0.04/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.04/0.12	% Command    : run_E %s %d THM
0.11/0.33	% Computer : n012.cluster.edu
0.11/0.33	% Model    : x86_64 x86_64
0.11/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.33	% Memory   : 8042.1875MB
0.11/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.11/0.33	% CPULimit   : 1440
0.11/0.33	% WCLimit    : 180
0.11/0.33	% DateTime   : Thu Jul  4 09:55:39 EDT 2024
0.11/0.33	% CPUTime    : 
0.19/0.46	Running higher-order theorem proving
0.19/0.52	Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox2/tmp/tmp.iNhhEWQb8d/E---3.1_16287.p
36.74/5.20	# Version: 3.2.0-ho
36.74/5.20	# Preprocessing class: HSLMSMSMLLLCHSA.
36.74/5.20	# Scheduled 5 strats onto 8 cores with 180 seconds (1440 total)
36.74/5.20	# Starting pre_casc_4 with 720s (4) cores
36.74/5.20	# Starting full_lambda_6 with 180s (1) cores
36.74/5.20	# Starting sh10 with 180s (1) cores
36.74/5.20	# Starting post_as_ho9 with 180s (1) cores
36.74/5.20	# Starting post_as_ho8 with 180s (1) cores
36.74/5.20	# post_as_ho9 with pid 16368 completed with status 0
36.74/5.20	# Result found by post_as_ho9
36.74/5.20	# Preprocessing class: HSLMSMSMLLLCHSA.
36.74/5.20	# Scheduled 5 strats onto 8 cores with 180 seconds (1440 total)
36.74/5.20	# Starting pre_casc_4 with 720s (4) cores
36.74/5.20	# Starting full_lambda_6 with 180s (1) cores
36.74/5.20	# Starting sh10 with 180s (1) cores
36.74/5.20	# Starting post_as_ho9 with 180s (1) cores
36.74/5.20	# SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true)
36.74/5.20	# Search class: HGUNF-FSLM21-DHSMMFBN
36.74/5.20	# partial match(5): HGUSM-FSLM31-DHSFFFBN
36.74/5.20	# Scheduled 6 strats onto 1 cores with 180 seconds (180 total)
36.74/5.20	# Starting new_bool_5 with 81s (1) cores
36.74/5.20	# new_bool_5 with pid 16377 completed with status 0
36.74/5.20	# Result found by new_bool_5
36.74/5.20	# Preprocessing class: HSLMSMSMLLLCHSA.
36.74/5.20	# Scheduled 5 strats onto 8 cores with 180 seconds (1440 total)
36.74/5.20	# Starting pre_casc_4 with 720s (4) cores
36.74/5.20	# Starting full_lambda_6 with 180s (1) cores
36.74/5.20	# Starting sh10 with 180s (1) cores
36.74/5.20	# Starting post_as_ho9 with 180s (1) cores
36.74/5.20	# SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true)
36.74/5.20	# Search class: HGUNF-FSLM21-DHSMMFBN
36.74/5.20	# partial match(5): HGUSM-FSLM31-DHSFFFBN
36.74/5.20	# Scheduled 6 strats onto 1 cores with 180 seconds (180 total)
36.74/5.20	# Starting new_bool_5 with 81s (1) cores
36.74/5.20	# Preprocessing time       : 0.010 s
36.74/5.20	# Presaturation interreduction done
36.74/5.20	
36.74/5.20	# Proof found!
36.74/5.20	# SZS status Theorem
36.74/5.20	# SZS output start CNFRefutation
36.74/5.20	thf(decl_22, type, is_of: $i > ($i > $o) > $o).
36.74/5.20	thf(decl_23, type, all_of: ($i > $o) > ($i > $o) > $o).
36.74/5.20	thf(decl_25, type, in: $i > $i > $o).
36.74/5.20	thf(decl_27, type, emptyset: $i).
36.74/5.20	thf(decl_42, type, d_Sep: $i > ($i > $o) > $i).
36.74/5.20	thf(decl_49, type, omega: $i).
36.74/5.20	thf(decl_58, type, ap: $i > $i > $i).
36.74/5.20	thf(decl_60, type, d_Pi: $i > ($i > $i) > $i).
36.74/5.20	thf(decl_61, type, imp: $o > $o > $o).
36.74/5.20	thf(decl_62, type, d_not: $o > $o).
36.74/5.20	thf(decl_67, type, l_or: $o > $o > $o).
36.74/5.20	thf(decl_123, type, nat: $i).
36.74/5.20	thf(decl_124, type, n_is: $i > $i > $o).
36.74/5.20	thf(decl_127, type, n_some: ($i > $o) > $o).
36.74/5.20	thf(decl_147, type, diffprop: $i > $i > $i > $o).
36.74/5.20	thf(decl_148, type, d_29_ii: $i > $i > $o).
36.74/5.20	thf(decl_149, type, iii: $i > $i > $o).
36.74/5.20	thf(decl_161, type, times: $i > $i).
36.74/5.20	thf(decl_162, type, n_ts: $i > $i > $i).
36.74/5.20	thf(decl_167, type, d_1to: $i > $i).
36.74/5.20	thf(decl_172, type, n_2: $i).
36.74/5.20	thf(decl_176, type, pair1type: $i > $i).
36.74/5.20	thf(decl_178, type, first1: $i > $i > $i).
36.74/5.20	thf(decl_179, type, second1: $i > $i > $i).
36.74/5.20	thf(decl_189, type, frac: $i).
36.74/5.20	thf(decl_191, type, num: $i > $i).
36.74/5.20	thf(decl_192, type, den: $i > $i).
36.74/5.20	thf(decl_193, type, n_eq: $i > $i > $o).
36.74/5.20	thf(decl_194, type, moref: $i > $i > $o).
36.74/5.20	thf(decl_195, type, lessf: $i > $i > $o).
36.74/5.20	thf(decl_197, type, lesseq: $i > $i > $o).
36.74/5.20	thf(decl_198, type, epred1_2: $i > $i > $o).
36.74/5.20	thf(decl_199, type, epred2_2: $i > $i > $o).
36.74/5.20	thf(decl_200, type, epred3_2: $i > $i > $o).
36.74/5.20	thf(decl_202, type, epred5_2: $i > $i > $o).
36.74/5.20	thf(decl_203, type, epred6_2: $i > $i > $o).
36.74/5.20	thf(decl_208, type, esk1_0: $i).
36.74/5.20	thf(decl_209, type, esk2_0: $i).
36.74/5.20	thf(decl_210, type, esk3_0: $i).
36.74/5.20	thf(def_nat, axiom, ((nat)=(d_Sep @ omega @ (^[X1:$i]:(((X1)!=(emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.iNhhEWQb8d/E---3.1_16287.p', def_nat)).
36.74/5.20	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/sandbox2/tmp/tmp.iNhhEWQb8d/E---3.1_16287.p', def_n_eq)).
36.74/5.20	thf(def_num, axiom, ((num)=(first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))))), file('/export/starexec/sandbox2/tmp/tmp.iNhhEWQb8d/E---3.1_16287.p', def_num)).
36.74/5.20	thf(def_den, axiom, ((den)=(second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))))), file('/export/starexec/sandbox2/tmp/tmp.iNhhEWQb8d/E---3.1_16287.p', def_den)).
36.74/5.20	thf(def_n_ts, axiom, ((n_ts)=(^[X1:$i]:(ap @ (times @ X1)))), file('/export/starexec/sandbox2/tmp/tmp.iNhhEWQb8d/E---3.1_16287.p', def_n_ts)).
36.74/5.20	thf(def_l_or, axiom, ((l_or)=(^[X42:$o]:(imp @ ((d_not @ ((X42))))))), file('/export/starexec/sandbox2/tmp/tmp.iNhhEWQb8d/E---3.1_16287.p', def_l_or)).
36.74/5.20	thf(def_d_not, axiom, ((d_not)=(^[X36:$o]:((imp @ ((X36)) @ (~($true)))))), file('/export/starexec/sandbox2/tmp/tmp.iNhhEWQb8d/E---3.1_16287.p', def_d_not)).
36.74/5.20	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/sandbox2/tmp/tmp.iNhhEWQb8d/E---3.1_16287.p', def_lessf)).
36.74/5.20	thf(def_iii, axiom, ((iii)=(^[X1:$i, X185:$i]:((n_some @ (diffprop @ X185 @ X1))))), file('/export/starexec/sandbox2/tmp/tmp.iNhhEWQb8d/E---3.1_16287.p', def_iii)).
36.74/5.20	thf(def_all_of, axiom, ((all_of)=(^[X3:$i > $o, X2:$i > $o]:(![X4:$i]:(((is_of @ X4 @ X3)=>(X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.iNhhEWQb8d/E---3.1_16287.p', def_all_of)).
36.74/5.20	thf(def_is_of, axiom, ((is_of)=(^[X1:$i, X2:$i > $o]:((X2 @ X1)))), file('/export/starexec/sandbox2/tmp/tmp.iNhhEWQb8d/E---3.1_16287.p', def_is_of)).
36.74/5.20	thf(def_moref, axiom, ((moref)=(^[X1:$i, X219:$i]:((d_29_ii @ (n_ts @ (num @ X1) @ (den @ X219)) @ (n_ts @ (num @ X219) @ (den @ X1)))))), file('/export/starexec/sandbox2/tmp/tmp.iNhhEWQb8d/E---3.1_16287.p', def_moref)).
36.74/5.20	thf(def_pair1type, axiom, ((pair1type)=(^[X1:$i]:(d_Pi @ (d_1to @ n_2) @ (^[X207:$i]:(X1))))), file('/export/starexec/sandbox2/tmp/tmp.iNhhEWQb8d/E---3.1_16287.p', def_pair1type)).
36.74/5.20	thf(def_lesseq, axiom, ((lesseq)=(^[X1:$i, X222:$i]:((l_or @ ((lessf @ X1 @ X222)) @ ((n_eq @ X1 @ X222)))))), file('/export/starexec/sandbox2/tmp/tmp.iNhhEWQb8d/E---3.1_16287.p', def_lesseq)).
36.74/5.20	thf(def_frac, axiom, ((frac)=(d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.iNhhEWQb8d/E---3.1_16287.p', def_frac)).
36.74/5.20	thf(satz41d, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X223:$i]:((in @ X223 @ frac))) @ (^[X224:$i]:(((d_not @ ((moref @ X1 @ X224)))<=(lesseq @ X1 @ X224)))))))), file('/export/starexec/sandbox2/tmp/tmp.iNhhEWQb8d/E---3.1_16287.p', satz41d)).
36.74/5.20	thf(satz37, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((n_eq @ X1 @ X1)))), file('/export/starexec/sandbox2/tmp/tmp.iNhhEWQb8d/E---3.1_16287.p', satz37)).
36.74/5.20	thf(satz51a, conjecture, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X228:$i]:((in @ X228 @ frac))) @ (^[X229:$i]:((all_of @ (^[X4:$i]:((in @ X4 @ frac))) @ (^[X4:$i]:((((lessf @ X229 @ X4)=>(lessf @ X1 @ X4))<=(lesseq @ X1 @ X229))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iNhhEWQb8d/E---3.1_16287.p', satz51a)).
36.74/5.20	thf(satz41g, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X266:$i]:((in @ X266 @ frac))) @ (^[X267:$i]:(((d_not @ ((lesseq @ X1 @ X267)))<=(moref @ X1 @ X267)))))))), file('/export/starexec/sandbox2/tmp/tmp.iNhhEWQb8d/E---3.1_16287.p', satz41g)).
36.74/5.20	thf(satz41k, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X359:$i]:((in @ X359 @ frac))) @ (^[X360:$i]:(((d_not @ ((lesseq @ X1 @ X360)))=>(moref @ X1 @ X360)))))))), file('/export/starexec/sandbox2/tmp/tmp.iNhhEWQb8d/E---3.1_16287.p', satz41k)).
36.74/5.20	thf(satz50, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X305:$i]:((in @ X305 @ frac))) @ (^[X306:$i]:((all_of @ (^[X4:$i]:((in @ X4 @ frac))) @ (^[X4:$i]:(((lessf @ X1 @ X306)=>((lessf @ X1 @ X4)<=(lessf @ X306 @ X4)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iNhhEWQb8d/E---3.1_16287.p', satz50)).
36.74/5.20	thf(satz42, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X393:$i]:((in @ X393 @ frac))) @ (^[X394:$i]:(((moref @ X1 @ X394)=>(lessf @ X394 @ X1)))))))), file('/export/starexec/sandbox2/tmp/tmp.iNhhEWQb8d/E---3.1_16287.p', satz42)).
36.74/5.20	thf(satz41e, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X264:$i]:((in @ X264 @ frac))) @ (^[X265:$i]:(((lesseq @ X1 @ X265)<=(d_not @ ((moref @ X1 @ X265)))))))))), file('/export/starexec/sandbox2/tmp/tmp.iNhhEWQb8d/E---3.1_16287.p', satz41e)).
36.74/5.20	thf(satz43, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X317:$i]:((in @ X317 @ frac))) @ (^[X318:$i]:(((moref @ X318 @ X1)<=(lessf @ X1 @ X318)))))))), file('/export/starexec/sandbox2/tmp/tmp.iNhhEWQb8d/E---3.1_16287.p', satz43)).
36.74/5.20	thf(satz45, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X234:$i]:((in @ X234 @ frac))) @ (^[X235:$i]:((all_of @ (^[X4:$i]:((in @ X4 @ frac))) @ (^[X4:$i]:((all_of @ (^[X10:$i]:((in @ X10 @ frac))) @ (^[X10:$i]:(((lessf @ X1 @ X235)=>((n_eq @ X1 @ X4)=>((n_eq @ X235 @ X10)=>(lessf @ X4 @ X10)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.iNhhEWQb8d/E---3.1_16287.p', satz45)).
36.74/5.20	thf(satz38, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ frac))) @ (^[X1:$i]:((all_of @ (^[X428:$i]:((in @ X428 @ frac))) @ (^[X429:$i]:(((n_eq @ X1 @ X429)=>(n_eq @ X429 @ X1)))))))), file('/export/starexec/sandbox2/tmp/tmp.iNhhEWQb8d/E---3.1_16287.p', satz38)).
36.74/5.20	thf(c_0_26, plain, ((nat)=(d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset)))))), inference(fof_simplification,[status(thm)],[def_nat])).
36.74/5.20	thf(c_0_27, 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])).
36.74/5.20	thf(c_0_28, axiom, ((num)=(first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))))), inference(apply_def,[status(thm)],[def_num, c_0_26])).
36.74/5.20	thf(c_0_29, axiom, ((den)=(second1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))))), inference(apply_def,[status(thm)],[def_den, c_0_26])).
36.74/5.20	thf(c_0_30, plain, ((n_ts)=(^[Z0/* 58 */:$i]:(ap @ (times @ Z0)))), inference(fof_simplification,[status(thm)],[def_n_ts])).
36.74/5.20	thf(c_0_31, plain, ((l_or)=(^[Z0/* 61 */:$o]:(imp @ (((imp @ (((Z0))) @ (~($true)))))))), inference(fof_simplification,[status(thm)],[def_l_or])).
36.74/5.20	thf(c_0_32, plain, ((d_not)=(^[Z0/* 3 */:$o]:((imp @ ((Z0)) @ (~($true)))))), inference(fof_simplification,[status(thm)],[def_d_not])).
36.74/5.20	thf(c_0_33, plain, ((lessf)=(^[Z0/* 19 */:$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 */:$i]:(((Z2)!=(emptyset))))) @ Z1)))))))), inference(fof_simplification,[status(thm)],[def_lessf])).
36.74/5.20	thf(c_0_34, plain, ((iii)=(^[Z0/* 19 */:$i, Z1:$i]:((n_some @ (diffprop @ Z1 @ Z0))))), inference(fof_simplification,[status(thm)],[def_iii])).
36.74/5.20	thf(c_0_35, plain, ((all_of)=(^[Z0/* 19 */:$i > $o, Z1:$i > $o]:(![X4:$i]:((((Z0 @ X4))=>(Z1 @ X4)))))), inference(fof_simplification,[status(thm)],[def_all_of])).
36.74/5.20	thf(c_0_36, plain, ((is_of)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((Z1 @ Z0)))), inference(fof_simplification,[status(thm)],[def_is_of])).
36.74/5.20	thf(c_0_37, plain, ((moref)=(^[Z0/* 19 */:$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 */:$i]:(((Z2)!=(emptyset))))) @ Z0)))))), inference(fof_simplification,[status(thm)],[def_moref])).
36.74/5.20	thf(c_0_38, plain, ((pair1type)=(^[Z0/* 60 */:$i]:(d_Pi @ (d_1to @ n_2) @ (^[Z1/* 1 */:$i]:(Z0))))), inference(fof_simplification,[status(thm)],[def_pair1type])).
36.74/5.20	thf(c_0_39, plain, ((lesseq)=(^[Z0/* 19 */:$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])).
36.74/5.20	thf(c_0_40, 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_27, c_0_28]), c_0_29]), c_0_30])).
36.74/5.20	thf(c_0_41, plain, ((l_or)=(^[Z0/* 61 */:$o]:(imp @ (((imp @ (((Z0))) @ (~($true)))))))), inference(apply_def,[status(thm)],[c_0_31, c_0_32])).
36.74/5.20	thf(c_0_42, 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_33, c_0_28]), c_0_29]), c_0_30]), c_0_34])).
36.74/5.20	thf(c_0_43, plain, ((all_of)=(^[Z0/* 19 */:$i > $o, Z1:$i > $o]:(![X4:$i]:((((Z0 @ X4))=>(Z1 @ X4)))))), inference(apply_def,[status(thm)],[c_0_35, c_0_36])).
36.74/5.20	thf(c_0_44, 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_37, c_0_28]), c_0_29]), c_0_30])).
36.74/5.20	thf(c_0_45, axiom, ((frac)=(d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[def_frac, c_0_26]), c_0_38])).
36.74/5.20	thf(c_0_46, 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 */:$i]:(((Z2)!=(emptyset))))) @ Z0))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_39, c_0_40]), c_0_41]), c_0_42])).
36.74/5.20	thf(c_0_47, plain, ![X505:$i]:(((in @ X505 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>![X504:$i]:(((in @ X504 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$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 @ $false)))))))))), inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz41d]), c_0_43]), c_0_44]), c_0_32]), c_0_45]), c_0_46])])])).
36.74/5.20	thf(c_0_48, plain, ![X502:$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 @ $false))))))), introduced(definition)).
36.74/5.20	thf(c_0_49, plain, ![X625:$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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*/:$i]:(~(((Z0)=(emptyset)))))) @ X626)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 @ $true)))|~(in @ X626 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X625 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])])])])).
36.74/5.22	thf(c_0_50, plain, ![X502:$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 @ $false))))))), inference(split_equiv,[status(thm)],[c_0_48])).
36.74/5.22	thf(c_0_51, plain, ![X4:$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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))), inference(split_conjunct,[status(thm)],[c_0_49])).
36.74/5.22	thf(c_0_52, 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))|~(($true))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))), inference(split_conjunct,[status(thm)],[c_0_49])).
36.74/5.22	thf(c_0_53, plain, ![X527:$i]:(((in @ X527 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X527)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X527)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X527)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X527))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz37]), c_0_43]), c_0_40]), c_0_45])).
36.74/5.22	thf(c_0_54, plain, ![X749:$i, X750:$i]:((((((~(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 @ $true @ $true)|(($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 @ 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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 @ (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 @ $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 @ $false)|(~($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 */:$i]:(~(((Z0)=(emptyset)))))) @ X749)))))|~(epred1_2 @ X750 @ X749))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])])])])).
36.74/5.22	thf(c_0_55, plain, ![X4:$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)) @ (($true))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(cn,[status(thm)],[c_0_51])).
36.74/5.22	thf(c_0_56, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))|~((imp @ (~($true)) @ (($true))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(cn,[status(thm)],[c_0_52])).
36.74/5.22	thf(c_0_57, plain, ![X654:$i]:((~(in @ X654 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X654)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X654)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X654)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X654))))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])])])).
36.74/5.22	thf(c_0_58, negated_conjecture, ~(![X503:$i]:(((in @ X503 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>![X502:$i]:(((in @ X502 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>![X501:$i]:(((in @ X501 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X501))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz51a])]), c_0_43]), c_0_45]), c_0_42]), c_0_46])])]), c_0_48])).
36.74/5.22	thf(c_0_59, plain, ![X508:$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 @ $false))))&(((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 @ $false))))))), introduced(definition)).
36.74/5.22	thf(c_0_60, plain, ![X1:$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_54])).
36.74/5.22	thf(c_0_61, 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))))|~(($true))|~((epred1_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_54])).
36.74/5.22	thf(c_0_62, plain, ![X4:$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 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (($true)))))), inference(cn,[status(thm)],[c_0_55])).
36.74/5.22	thf(c_0_63, plain, ![X4:$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 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (($true)))))), inference(cn,[status(thm)],[c_0_56])).
36.74/5.22	thf(c_0_64, plain, ![X1:$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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))), inference(split_conjunct,[status(thm)],[c_0_57])).
36.74/5.22	thf(c_0_65, negated_conjecture, ((in @ esk1_0 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))&((in @ esk2_0 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))&((in @ esk3_0 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$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_58])])])])).
36.74/5.22	thf(c_0_66, 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 @ $false))))&(((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 @ $false))))))), inference(split_equiv,[status(thm)],[c_0_59])).
36.74/5.22	thf(c_0_67, plain, ![X1:$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_54])).
36.74/5.22	thf(c_0_68, 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_60])).
36.74/5.22	thf(c_0_69, 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_61])).
36.74/5.22	thf(c_0_70, 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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (($true)))))), inference(csr,[status(thm)],[c_0_62, c_0_63])).
36.74/5.22	thf(c_0_71, 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 */:$i]:(((Z0)!=(emptyset))))) @ X1)))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[c_0_64])).
36.74/5.22	thf(c_0_72, negated_conjecture, (in @ esk3_0 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))), inference(split_conjunct,[status(thm)],[c_0_65])).
36.74/5.22	thf(c_0_73, plain, ![X753:$i, X754:$i]:((((((((($true)|(imp @ $true @ $true)|(~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 @ $true)|(($true)|~(imp @ $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 */:$i]:(~(((Z0)=(emptyset)))))) @ X753))))))|~(epred3_2 @ X754 @ X753))&(~($true)|(imp @ $true @ $false)|(~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 @ $true)|(($true)|~(imp @ $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 */:$i]:(~(((Z0)=(emptyset)))))) @ X753))))))|~(epred3_2 @ X754 @ X753)))&((($true)|(imp @ $true @ $true)|((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 @ $false)|(($true)|~(imp @ $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 */:$i]:(~(((Z0)=(emptyset)))))) @ X753))))))|~(epred3_2 @ X754 @ X753))&(~($true)|(imp @ $true @ $false)|((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 @ $false)|(($true)|~(imp @ $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 */:$i]:(~(((Z0)=(emptyset)))))) @ X753))))))|~(epred3_2 @ X754 @ X753))))&(((($true)|(imp @ $true @ $true)|(~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 @ $true)|(~($true)|~(imp @ $true @ $false)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 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*/:$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)|(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 @ $false @ $false)|(~($true)|(imp @ $true @ $false)|~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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)|(imp @ $false @ $true)|(~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 @ $true)|(($true)|(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 */:$i]:(~(((Z0)=(emptyset)))))) @ X753))))))|~(epred3_2 @ X754 @ X753))&(~($true)|(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 @ $false @ $true)|(($true)|(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 */:$i]:(~(((Z0)=(emptyset)))))) @ X753))))))|~(epred3_2 @ X754 @ X753)))&((($true)|(imp @ $false @ $true)|((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 @ $false)|(($true)|(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 */:$i]:(~(((Z0)=(emptyset)))))) @ X753))))))|~(epred3_2 @ X754 @ X753))&(~($true)|(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 @ $false @ $false)|(($true)|(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 */:$i]:(~(((Z0)=(emptyset)))))) @ X753))))))|~(epred3_2 @ X754 @ X753))))&(((($true)|(imp @ $false @ $true)|(~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 @ $true)|(~($true)|(imp @ $false @ $false)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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)|(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 @ $false @ $true)|(~($true)|(imp @ $false @ $false)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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)|(imp @ $false @ $true)|((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 @ $false)|(~($true)|(imp @ $false @ $false)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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)|(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 @ $false @ $false)|(~($true)|(imp @ $false @ $false)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X753))))))|~(epred3_2 @ X754 @ X753))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_66])])])])).
36.74/5.22	thf(c_0_74, plain, ![X1:$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_54])).
36.74/5.22	thf(c_0_75, 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_67])).
36.74/5.22	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))))|(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_68])).
36.74/5.22	thf(c_0_77, 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_69])).
36.74/5.22	thf(c_0_78, plain, ![X1:$i]:(((imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (($true)))))), inference(spm,[status(thm)],[c_0_70, c_0_71])).
36.74/5.22	thf(c_0_79, negated_conjecture, (in @ esk3_0 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))), inference(cn,[status(thm)],[c_0_72])).
36.74/5.22	thf(c_0_80, plain, ![X1:$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)) @ (~($true)))|(imp @ (($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 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)))))|~((epred3_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_73])).
36.74/5.22	thf(c_0_81, plain, ![X1:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)))))|~((epred3_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_73])).
36.74/5.22	thf(c_0_82, plain, ![X1:$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_54])).
36.74/5.22	thf(c_0_83, 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)))))|~((epred3_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_73])).
36.74/5.22	thf(c_0_84, 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_74])).
36.74/5.22	thf(c_0_85, 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_75])).
36.74/5.22	thf(c_0_86, 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_76, c_0_77])).
36.74/5.22	thf(c_0_87, negated_conjecture, ((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))|~((imp @ (~($true)) @ (($true))))), inference(spm,[status(thm)],[c_0_78, c_0_79])).
36.74/5.22	thf(c_0_88, plain, ![X514:$i, X515:$i]:(((epred5_2 @ X515 @ X514)<=>(((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514))))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514))))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)))|~(imp @ $true @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)))|~(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)))|~(imp @ $false @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)))|~(imp @ $false @ $false)))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false)))))), introduced(definition)).
36.74/5.22	thf(c_0_89, plain, ![X514:$i, X515:$i]:(((epred6_2 @ X515 @ X514)<=>(((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514))))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514))))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)))|(imp @ $true @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)))|(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)))|(imp @ $false @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)))|(imp @ $false @ $false)))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))), introduced(definition)).
36.74/5.22	thf(c_0_90, plain, ![X1:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|~((epred3_2 @ X1 @ X4))|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))))), inference(cn,[status(thm)],[c_0_80])).
36.74/5.22	thf(c_0_91, plain, ![X1:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|~((epred3_2 @ X1 @ X4))|~((imp @ (~($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 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))))), inference(cn,[status(thm)],[c_0_81])).
36.74/5.22	thf(c_0_92, plain, ![X1:$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)) @ (~($true)))))), inference(cn,[status(thm)],[c_0_82])).
36.74/5.22	thf(c_0_93, plain, ![X1:$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)) @ (~($true))))|~((epred3_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_73])).
36.74/5.22	thf(c_0_94, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|~((epred3_2 @ X1 @ X4))|~((imp @ (~($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 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))))), inference(cn,[status(thm)],[c_0_83])).
36.74/5.22	thf(c_0_95, plain, ![X4:$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)) @ (~($true))))|~((epred1_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_84])).
36.74/5.22	thf(c_0_96, plain, ![X1:$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 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((epred1_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_85, c_0_86]), c_0_87])).
36.74/5.22	thf(c_0_97, plain, ![X509:$i]:(((in @ X509 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>![X508:$i]:(((in @ X508 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X509)))=>(epred3_2 @ X509 @ X508)))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz41g]), c_0_43]), c_0_44]), c_0_32]), c_0_45]), c_0_46])])]), c_0_59])).
36.74/5.22	thf(c_0_98, plain, ![X515:$i]:(((in @ X515 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>![X514:$i]:(((in @ X514 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>(((epred5_2 @ X515 @ X514)&(epred6_2 @ X515 @ X514))=>(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz41k]), c_0_43]), c_0_44]), c_0_32]), c_0_45]), c_0_46])]), c_0_88]), c_0_89])).
36.74/5.22	thf(c_0_99, plain, ![X514:$i, X515:$i]:(((((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514))))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514))))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)))|~(imp @ $true @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)))|~(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)))|~(imp @ $false @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)))|~(imp @ $false @ $false)))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))=>(epred5_2 @ X515 @ X514))), inference(split_equiv,[status(thm)],[c_0_88])).
36.74/5.22	thf(c_0_100, plain, ![X1:$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)) @ (~($true)))|(imp @ (($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 */:$i]:(((Z0)!=(emptyset))))) @ X4)))))|~((epred3_2 @ X1 @ X4)))), inference(cn,[status(thm)],[c_0_90])).
36.74/5.22	thf(c_0_101, plain, ![X1:$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)) @ (~($true))))|~((epred3_2 @ X1 @ X4)))), inference(cn,[status(thm)],[c_0_91])).
36.74/5.22	thf(c_0_102, plain, ![X4:$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)) @ (~($true))))|~((epred1_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_92])).
36.74/5.22	thf(c_0_103, plain, ![X4:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~((epred3_2 @ X1 @ X4))|~((imp @ (($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 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(cn,[status(thm)],[c_0_93])).
36.74/5.22	thf(c_0_104, plain, ![X4:$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)) @ (($true))))|~((epred3_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_94])).
36.74/5.22	thf(c_0_105, plain, ![X1:$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 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((epred1_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_85, c_0_95]), c_0_96])).
36.74/5.22	thf(c_0_106, plain, ![X629:$i, X630:$i]:((~(in @ X629 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X630 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X629)))|(epred3_2 @ X629 @ X630))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_97])])])])).
36.74/5.22	thf(c_0_107, plain, ![X635:$i, X636:$i]:((~(in @ X635 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X636 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(epred5_2 @ X635 @ X636)|~(epred6_2 @ X635 @ X636)|(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X635)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X636)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X636)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X635))))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_98])])])])).
36.74/5.22	thf(c_0_108, plain, ![X757:$i, X758:$i]:(((((((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X757))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X757))))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X757))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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)|~($true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X757))))|(~(n_some @ 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*/:$i]:(~(((Z0)=(emptyset)))))) @ X757))))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))&(~(imp @ $false @ $false)|~($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))))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757)))&((($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))))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))&(~(imp @ $false @ $false)|~(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))))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757)))))&((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X757))))|(($true)|~($true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))&(((($true)|~($true)|(($true)|~($true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))&(~(imp @ $false @ $false)|~($true)|(($true)|~($true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757)))&((($true)|~(imp @ $false @ $true)|(($true)|~($true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(($true)|~($true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757)))))&((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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))))|(~(imp @ $true @ $false)|~($true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))&(((($true)|~($true)|(~(imp @ $true @ $false)|~($true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))&(~(imp @ $false @ $false)|~($true)|(~(imp @ $true @ $false)|~($true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757)))&((($true)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~($true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~($true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X757))))|(($true)|~(imp @ $true @ $true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))&(((($true)|~($true)|(($true)|~(imp @ $true @ $true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))&(~(imp @ $false @ $false)|~($true)|(($true)|~(imp @ $true @ $true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757)))&((($true)|~(imp @ $false @ $true)|(($true)|~(imp @ $true @ $true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(($true)|~(imp @ $true @ $true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757)))))&((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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))))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))&(((($true)|~($true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))&(~(imp @ $false @ $false)|~($true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757)))&((($true)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))))))))&(((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X758)))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))&((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 @ $true @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757)))&((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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)|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))&((imp @ $false @ $false)|(imp @ $false @ $true)|((imp @ $true @ $false)|(imp @ $true @ $true))|(epred5_2 @ X758 @ X757))))))))&(((($true)|~($true)|(epred5_2 @ X758 @ X757))&(~(imp @ $true @ $false)|~($true)|(epred5_2 @ X758 @ X757)))&((($true)|~(imp @ $true @ $true)|(epred5_2 @ X758 @ X757))&(~(imp @ $true @ $false)|~(imp @ $true @ $true)|(epred5_2 @ X758 @ X757)))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_99])])])])).
36.74/5.22	thf(c_0_109, plain, ![X506:$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 @ $false))))))), introduced(definition)).
36.74/5.22	thf(c_0_110, plain, ![X1:$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 */:$i]:(((Z0)!=(emptyset))))) @ X4)))))|~((epred3_2 @ X1 @ X4)))), inference(csr,[status(thm)],[c_0_100, c_0_101])).
36.74/5.22	thf(c_0_111, plain, ![X4:$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 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$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)) @ (~($true)))|~((epred1_2 @ X4 @ X1)))), inference(csr,[status(thm)],[c_0_102, c_0_77])).
36.74/5.22	thf(c_0_112, plain, ![X4:$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)) @ (~($true))))|~((epred3_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_103])).
36.74/5.22	thf(c_0_113, plain, ![X1:$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 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((epred3_2 @ X1 @ X4))|~((epred1_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104, c_0_95]), c_0_87]), c_0_105])).
36.74/5.22	thf(c_0_114, plain, ![X4:$i, X1:$i]:(((epred3_2 @ X1 @ X4)|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(split_conjunct,[status(thm)],[c_0_106])).
36.74/5.22	thf(c_0_115, plain, ![X1:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((epred5_2 @ X1 @ X4))|~((epred6_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_107])).
36.74/5.22	thf(c_0_116, plain, ![X522:$i]:(((in @ X522 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>![X521:$i]:(((in @ X521 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>![X520:$i]:(((in @ X520 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$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_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X520)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X521)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X521)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X520))))=>(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X520)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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)))))) @ X520)))))))))))), 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_43]), c_0_45]), c_0_42])])).
36.74/5.22	thf(c_0_117, 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)))|(epred5_2 @ X4 @ X1)|~((imp @ (~($true)) @ (~($true))))|~(($true)))), inference(split_conjunct,[status(thm)],[c_0_108])).
36.74/5.22	thf(c_0_118, plain, ![X1:$i, X4:$i]:(((epred5_2 @ X1 @ X4)|~((imp @ (($true)) @ (~($true))))|~(($true)))), inference(split_conjunct,[status(thm)],[c_0_108])).
36.74/5.22	thf(c_0_119, 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 @ $false))))))), inference(split_equiv,[status(thm)],[c_0_109])).
36.74/5.22	thf(c_0_120, plain, ![X1:$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)) @ (~($true)))|~((epred3_2 @ X1 @ X4))|~((epred1_2 @ X1 @ X4)))), inference(spm,[status(thm)],[c_0_110, c_0_111])).
36.74/5.22	thf(c_0_121, plain, ![X1:$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 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((epred1_2 @ X1 @ X4))|~((epred3_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_85, c_0_112]), c_0_96]), c_0_113])).
36.74/5.22	thf(c_0_122, plain, ![X4:$i, X1:$i]:(((epred3_2 @ X1 @ X4)|~((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$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 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[c_0_114])).
36.74/5.22	thf(c_0_123, plain, ![X1:$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 */:$i]:(((Z0)!=(emptyset))))) @ X1)))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((epred5_2 @ X1 @ X4))|~((epred6_2 @ X1 @ X4)))), inference(cn,[status(thm)],[c_0_115])).
36.74/5.22	thf(c_0_124, negated_conjecture, (in @ esk2_0 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))), inference(split_conjunct,[status(thm)],[c_0_65])).
36.74/5.22	thf(c_0_125, plain, ![X1:$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_54])).
36.74/5.22	thf(c_0_126, plain, ![X641:$i, X642:$i, X643:$i]:((~(in @ X641 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X642 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X643 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X642)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X641)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X641)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X642))))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X643))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X643)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X641)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X641)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X643)))))))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_116])])])])).
36.74/5.22	thf(c_0_127, plain, ![X4:$i, X1:$i]:(((epred5_2 @ X4 @ X1)|(imp @ (($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)) @ (~($true)))))), inference(cn,[status(thm)],[c_0_117])).
36.74/5.22	thf(c_0_128, plain, ![X1:$i, X4:$i]:(((epred5_2 @ X1 @ X4)|~((imp @ (($true)) @ (~($true)))))), inference(cn,[status(thm)],[c_0_118])).
36.74/5.22	thf(c_0_129, plain, ![X751:$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 @ 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@ $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 @ 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$false)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 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36.74/5.22	thf(c_0_130, plain, ![X514:$i, X515:$i]:(((((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514))))|((~(~($true))|~(imp @ $true @ $true))&(~($true)|~(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514))))|((~(~($true))|~(imp @ $false @ $true))&(~($true)|~(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)))|(imp @ $true @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)))|(imp @ $true @ $false))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514))))|((~(~($true))|(imp @ $true @ $true))&(~($true)|(imp @ $true @ $false))))&((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false)))))|((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)))|(imp @ $false @ $true))&((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X514)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X515)))|(imp @ $false @ $false)))))|((~(~($true))|(imp @ $false @ $true))&(~($true)|(imp @ $false @ $false))))=>(epred6_2 @ X515 @ X514))), inference(split_equiv,[status(thm)],[c_0_89])).
36.74/5.22	thf(c_0_131, plain, ![X1:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)))))|~((epred3_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_73])).
36.74/5.22	thf(c_0_132, plain, ![X1:$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))))|~(($true))|~((epred3_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_73])).
36.74/5.22	thf(c_0_133, plain, ![X1:$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))))|~(($true))|~((epred3_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_73])).
36.74/5.22	thf(c_0_134, plain, ![X1:$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))|~(($true))|~((epred3_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_73])).
36.74/5.22	thf(c_0_135, plain, ![X1:$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)) @ (($true))))|~((epred3_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104, c_0_112]), c_0_87])).
36.74/5.22	thf(c_0_136, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|(imp @ (($true)) @ (($true)))|~((epred3_2 @ X1 @ X4))|~((epred1_2 @ X1 @ X4)))), inference(spm,[status(thm)],[c_0_113, c_0_120])).
36.74/5.22	thf(c_0_137, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (($true)))|~((epred1_2 @ X1 @ X4))|~((epred3_2 @ X1 @ X4)))), inference(spm,[status(thm)],[c_0_121, c_0_120])).
36.74/5.22	thf(c_0_138, plain, ![X1:$i, X4:$i]:(((epred3_2 @ X1 @ X4)|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((epred5_2 @ X1 @ X4))|~((epred6_2 @ X1 @ X4)))), inference(spm,[status(thm)],[c_0_122, c_0_123])).
36.74/5.22	thf(c_0_139, negated_conjecture, (in @ esk2_0 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))), inference(cn,[status(thm)],[c_0_124])).
36.74/5.22	thf(c_0_140, negated_conjecture, (in @ esk1_0 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))), inference(split_conjunct,[status(thm)],[c_0_65])).
36.74/5.22	thf(c_0_141, plain, ![X1:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))))), inference(cn,[status(thm)],[c_0_125])).
36.74/5.22	thf(c_0_142, plain, ![X1:$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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X5 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$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_126])).
36.74/5.22	thf(c_0_143, 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_65])).
36.74/5.22	thf(c_0_144, 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)))|(epred5_2 @ X4 @ X1)|~((imp @ (~($true)) @ (~($true)))))), inference(csr,[status(thm)],[inference(cn,[status(thm)],[c_0_127]), c_0_128])).
36.74/5.22	thf(c_0_145, 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))))|~(($true))|~((epred2_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_129])).
36.74/5.22	thf(c_0_146, plain, ![X1:$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_129])).
36.74/5.22	thf(c_0_147, plain, ![X759:$i, X760:$i]:(((((((((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759))))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)))))|(epred6_2 @ X760 @ X759))&(((($true)|~($true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759))))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)))))|(epred6_2 @ X760 @ X759))&(~(imp @ $false @ $false)|~($true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759))))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)))))|(epred6_2 @ X760 @ X759)))&((($true)|~(imp @ $false @ $true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759))))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)))))|(epred6_2 @ X760 @ X759))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759))))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759))))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ 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(second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759))))|(($true)|~($true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred6_2 @ X760 @ X759))&(((($true)|~($true)|(($true)|~($true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred6_2 @ X760 @ X759))&(~(imp @ $false @ $false)|~($true)|(($true)|~($true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred6_2 @ X760 @ X759)))&((($true)|~(imp @ $false @ $true)|(($true)|~($true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred6_2 @ X760 @ X759))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(($true)|~($true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred6_2 @ X760 @ X759)))))&((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759))))|(~(imp @ $true @ $false)|~($true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred6_2 @ X760 @ X759))&(((($true)|~($true)|(~(imp @ $true @ $false)|~($true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred6_2 @ X760 @ X759))&(~(imp @ $false @ $false)|~($true)|(~(imp @ $true @ $false)|~($true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred6_2 @ X760 @ X759)))&((($true)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~($true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred6_2 @ X760 @ X759))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~($true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred6_2 @ X760 @ X759))))))&(((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759))))|(($true)|~(imp @ $true @ $true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred6_2 @ X760 @ X759))&(((($true)|~($true)|(($true)|~(imp @ $true @ $true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred6_2 @ X760 @ X759))&(~(imp @ $false @ $false)|~($true)|(($true)|~(imp @ $true @ $true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred6_2 @ X760 @ X759)))&((($true)|~(imp @ $false @ $true)|(($true)|~(imp @ $true @ $true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred6_2 @ X760 @ X759))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(($true)|~(imp @ $true @ $true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred6_2 @ X760 @ X759)))))&((~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759))))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred6_2 @ X760 @ X759))&(((($true)|~($true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred6_2 @ X760 @ X759))&(~(imp @ $false @ $false)|~($true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred6_2 @ X760 @ X759)))&((($true)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred6_2 @ X760 @ X759))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred6_2 @ X760 @ X759))))))))&(((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred6_2 @ X760 @ X759))&(~(imp @ $false @ $false)|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)))|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred6_2 @ X760 @ X759)))&((~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X759)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X760)))|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred6_2 @ X760 @ X759))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred6_2 @ X760 @ X759))))))))&(((($true)|~($true)|(epred6_2 @ X760 @ X759))&(~(imp @ $false @ $false)|~($true)|(epred6_2 @ X760 @ X759)))&((($true)|~(imp @ $false @ $true)|(epred6_2 @ X760 @ X759))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(epred6_2 @ X760 @ X759)))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_130])])])])).
36.74/5.22	thf(c_0_148, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (($true)))|(imp @ (~($true)) @ (~($true)))|~((epred3_2 @ X1 @ X4))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))))), inference(cn,[status(thm)],[c_0_131])).
36.74/5.22	thf(c_0_149, plain, ![X4:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~((epred3_2 @ X1 @ X4))|~((imp @ (~($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 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(cn,[status(thm)],[c_0_132])).
36.74/5.22	thf(c_0_150, plain, ![X4:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~((epred3_2 @ X1 @ X4))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(cn,[status(thm)],[c_0_133])).
36.74/5.22	thf(c_0_151, plain, ![X1:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|~((epred3_2 @ X1 @ X4)))), inference(cn,[status(thm)],[c_0_134])).
36.74/5.22	thf(c_0_152, plain, ![X545:$i]:(((in @ X545 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>![X544:$i]:(((in @ X544 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>((d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X545)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X544)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X544)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X545)))=>(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X545)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X544)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X544)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X545))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz42]), c_0_43]), c_0_44]), c_0_45]), c_0_42])).
36.74/5.22	thf(c_0_153, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|~((epred3_2 @ X1 @ X4))|~((epred1_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_135, c_0_120]), c_0_136]), c_0_137])).
36.74/5.22	thf(c_0_154, negated_conjecture, (epred1_2 @ esk1_0 @ esk2_0), inference(split_conjunct,[status(thm)],[c_0_65])).
36.74/5.22	thf(c_0_155, negated_conjecture, ![X1:$i]:(((epred3_2 @ X1 @ esk2_0)|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((epred5_2 @ X1 @ esk2_0))|~((epred6_2 @ X1 @ esk2_0)))), inference(spm,[status(thm)],[c_0_138, c_0_139])).
36.74/5.22	thf(c_0_156, negated_conjecture, (in @ esk1_0 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))), inference(cn,[status(thm)],[c_0_140])).
36.74/5.22	thf(c_0_157, 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_141])).
36.74/5.22	thf(c_0_158, 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 */:$i]:(((Z0)!=(emptyset))))) @ X5)))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X5 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[c_0_142])).
36.74/5.22	thf(c_0_159, negated_conjecture, (n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$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 */:$i]:(((Z0)!=(emptyset))))) @ esk3_0)))), inference(cn,[status(thm)],[c_0_143])).
36.74/5.22	thf(c_0_160, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (($true)))|(epred5_2 @ X4 @ X1)|((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$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)) @ (~($true)))))), inference(ext_eqfact,[status(thm)],[c_0_144])).
36.74/5.22	thf(c_0_161, plain, ![X1:$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_129])).
36.74/5.22	thf(c_0_162, 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_145])).
36.74/5.22	thf(c_0_163, 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_146])).
36.74/5.22	thf(c_0_164, 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 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)))))|~((epred2_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_129])).
36.74/5.22	thf(c_0_165, plain, ![X4:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))|(epred6_2 @ X1 @ X4)|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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_147])).
36.74/5.22	thf(c_0_166, plain, ![X1:$i, X4:$i]:(((epred6_2 @ X1 @ X4)|~((imp @ (~($true)) @ (~($true))))|~(($true)))), inference(split_conjunct,[status(thm)],[c_0_147])).
36.74/5.22	thf(c_0_167, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|(epred6_2 @ X1 @ X4)|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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))|~(($true)))), inference(split_conjunct,[status(thm)],[c_0_147])).
36.74/5.22	thf(c_0_168, plain, ![X4:$i, X1:$i]:(((epred6_2 @ X1 @ X4)|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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)) @ (($true)))))), inference(split_conjunct,[status(thm)],[c_0_147])).
36.74/5.22	thf(c_0_169, plain, ![X4:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)))|(epred6_2 @ X4 @ X1)|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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_147])).
36.74/5.22	thf(c_0_170, plain, ![X507:$i]:(((in @ X507 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>![X506:$i]:(((in @ X506 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$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 @ $false)))))=>(epred2_2 @ X507 @ X506)))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz41e]), c_0_43]), c_0_44]), c_0_32]), c_0_45]), c_0_46])])]), c_0_109])).
36.74/5.22	thf(c_0_171, plain, ![X1:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)))))|~((epred3_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_73])).
36.74/5.22	thf(c_0_172, plain, ![X4:$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 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((epred3_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_148])).
36.74/5.22	thf(c_0_173, plain, ![X4:$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)) @ (($true))))|~((epred3_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_149])).
36.74/5.22	thf(c_0_174, plain, ![X4:$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 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((epred3_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_150])).
36.74/5.22	thf(c_0_175, plain, ![X4:$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)) @ (~($true)))|~((epred3_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_151])).
36.74/5.22	thf(c_0_176, plain, ![X671:$i, X672:$i]:((~(in @ X671 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X672 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X671)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X672)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X672)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X671)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X671)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X672)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X672)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X671)))))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_152])])])])).
36.74/5.22	thf(c_0_177, negated_conjecture, ((imp @ (($true)) @ (~($true)))|~((epred3_2 @ esk1_0 @ esk2_0))), inference(spm,[status(thm)],[c_0_153, c_0_154])).
36.74/5.22	thf(c_0_178, negated_conjecture, ((epred3_2 @ esk1_0 @ esk2_0)|~((epred5_2 @ esk1_0 @ esk2_0))|~((epred6_2 @ esk1_0 @ esk2_0))), inference(spm,[status(thm)],[c_0_155, c_0_156])).
36.74/5.22	thf(c_0_179, plain, ![X1:$i, X4:$i]:(((imp @ (~($true)) @ (~($true)))|(imp @ (($true)) @ (~($true)))|~((epred1_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_157, c_0_77]), c_0_96])).
36.74/5.22	thf(c_0_180, negated_conjecture, ~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ esk3_0))))), inference(split_conjunct,[status(thm)],[c_0_65])).
36.74/5.22	thf(c_0_181, negated_conjecture, ![X1:$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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158, c_0_159]), c_0_79]), c_0_139])])).
36.74/5.22	thf(c_0_182, 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)))|(epred5_2 @ X4 @ X1)|~((imp @ (~($true)) @ (~($true)))))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_160])])])).
36.74/5.22	thf(c_0_183, 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_161])).
36.74/5.22	thf(c_0_184, 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_162])).
36.74/5.22	thf(c_0_185, 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_163])).
36.74/5.22	thf(c_0_186, 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_164])).
36.74/5.22	thf(c_0_187, plain, ![X4:$i, X1:$i]:(((epred6_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_165])).
36.74/5.22	thf(c_0_188, plain, ![X1:$i, X4:$i]:(((epred6_2 @ X1 @ X4)|~((imp @ (~($true)) @ (~($true)))))), inference(cn,[status(thm)],[c_0_166])).
36.74/5.22	thf(c_0_189, plain, ![X4:$i, X1:$i]:(((epred6_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_167])).
36.74/5.22	thf(c_0_190, plain, ![X4:$i, X1:$i]:(((epred6_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_168])).
36.74/5.22	thf(c_0_191, plain, ![X4:$i, X1:$i]:(((epred6_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_169])).
36.74/5.22	thf(c_0_192, 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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X627)))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X627)))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$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)|~($true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))&(((($true)|~($true)|(($true)|~($true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))&((($true)|~(imp @ $false @ $true)|(($true)|~($true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(($true)|~($true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))&(((($true)|~($true)|(~(imp @ $true @ $false)|~($true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))&(~(imp @ $false @ $false)|~($true)|(~(imp @ $true @ $false)|~($true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))&((($true)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~($true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$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 @ $true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))&(((($true)|~($true)|(($true)|~(imp @ $true @ $true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))&(~(imp @ $false @ $false)|~($true)|(($true)|~(imp @ $true @ $true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))&((($true)|~(imp @ $false @ $true)|(($true)|~(imp @ $true @ $true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(($true)|~(imp @ $true @ $true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$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 @ $true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))&(((($true)|~($true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))&(~(imp @ $false @ $false)|~($true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))&((($true)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))&(~(imp @ $false @ $false)|~(imp @ $false @ $true)|(~(imp @ $true @ $false)|~(imp @ $true @ $true))|(epred2_2 @ X627 @ X628)|~(in @ X628 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|~(in @ X627 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_170])])])])])).
36.74/5.22	thf(c_0_193, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (($true)))|(imp @ (~($true)) @ (~($true)))|~((epred3_2 @ X1 @ X4))|~((imp @ (($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 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))))), inference(cn,[status(thm)],[c_0_171])).
36.74/5.22	thf(c_0_194, plain, ![X4:$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 */:$i]:(((Z0)!=(emptyset))))) @ X4))))|~((epred3_2 @ X4 @ X1)))), inference(csr,[status(thm)],[c_0_172, c_0_104])).
36.74/5.22	thf(c_0_195, plain, ![X4:$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)) @ (~($true)))|~((epred3_2 @ X4 @ X1)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_173, c_0_174]), c_0_175])).
36.74/5.22	thf(c_0_196, plain, ![X4:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(split_conjunct,[status(thm)],[c_0_176])).
36.74/5.22	thf(c_0_197, negated_conjecture, ((imp @ (($true)) @ (~($true)))|~((epred5_2 @ esk1_0 @ esk2_0))|~((epred6_2 @ esk1_0 @ esk2_0))), inference(spm,[status(thm)],[c_0_177, c_0_178])).
36.74/5.22	thf(c_0_198, negated_conjecture, ((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (~($true)))), inference(spm,[status(thm)],[c_0_179, c_0_154])).
36.74/5.22	thf(c_0_199, negated_conjecture, ~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$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 */:$i]:(((Z0)!=(emptyset))))) @ esk3_0))))), inference(cn,[status(thm)],[c_0_180])).
36.74/5.22	thf(c_0_200, plain, ![X1:$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)))|(epred5_2 @ X1 @ esk2_0)|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (~($true)))))), inference(spm,[status(thm)],[c_0_181, c_0_182])).
36.74/5.22	thf(c_0_201, 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_183])).
36.74/5.22	thf(c_0_202, 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_184, c_0_185])).
36.74/5.22	thf(c_0_203, 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_186])).
36.74/5.22	thf(c_0_204, 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))))|(epred6_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_187]), c_0_188])).
36.74/5.22	thf(c_0_205, plain, ![X4:$i, X1:$i]:(((imp @ (($true)) @ (~($true)))|(epred6_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_189]), c_0_188])).
36.74/5.22	thf(c_0_206, plain, ![X4:$i, X1:$i]:(((epred6_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_190])).
36.74/5.22	thf(c_0_207, 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)))|(epred6_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_191])).
36.74/5.22	thf(c_0_208, 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))))|~(($true))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))), inference(split_conjunct,[status(thm)],[c_0_192])).
36.74/5.22	thf(c_0_209, plain, ![X543:$i]:(((in @ X543 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>![X542:$i]:(((in @ X542 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X542)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X543)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X543)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X542))))=>(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X542)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X543)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X543)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X542)))))))), inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz43]), c_0_43]), c_0_44]), c_0_45]), c_0_42])])).
36.74/5.22	thf(c_0_210, plain, ![X4:$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)) @ (~($true))))|~((epred3_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_193])).
36.74/5.22	thf(c_0_211, plain, ![X1:$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 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((epred3_2 @ X1 @ X4)))), inference(spm,[status(thm)],[c_0_194, c_0_195])).
36.74/5.22	thf(c_0_212, plain, ![X4:$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 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[c_0_196])).
36.74/5.22	thf(c_0_213, plain, ((imp @ (($true)) @ (~($true)))|~((epred5_2 @ esk1_0 @ esk2_0))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_197, c_0_188]), c_0_198])).
36.74/5.22	thf(c_0_214, negated_conjecture, ((epred5_2 @ esk1_0 @ esk2_0)|(imp @ (($true)) @ (($true)))|~((imp @ (~($true)) @ (~($true))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199, c_0_200]), c_0_156])])).
36.74/5.22	thf(c_0_215, plain, ![X1:$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 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((epred2_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_201, c_0_202]), c_0_87])).
36.74/5.22	thf(c_0_216, plain, ![X1:$i, X4:$i]:(((epred6_2 @ X1 @ X4)|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$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)) @ (($true))))|~((epred2_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_203, c_0_204]), c_0_205]), c_0_206])).
36.74/5.22	thf(c_0_217, plain, ![X1:$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 */:$i]:(((Z0)!=(emptyset))))) @ X1)))|(epred6_2 @ X1 @ X4)|~((epred2_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_207, c_0_185]), c_0_198]), c_0_188])).
36.74/5.22	thf(c_0_218, plain, ![X4:$i, X1:$i]:(((epred2_2 @ X1 @ X4)|~((imp @ (($true)) @ (~($true))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X1)))))), inference(cn,[status(thm)],[c_0_208])).
36.74/5.22	thf(c_0_219, plain, ![X669:$i, X670:$i]:((~(in @ X669 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X670 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X670)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X669)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X669)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X670))))|(d_29_ii @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X670)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X669)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X669)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X670))))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_209])])])])).
36.74/5.22	thf(c_0_220, plain, ![X4:$i, X1:$i]:(((epred6_2 @ X4 @ X1)|~((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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_147])).
36.74/5.22	thf(c_0_221, 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))))|~((epred3_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_210, c_0_174]), c_0_211])).
36.74/5.22	thf(c_0_222, 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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (($true)) @ (~($true))))|~((epred2_2 @ X1 @ X4)))), inference(spm,[status(thm)],[c_0_203, c_0_212])).
36.74/5.22	thf(c_0_223, plain, ((imp @ (($true)) @ (($true)))|(imp @ (($true)) @ (~($true)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_213, c_0_214]), c_0_198])).
36.74/5.22	thf(c_0_224, 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_203, c_0_202]), c_0_215])).
36.74/5.22	thf(c_0_225, plain, ![X1:$i, X4:$i]:(((epred6_2 @ X1 @ X4)|~((imp @ (~($true)) @ (($true))))|~((epred2_2 @ X1 @ X4)))), inference(spm,[status(thm)],[c_0_216, c_0_217])).
36.74/5.22	thf(c_0_226, 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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (($true)) @ (~($true)))))), inference(cn,[status(thm)],[c_0_218])).
36.74/5.22	thf(c_0_227, 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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$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_219])).
36.74/5.22	thf(c_0_228, plain, ![X4:$i, X1:$i]:(((epred6_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_220])).
36.74/5.22	thf(c_0_229, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (($true)))|(epred6_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))))|~((epred3_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_210, c_0_204]), c_0_221]), c_0_211]), c_0_188])).
36.74/5.22	thf(c_0_230, 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)))|(epred6_2 @ X1 @ X4)|~((epred3_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_207, c_0_175]), c_0_198]), c_0_188])).
36.74/5.22	thf(c_0_231, 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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((epred2_2 @ X1 @ X4))|~((epred6_2 @ X4 @ X1)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_222, c_0_123]), c_0_128]), c_0_223])).
36.74/5.22	thf(c_0_232, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (($true)))|(epred6_2 @ X1 @ X4)|~((epred2_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_224, c_0_217]), c_0_225]), c_0_188])).
36.74/5.22	thf(c_0_233, plain, ![X1:$i, X4:$i]:(((epred2_2 @ X1 @ X4)|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (($true)) @ (~($true))))|~((epred6_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_226, c_0_123]), c_0_128])).
36.74/5.22	thf(c_0_234, 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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[c_0_227])).
36.74/5.22	thf(c_0_235, plain, ![X1:$i, X4:$i]:(((epred6_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_228])).
36.74/5.22	thf(c_0_236, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (($true)))|(epred6_2 @ X1 @ X4)|~((epred3_2 @ X1 @ X4)))), inference(spm,[status(thm)],[c_0_229, c_0_230])).
36.74/5.22	thf(c_0_237, plain, ![X1:$i]:(((imp @ (($true)) @ (($true)))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((epred2_2 @ X1 @ X1)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_231, c_0_71]), c_0_232])).
36.74/5.22	thf(c_0_238, negated_conjecture, ![X1:$i]:(((epred2_2 @ X1 @ esk3_0)|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (($true)) @ (~($true))))|~((epred6_2 @ X1 @ esk3_0)))), inference(spm,[status(thm)],[c_0_233, c_0_79])).
36.74/5.22	thf(c_0_239, 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_86])).
36.74/5.22	thf(c_0_240, 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)))|(epred6_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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (($true)))))), inference(spm,[status(thm)],[c_0_234, c_0_204])).
36.74/5.22	thf(c_0_241, plain, ![X1:$i, X4:$i]:(((imp @ (~($true)) @ (($true)))|(epred6_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))))|~((epred3_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_235, c_0_174]), c_0_211]), c_0_229]), c_0_188])).
36.74/5.22	thf(c_0_242, plain, ![X1:$i, X4:$i]:(((epred6_2 @ X1 @ X4)|~((imp @ (~($true)) @ (($true))))|~((epred3_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_206, c_0_230]), c_0_236])).
36.74/5.22	thf(c_0_243, negated_conjecture, ((imp @ (($true)) @ (($true)))|~((epred2_2 @ esk3_0 @ esk3_0))), inference(spm,[status(thm)],[c_0_237, c_0_79])).
36.74/5.22	thf(c_0_244, negated_conjecture, ((epred2_2 @ esk3_0 @ esk3_0)|~((imp @ (($true)) @ (~($true))))|~((epred6_2 @ esk3_0 @ esk3_0))), inference(spm,[status(thm)],[c_0_238, c_0_79])).
36.74/5.22	thf(c_0_245, 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_239])])])).
36.74/5.22	thf(c_0_246, 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)))|~(($true))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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)) @ (($true))))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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)) @ (($true))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))), inference(split_conjunct,[status(thm)],[c_0_49])).
36.74/5.22	thf(c_0_247, plain, ![X1:$i, X4:$i]:(((epred6_2 @ X1 @ X4)|(epred3_2 @ X4 @ X1)|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$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 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (($true)))))), inference(spm,[status(thm)],[c_0_122, c_0_240])).
36.74/5.22	thf(c_0_248, plain, ![X1:$i, X4:$i]:(((epred6_2 @ X1 @ X4)|~((epred3_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_241, c_0_230]), c_0_242])).
36.74/5.22	thf(c_0_249, negated_conjecture, ((imp @ (($true)) @ (($true)))|~((epred6_2 @ esk3_0 @ esk3_0))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_243, c_0_244]), c_0_223])).
36.74/5.22	thf(c_0_250, plain, ![X1:$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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((epred1_2 @ X1 @ esk2_0)))), inference(spm,[status(thm)],[c_0_181, c_0_245])).
36.74/5.22	thf(c_0_251, 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))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$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_246])).
36.74/5.22	thf(c_0_252, plain, ![X1:$i]:(((epred6_2 @ X1 @ X1)|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (($true)))))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_247, c_0_71]), c_0_248])).
36.74/5.22	thf(c_0_253, plain, ((imp @ (($true)) @ (($true)))|~((imp @ (~($true)) @ (~($true))))), inference(spm,[status(thm)],[c_0_249, c_0_188])).
36.74/5.22	thf(c_0_254, negated_conjecture, ((imp @ (~($true)) @ (($true)))|(imp @ (~($true)) @ (~($true)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199, c_0_250]), c_0_156]), c_0_154])])).
36.74/5.22	thf(c_0_255, plain, ![X4:$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)) @ (~($true)))|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$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 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (($true)) @ (($true))))|~((imp @ (~($true)) @ (($true)))))), inference(cn,[status(thm)],[c_0_251])).
36.74/5.22	thf(c_0_256, negated_conjecture, ((epred6_2 @ esk3_0 @ esk3_0)|~((imp @ (~($true)) @ (($true))))), inference(spm,[status(thm)],[c_0_252, c_0_79])).
36.74/5.22	thf(c_0_257, negated_conjecture, ((imp @ (~($true)) @ (($true)))|(imp @ (($true)) @ (($true)))), inference(spm,[status(thm)],[c_0_253, c_0_254])).
36.74/5.22	thf(c_0_258, plain, ![X1:$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))))|~((epred2_2 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_129])).
36.74/5.22	thf(c_0_259, 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))))|~(($true))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))), inference(split_conjunct,[status(thm)],[c_0_192])).
36.74/5.22	thf(c_0_260, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (~($true)))|(epred3_2 @ X1 @ X4)|~((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$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 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (($true)) @ (($true))))|~((imp @ (~($true)) @ (($true)))))), inference(spm,[status(thm)],[c_0_122, c_0_255])).
36.74/5.22	thf(c_0_261, negated_conjecture, (imp @ (($true)) @ (($true))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_249, c_0_256]), c_0_257])).
36.74/5.22	thf(c_0_262, plain, ![X1:$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_129])).
36.74/5.22	thf(c_0_263, 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))))|~((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)))))), inference(cn,[status(thm)],[c_0_258])).
36.74/5.22	thf(c_0_264, 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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))), inference(cn,[status(thm)],[c_0_259])).
36.74/5.22	thf(c_0_265, plain, ![X1:$i, X4:$i]:(((epred6_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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (($true)) @ (($true))))|~((imp @ (($true)) @ (~($true)))))), inference(spm,[status(thm)],[c_0_235, c_0_212])).
36.74/5.22	thf(c_0_266, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (~($true)))|(epred3_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))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset))))))))))), inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_260, c_0_261])]), c_0_254])).
36.74/5.22	thf(c_0_267, 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)))|(epred6_2 @ X1 @ X4)|~((epred1_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_207, c_0_77]), c_0_198]), c_0_188])).
36.74/5.22	thf(c_0_268, 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_199, c_0_212]), c_0_156]), c_0_79])])).
36.74/5.22	thf(c_0_269, 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)))|(epred5_2 @ X1 @ X4)|~(($true))|~(($true)))), inference(split_conjunct,[status(thm)],[c_0_108])).
36.74/5.22	thf(c_0_270, 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_262])).
36.74/5.22	thf(c_0_271, 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))))|~((epred2_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_263])).
36.74/5.22	thf(c_0_272, 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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (~($true)))))), inference(cn,[status(thm)],[c_0_264])).
36.74/5.22	thf(c_0_273, plain, ![X4:$i, X1:$i]:(((epred6_2 @ X1 @ X4)|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (($true)) @ (($true))))|~((imp @ (($true)) @ (~($true))))|~((epred6_2 @ X4 @ X1)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_265, c_0_123]), c_0_128])).
36.74/5.22	thf(c_0_274, plain, ![X1:$i, X4:$i]:(((epred6_2 @ X1 @ X4)|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((epred1_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_266, c_0_267]), c_0_248]), c_0_188])).
36.74/5.22	thf(c_0_275, plain, ![X519:$i]:(((in @ X519 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>![X518:$i]:(((in @ X518 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>![X517:$i]:(((in @ X517 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>![X516:$i]:(((in @ X516 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>((n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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)))))) @ X518))))=>((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X519)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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)))))) @ X519)))=>((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X518)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X516)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X516)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X518)))=>(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))))))))))))))), 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_43]), c_0_40]), c_0_45]), c_0_42])).
36.74/5.22	thf(c_0_276, 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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))))), inference(split_conjunct,[status(thm)],[c_0_49])).
36.74/5.22	thf(c_0_277, negated_conjecture, (~((epred5_2 @ esk3_0 @ esk1_0))|~((epred6_2 @ esk3_0 @ esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_268, c_0_123]), c_0_156]), c_0_79])])).
36.74/5.22	thf(c_0_278, 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)))|(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)))|(epred5_2 @ X4 @ X1)|~((imp @ (~($true)) @ (~($true))))|~(($true)))), inference(split_conjunct,[status(thm)],[c_0_108])).
36.74/5.22	thf(c_0_279, plain, ![X4:$i, X1:$i]:(((epred5_2 @ X1 @ X4)|(imp @ (($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 */:$i]:(~(((Z0)=(emptyset)))))) @ X1))))), inference(cn,[status(thm)],[c_0_269])).
36.74/5.22	thf(c_0_280, plain, ![X4:$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)) @ (~($true))))|~((epred2_2 @ X4 @ X1)))), inference(cn,[status(thm)],[c_0_270])).
36.74/5.22	thf(c_0_281, plain, ![X1:$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 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((epred2_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_201, c_0_271]), c_0_215])).
36.74/5.22	thf(c_0_282, plain, ![X4:$i, X1:$i]:(((epred2_2 @ X1 @ X4)|(epred3_2 @ X1 @ X4)|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (~($true)))))), inference(spm,[status(thm)],[c_0_122, c_0_272])).
36.74/5.22	thf(c_0_283, negated_conjecture, ![X1:$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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181, c_0_212]), c_0_139])])).
36.74/5.22	thf(c_0_284, plain, ![X4:$i, X1:$i]:(((epred6_2 @ X1 @ X4)|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (($true)) @ (~($true))))|~((epred6_2 @ X4 @ X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_273, c_0_261])])).
36.74/5.22	thf(c_0_285, negated_conjecture, ![X1:$i]:(((epred6_2 @ X1 @ esk2_0)|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((epred1_2 @ X1 @ esk2_0)))), inference(spm,[status(thm)],[c_0_274, c_0_139])).
36.74/5.22	thf(c_0_286, plain, ![X637:$i, X638:$i, X639:$i, X640:$i]:((~(in @ X637 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X638 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X639 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X640 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X638))))|(~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X637)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X639)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X639)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X637)))|(~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X638)) @ (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 */:$i]:(~(((Z0)=(emptyset)))))) @ X638)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X640)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X639)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X639)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X640)))))))))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_275])])])])).
36.74/5.22	thf(c_0_287, plain, ![X1:$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)) @ (~($true))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X4))))))), inference(cn,[status(thm)],[c_0_276])).
36.74/5.22	thf(c_0_288, plain, (~((epred5_2 @ esk3_0 @ esk1_0))|~((imp @ (~($true)) @ (~($true))))), inference(spm,[status(thm)],[c_0_277, c_0_188])).
36.74/5.22	thf(c_0_289, plain, ![X4:$i, X1:$i]:(((epred5_2 @ X4 @ X1)|(imp @ (($true)) @ (~($true)))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)))|(n_some @ (diffprop @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$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)) @ (~($true)))))), inference(cn,[status(thm)],[c_0_278])).
36.74/5.22	thf(c_0_290, plain, ![X1:$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)) @ (~($true)))|(epred5_2 @ X1 @ X4))), inference(csr,[status(thm)],[inference(cn,[status(thm)],[c_0_279]), c_0_128])).
36.74/5.22	thf(c_0_291, plain, ![X529:$i]:(((in @ X529 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>![X528:$i]:(((in @ X528 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))=>((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X529)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X528)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X528)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X529)))=>(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X528)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X529)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X529)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X528)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz38]), c_0_43]), c_0_40]), c_0_45])).
36.74/5.22	thf(c_0_292, plain, ![X4:$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)) @ (~($true)))|~((epred2_2 @ X4 @ X1)))), inference(csr,[status(thm)],[c_0_280, c_0_185])).
36.74/5.22	thf(c_0_293, plain, ![X1:$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 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((epred3_2 @ X1 @ X4))|~((epred2_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104, c_0_271]), c_0_87]), c_0_281])).
36.74/5.22	thf(c_0_294, negated_conjecture, ![X1:$i]:(((epred3_2 @ X1 @ esk2_0)|(epred2_2 @ X1 @ esk2_0)|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (~($true)))))), inference(spm,[status(thm)],[c_0_282, c_0_139])).
36.74/5.22	thf(c_0_295, 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_199, c_0_283]), c_0_156])])).
36.74/5.22	thf(c_0_296, negated_conjecture, ![X1:$i]:(((epred6_2 @ esk2_0 @ X1)|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (($true)) @ (~($true))))|~((epred6_2 @ X1 @ esk2_0)))), inference(spm,[status(thm)],[c_0_284, c_0_139])).
36.74/5.22	thf(c_0_297, negated_conjecture, (epred6_2 @ esk1_0 @ esk2_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_285, c_0_156]), c_0_154])])).
36.74/5.22	thf(c_0_298, plain, ![X1:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X6))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X5 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X6 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$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 */:$i]:(~(((Z0)=(emptyset)))))) @ X4)))))), inference(split_conjunct,[status(thm)],[c_0_286])).
36.74/5.22	thf(c_0_299, plain, ![X4:$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 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (~($true)))))), inference(cn,[status(thm)],[c_0_287])).
36.74/5.22	thf(c_0_300, plain, (~((imp @ (~($true)) @ (~($true))))|~((imp @ (($true)) @ (~($true))))), inference(spm,[status(thm)],[c_0_288, c_0_128])).
36.74/5.22	thf(c_0_301, plain, ![X4:$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 */:$i]:(((Z0)!=(emptyset))))) @ X4)))|(epred5_2 @ X4 @ X1)|~((imp @ (~($true)) @ (~($true)))))), inference(csr,[status(thm)],[inference(cn,[status(thm)],[c_0_289]), c_0_128])).
36.74/5.22	thf(c_0_302, plain, ![X4:$i, X1:$i]:(((imp @ (~($true)) @ (~($true)))|(epred5_2 @ X1 @ X4)|((n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 4 */:$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)) @ (~($true)))))), inference(ext_eqfact,[status(thm)],[c_0_290])).
36.74/5.22	thf(c_0_303, plain, ![X655:$i, X656:$i]:((~(in @ X655 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(in @ X656 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset)))))))))|(~(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X655)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X656)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X656)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X655)))|(n_is @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X656)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X655)) @ (ap @ (times @ (first1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X655)) @ (second1 @ (d_Sep @ omega @ (^[Z0/* 7 */:$i]:(~(((Z0)=(emptyset)))))) @ X656))))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_291])])])])).
36.74/5.22	thf(c_0_304, plain, ![X1:$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)) @ (~($true)))|~((epred3_2 @ X1 @ X4))|~((epred2_2 @ X1 @ X4)))), inference(spm,[status(thm)],[c_0_110, c_0_292])).
36.74/5.22	thf(c_0_305, plain, ![X1:$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 */:$i]:(((Z0)!=(emptyset))))) @ X1))))|~((epred2_2 @ X1 @ X4))|~((epred3_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_201, c_0_112]), c_0_215]), c_0_293])).
36.74/5.22	thf(c_0_306, negated_conjecture, ![X1:$i]:(((epred2_2 @ X1 @ esk2_0)|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (($true)) @ (~($true))))|~((epred6_2 @ X1 @ esk2_0)))), inference(spm,[status(thm)],[c_0_233, c_0_139])).
36.74/5.22	thf(c_0_307, negated_conjecture, ((epred2_2 @ esk1_0 @ esk2_0)|(epred3_2 @ esk1_0 @ esk2_0)|~((imp @ (~($true)) @ (~($true))))), inference(spm,[status(thm)],[c_0_294, c_0_156])).
36.74/5.22	thf(c_0_308, negated_conjecture, (~((epred5_2 @ esk2_0 @ esk1_0))|~((epred6_2 @ esk2_0 @ esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_295, c_0_123]), c_0_156]), c_0_139])])).
36.74/5.22	thf(c_0_309, negated_conjecture, ((epred6_2 @ esk2_0 @ esk1_0)|~((imp @ (($true)) @ (~($true))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_296, c_0_156]), c_0_297])])).
36.74/5.22	thf(c_0_310, 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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X5 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X6 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[c_0_298])).
36.74/5.22	thf(c_0_311, 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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((imp @ (~($true)) @ (~($true)))))), inference(csr,[status(thm)],[c_0_299, c_0_300])).
36.74/5.22	thf(c_0_312, 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)))|(epred5_2 @ X4 @ X1))), inference(csr,[status(thm)],[c_0_301, c_0_290])).
36.74/5.22	thf(c_0_313, 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))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_302])])])).
36.74/5.22	thf(c_0_314, 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)))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$i]:(~(((Z1)=(emptyset))))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 7 */:$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(split_conjunct,[status(thm)],[c_0_303])).
36.74/5.22	thf(c_0_315, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|(imp @ (($true)) @ (($true)))|~((epred3_2 @ X1 @ X4))|~((epred2_2 @ X1 @ X4)))), inference(spm,[status(thm)],[c_0_293, c_0_304])).
36.74/5.22	thf(c_0_316, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|(imp @ (~($true)) @ (($true)))|~((epred2_2 @ X1 @ X4))|~((epred3_2 @ X1 @ X4)))), inference(spm,[status(thm)],[c_0_305, c_0_304])).
36.74/5.22	thf(c_0_317, negated_conjecture, ((epred2_2 @ esk1_0 @ esk2_0)|~((imp @ (($true)) @ (~($true))))|~((epred6_2 @ esk1_0 @ esk2_0))), inference(spm,[status(thm)],[c_0_306, c_0_156])).
36.74/5.22	thf(c_0_318, negated_conjecture, ((epred2_2 @ esk1_0 @ esk2_0)|(imp @ (($true)) @ (~($true)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_177, c_0_307]), c_0_198])).
36.74/5.22	thf(c_0_319, negated_conjecture, ~((imp @ (($true)) @ (~($true)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_308, c_0_309]), c_0_128])).
36.74/5.22	thf(c_0_320, 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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_310, c_0_159]), c_0_79]), c_0_139])])).
36.74/5.22	thf(c_0_321, 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)))|(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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset))))))))))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_311, c_0_312]), c_0_313])).
36.74/5.22	thf(c_0_322, 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)))|(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)))|(epred5_2 @ X1 @ X4)|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset))))))))))), inference(spm,[status(thm)],[c_0_234, c_0_312])).
36.74/5.22	thf(c_0_323, 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)))|~((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/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset))))))))))), inference(cn,[status(thm)],[c_0_314])).
36.74/5.22	thf(c_0_324, plain, ![X1:$i, X4:$i]:(((imp @ (($true)) @ (~($true)))|~((epred3_2 @ X1 @ X4))|~((epred2_2 @ X1 @ X4)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_135, c_0_304]), c_0_315]), c_0_316])).
36.74/5.22	thf(c_0_325, negated_conjecture, ((epred3_2 @ esk1_0 @ esk2_0)|~((epred5_2 @ esk1_0 @ esk2_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_178, c_0_297])])).
36.74/5.22	thf(c_0_326, negated_conjecture, (epred2_2 @ esk1_0 @ esk2_0), inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_317, c_0_297])]), c_0_318])).
36.74/5.22	thf(c_0_327, plain, (~((epred5_2 @ esk2_0 @ esk1_0))|~((imp @ (~($true)) @ (~($true))))), inference(spm,[status(thm)],[c_0_308, c_0_188])).
36.74/5.22	thf(c_0_328, negated_conjecture, (imp @ (~($true)) @ (~($true))), inference(sr,[status(thm)],[c_0_198, c_0_319])).
36.74/5.22	thf(c_0_329, 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_199, c_0_320]), c_0_79]), c_0_156])])).
36.74/5.22	thf(c_0_330, 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)))|(epred5_2 @ X4 @ X1)|(epred5_2 @ X1 @ X4)|~((in @ X4 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset)))))))))|~((in @ X1 @ (d_Pi @ (d_1to @ n_2) @ (^[Z0/* 42 */:$i]:(d_Sep @ omega @ (^[Z1/* 4 */:$i]:(((Z1)!=(emptyset))))))))))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_321, c_0_322]), c_0_323])).
36.74/5.22	thf(c_0_331, plain, ~((epred5_2 @ esk1_0 @ esk2_0)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_324, c_0_325]), c_0_326])]), c_0_319])).
36.74/5.22	thf(c_0_332, plain, ~((epred5_2 @ esk2_0 @ esk1_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_327, c_0_328])])).
36.74/5.22	thf(c_0_333, 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(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_329, c_0_330]), c_0_156]), c_0_139])]), c_0_331]), c_0_332])).
36.74/5.22	thf(c_0_334, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_333, c_0_71]), c_0_79])]), ['proof']).
36.74/5.22	# SZS output end CNFRefutation
36.74/5.22	# Parsed axioms                        : 565
36.74/5.22	# Removed by relevancy pruning/SinE    : 499
36.74/5.22	# Initial clauses                      : 11240
36.74/5.22	# Removed in clause preprocessing      : 10869
36.74/5.22	# Initial clauses in saturation        : 371
36.74/5.22	# Processed clauses                    : 6031
36.74/5.22	# ...of these trivial                  : 10
36.74/5.22	# ...subsumed                          : 3562
36.74/5.22	# ...remaining for further processing  : 2459
36.74/5.22	# Other redundant clauses eliminated   : 0
36.74/5.22	# Clauses deleted for lack of memory   : 0
36.74/5.22	# Backward-subsumed                    : 877
36.74/5.22	# Backward-rewritten                   : 604
36.74/5.22	# Generated clauses                    : 38839
36.74/5.22	# ...of the previous two non-redundant : 19648
36.74/5.22	# ...aggressively subsumed             : 0
36.74/5.22	# Contextual simplify-reflections      : 653
36.74/5.22	# Paramodulations                      : 24240
36.74/5.22	# Factorizations                       : 0
36.74/5.22	# NegExts                              : 0
36.74/5.22	# Equation resolutions                 : 0
36.74/5.22	# Disequality decompositions           : 0
36.74/5.22	# Total rewrite steps                  : 16666
36.74/5.22	# ...of those cached                   : 16607
36.74/5.22	# Propositional unsat checks           : 0
36.74/5.22	#    Propositional check models        : 0
36.74/5.22	#    Propositional check unsatisfiable : 0
36.74/5.22	#    Propositional clauses             : 0
36.74/5.22	#    Propositional clauses after purity: 0
36.74/5.22	#    Propositional unsat core size     : 0
36.74/5.22	#    Propositional preprocessing time  : 0.000
36.74/5.22	#    Propositional encoding time       : 0.000
36.74/5.22	#    Propositional solver time         : 0.000
36.74/5.22	#    Success case prop preproc time    : 0.000
36.74/5.22	#    Success case prop encoding time   : 0.000
36.74/5.22	#    Success case prop solver time     : 0.000
36.74/5.22	# Current number of processed clauses  : 680
36.74/5.22	#    Positive orientable unit clauses  : 31
36.74/5.22	#    Positive unorientable unit clauses: 0
36.74/5.22	#    Negative unit clauses             : 11
36.74/5.22	#    Non-unit-clauses                  : 638
36.74/5.22	# Current number of unprocessed clauses: 12467
36.74/5.22	# ...number of literals in the above   : 101967
36.74/5.22	# Current number of archived formulas  : 0
36.74/5.22	# Current number of archived clauses   : 1779
36.74/5.22	# Clause-clause subsumption calls (NU) : 2524641
36.74/5.22	# Rec. Clause-clause subsumption calls : 159092
36.74/5.22	# Non-unit clause-clause subsumptions  : 4918
36.74/5.22	# Unit Clause-clause subsumption calls : 16462
36.74/5.22	# Rewrite failures with RHS unbound    : 0
36.74/5.22	# BW rewrite match attempts            : 209
36.74/5.22	# BW rewrite match successes           : 48
36.74/5.22	# Condensation attempts                : 6031
36.74/5.22	# Condensation successes               : 1
36.74/5.22	# Termbank termtop insertions          : 4910931
36.74/5.22	# Search garbage collected termcells   : 89229
36.74/5.22	
36.74/5.22	# -------------------------------------------------
36.74/5.22	# User time                : 4.478 s
36.74/5.22	# System time              : 0.069 s
36.74/5.22	# Total time               : 4.547 s
36.74/5.22	# Maximum resident set size: 30040 pages
36.74/5.22	
36.74/5.22	# -------------------------------------------------
36.74/5.22	# User time                : 4.500 s
36.74/5.22	# System time              : 0.084 s
36.74/5.22	# Total time               : 4.584 s
36.74/5.22	# Maximum resident set size: 7508 pages
36.74/5.22	% E---3.1 exiting
36.74/5.22	% E exiting
36.74/5.23	EOF