm)],[c_0_291])).
75.37/9.03	thf(c_0_298, plain, ![X4:$i, X1:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)))))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (~($true)))))), inference(csr,[status(thm)],[c_0_292, c_0_268])).
75.37/9.03	thf(c_0_299, plain, ![X4:$i, X1:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)))|(imp @ (($true)) @ (~($true)))|((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))<~>(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((epred1_2 @ X4 @ X1)))), inference(ext_eqfact,[status(thm)],[c_0_110])).
75.37/9.03	thf(c_0_300, plain, ![X4:$i, X1:$i]:((~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (($true)))))), inference(spm,[status(thm)],[c_0_293, c_0_294])).
75.37/9.03	thf(c_0_301, plain, ![X4:$i, X1:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)))|(imp @ (($true)) @ (~($true)))|((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))<~>(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((epred2_2 @ X4 @ X1)))), inference(ext_eqfact,[status(thm)],[c_0_295])).
75.37/9.03	thf(c_0_302, plain, ![X4:$i, X1:$i]:(((epred2_2 @ X1 @ X4)|(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|~((imp @ (~($true)) @ (~($true))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))), inference(cn,[status(thm)],[c_0_296])).
75.37/9.03	thf(c_0_303, plain, ![X1:$i, X4:$i, X5:$i, X6:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X5)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X6)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X6)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X5)))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X5)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X5))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X6)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X6))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X5 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X6 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[c_0_297])).
75.37/9.03	thf(c_0_304, plain, ![X4:$i, X1:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)))))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_298, c_0_288])])).
75.37/9.03	thf(c_0_305, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)))|(imp @ (($true)) @ (~($true)))|~((epred1_2 @ X4 @ X1)))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_299])])])).
75.37/9.03	thf(c_0_306, plain, ![X1:$i, X4:$i]:((~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((epred1_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_294]), c_0_282]), c_0_300])).
75.37/9.03	thf(c_0_307, plain, ![X4:$i, X1:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)))|(imp @ (($true)) @ (~($true)))|~((epred2_2 @ X4 @ X1)))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_301])])])).
75.37/9.03	thf(c_0_308, plain, ![X4:$i, X1:$i]:(((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))|(epred2_2 @ X1 @ X4)|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (~($true)))))), inference(cn,[status(thm)],[c_0_302])).
75.37/9.03	thf(c_0_309, negated_conjecture, ![X1:$i, X4:$i]:(((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk3_0))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk2_0))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_303, c_0_156]), c_0_78]), c_0_136])])).
75.37/9.03	thf(c_0_310, plain, ![X1:$i, X4:$i]:((~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((epred1_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_304, c_0_305]), c_0_282]), c_0_306])).
75.37/9.03	thf(c_0_311, plain, ![X1:$i, X4:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))|(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)))|(imp @ (($true)) @ (~($true)))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((epred2_2 @ X1 @ X4)))), inference(spm,[status(thm)],[c_0_230, c_0_307])).
75.37/9.03	thf(c_0_312, negated_conjecture, ((epred2_2 @ esk2_0 @ esk1_0)|~((imp @ (~($true)) @ (~($true))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_270, c_0_308]), c_0_153]), c_0_136])])).
75.37/9.03	thf(c_0_313, negated_conjecture, (~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk3_0))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk2_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk1_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk2_0))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196, c_0_309]), c_0_78]), c_0_153])])).
75.37/9.03	thf(c_0_314, plain, ![X1:$i, X4:$i]:(((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X4)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ X1)))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 43 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((epred1_2 @ X4 @ X1))|~((epred2_2 @ X1 @ X4)))), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_310, c_0_311]), c_0_282])).
75.37/9.03	thf(c_0_315, negated_conjecture, (epred2_2 @ esk2_0 @ esk1_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_312, c_0_288])])).
75.37/9.03	thf(c_0_316, negated_conjecture, ~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk3_0)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))) @ esk3_0)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_313, c_0_314]), c_0_136]), c_0_153]), c_0_151]), c_0_315])])).
75.37/9.03	thf(c_0_317, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_316, c_0_70]), c_0_78])]), ['proof']).
75.37/9.03	# SZS output end CNFRefutation
75.37/9.03	# Parsed axioms                        : 565
75.37/9.03	# Removed by relevancy pruning/SinE    : 499
75.37/9.03	# Initial clauses                      : 11240
75.37/9.03	# Removed in clause preprocessing      : 10869
75.37/9.03	# Initial clauses in saturation        : 371
75.37/9.03	# Processed clauses                    : 8103
75.37/9.03	# ...of these trivial                  : 41
75.37/9.03	# ...subsumed                          : 4682
75.37/9.03	# ...remaining for further processing  : 3380
75.37/9.03	# Other redundant clauses eliminated   : 0
75.37/9.03	# Clauses deleted for lack of memory   : 0
75.37/9.03	# Backward-subsumed                    : 1050
75.37/9.03	# Backward-rewritten                   : 672
75.37/9.03	# Generated clauses                    : 55019
75.37/9.03	# ...of the previous two non-redundant : 34755
75.37/9.03	# ...aggressively subsumed             : 0
75.37/9.03	# Contextual simplify-reflections      : 771
75.37/9.03	# Paramodulations                      : 41155
75.37/9.03	# Factorizations                       : 0
75.37/9.03	# NegExts                              : 0
75.37/9.03	# Equation resolutions                 : 0
75.37/9.03	# Disequality decompositions           : 0
75.37/9.03	# Total rewrite steps                  : 29691
75.37/9.03	# ...of those cached                   : 29622
75.37/9.03	# Propositional unsat checks           : 0
75.37/9.03	#    Propositional check models        : 0
75.37/9.03	#    Propositional check unsatisfiable : 0
75.37/9.03	#    Propositional clauses             : 0
75.37/9.03	#    Propositional clauses after purity: 0
75.37/9.03	#    Propositional unsat core size     : 0
75.37/9.03	#    Propositional preprocessing time  : 0.000
75.37/9.03	#    Propositional encoding time       : 0.000
75.37/9.03	#    Propositional solver time         : 0.000
75.37/9.03	#    Success case prop preproc time    : 0.000
75.37/9.03	#    Success case prop encoding time   : 0.000
75.37/9.03	#    Success case prop solver time     : 0.000
75.37/9.03	# Current number of processed clauses  : 1358
75.37/9.03	#    Positive orientable unit clauses  : 38
75.37/9.03	#    Positive unorientable unit clauses: 0
75.37/9.03	#    Negative unit clauses             : 21
75.37/9.03	#    Non-unit-clauses                  : 1299
75.37/9.03	# Current number of unprocessed clauses: 12486
75.37/9.03	# ...number of literals in the above   : 98842
75.37/9.03	# Current number of archived formulas  : 0
75.37/9.03	# Current number of archived clauses   : 2022
75.37/9.03	# Clause-clause subsumption calls (NU) : 3474626
75.37/9.03	# Rec. Clause-clause subsumption calls : 166472
75.37/9.03	# Non-unit clause-clause subsumptions  : 5965
75.37/9.03	# Unit Clause-clause subsumption calls : 16810
75.37/9.03	# Rewrite failures with RHS unbound    : 0
75.37/9.03	# BW rewrite match attempts            : 255
75.37/9.03	# BW rewrite match successes           : 53
75.37/9.03	# Condensation attempts                : 8103
75.37/9.03	# Condensation successes               : 2
75.37/9.03	# Termbank termtop insertions          : 7604394
75.37/9.03	# Search garbage collected termcells   : 89221
75.37/9.03	
75.37/9.03	# -------------------------------------------------
75.37/9.03	# User time                : 8.296 s
75.37/9.03	# System time              : 0.064 s
75.37/9.03	# Total time               : 8.360 s
75.37/9.03	# Maximum resident set size: 30044 pages
75.37/9.03	
75.37/9.03	# -------------------------------------------------
75.37/9.03	# User time                : 8.319 s
75.37/9.03	# System time              : 0.078 s
75.37/9.03	# Total time               : 8.397 s
75.37/9.03	# Maximum resident set size: 7524 pages
75.37/9.03	% E exiting
75.37/9.03	% E exiting
75.37/9.03	EOF
