%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, del: $tType).
thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_0, type, bool: del).
thf(func_def_1, type, ind: del).
thf(func_def_2, type, arr: (del > del > del)).
thf(func_def_3, type, mem: ($i > del > $o)).
thf(func_def_4, type, ap: ($i > $i > $i)).
thf(func_def_5, type, lam: (del > ($i > $i) > $i)).
thf(func_def_6, type, p: ($i > $o)).
thf(func_def_7, type, inj__o: ($o > $i)).
thf(func_def_9, type, ty_2Eoption_2Eoption: (del > del)).
thf(func_def_10, type, c_2Eoption_2EOPTION__JOIN: (del > $i)).
thf(func_def_11, type, c_2Eoption_2EOPTION__MAP: (del > del > $i)).
thf(func_def_12, type, c_2Eoption_2Eoption__CASE: (del > del > $i)).
thf(func_def_14, type, c_2Eoption_2EIS__NONE: (del > $i)).
thf(func_def_17, type, c_2Eoption_2EIS__SOME: (del > $i)).
thf(func_def_19, type, c_2Eoption_2ETHE: (del > $i)).
thf(func_def_20, type, c_2Eoption_2ESOME: (del > $i)).
thf(func_def_21, type, c_2Ebool_2E_3F: (del > $i)).
thf(func_def_22, type, c_2Eoption_2ENONE: (del > $i)).
thf(func_def_25, type, c_2Eoption_2EOPTREL: (del > del > $i)).
thf(func_def_26, type, c_2Emin_2E_3D: (del > $i)).
thf(func_def_27, type, c_2Ebool_2E_21: (del > $i)).
thf(func_def_30, type, sP0: ($i > del > $i > $i > del > $o)).
thf(func_def_31, type, sP1: (del > $o)).
thf(func_def_32, type, sP2: (del > $o)).
thf(func_def_33, type, sP3: (del > $o)).
thf(func_def_34, type, sP4: ($i > $i > $i > del > del > $o)).
thf(func_def_35, type, sK5: ($i > del > $i > $i > del > $i)).
thf(func_def_36, type, sK6: ($i > del > $i > $i > del > $i)).
thf(func_def_37, type, sK7: (del > $i > $i)).
thf(func_def_38, type, sK8: del).
thf(func_def_42, type, sK12: ($i > del > $i > $i)).
thf(func_def_43, type, vNOT: ($o > $o)).
thf(f5,axiom,(
  ! [X0 : del,X2 : $i,X1 : del] : ((mem @ X2 @ (arr @ X0 @ X1)) => ! [X3 : $i] : ((mem @ X3 @ X0) => (mem @ (ap @ X2 @ X3) @ X1)))),
  file('/export/starexec/sandbox2/benchmark/Axioms/ITP001/ITP001^2.ax',ap_tp)).
thf(f21,axiom,(
  ! [X1 : del,X0 : del,X2 : $i] : ((mem @ X2 @ X1) => ! [X3 : $i] : ((mem @ X3 @ (arr @ X0 @ X1)) => ! [X4 : $i] : ((mem @ X4 @ (ty_2Eoption_2Eoption @ X0)) => (! [X27 : $i] : ((mem @ X27 @ X0) => (((ap @ (c_2Eoption_2ETHE @ X0) @ (ap @ (c_2Eoption_2ESOME @ X0) @ X27))) = X27)) & ! [X7 : $i] : ((mem @ X7 @ X0) => (((c_2Eoption_2ENONE @ X0)) != ((ap @ (c_2Eoption_2ESOME @ X0) @ X7)))) & ! [X17 : $i] : ((mem @ X17 @ X0) => ! [X18 : $i] : ((mem @ X18 @ X1) => ! [X19 : $i] : ((mem @ X19 @ (arr @ X0 @ X1)) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X0 @ X1) @ (ap @ (c_2Eoption_2ESOME @ X0) @ X17)) @ X18) @ X19)) = ((ap @ X19 @ X17)))))) & ! [X5 : $i] : ((mem @ X5 @ X0) => ! [X6 : $i] : ((mem @ X6 @ X0) => ((((ap @ (c_2Eoption_2ESOME @ X0) @ X5)) = ((ap @ (c_2Eoption_2ESOME @ X0) @ X6))) <=> (X5 = X6)))) & ! [X11 : $i] : ((mem @ X11 @ (ty_2Eoption_2Eoption @ X0)) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X0 @ (ty_2Eoption_2Eoption @ X0)) @ X11) @ X11) @ (c_2Eoption_2ESOME @ X0))) = X11)) & ! [X13 : $i] : ((mem @ X13 @ (arr @ X0 @ X1)) => (((ap @ (ap @ (c_2Eoption_2EOPTION__MAP @ X0 @ X1) @ X13) @ (c_2Eoption_2ENONE @ X0))) = ((c_2Eoption_2ENONE @ X1)))) & ! [X20 : $i] : ((mem @ X20 @ X1) => ! [X21 : $i] : ((mem @ X21 @ (arr @ X0 @ X1)) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X0 @ X1) @ (c_2Eoption_2ENONE @ X0)) @ X20) @ X21)) = X20))) & ! [X9 : $i] : ((mem @ X9 @ X0) => ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X0) @ (ap @ (c_2Eoption_2ESOME @ X0) @ X9))) <=> $true)) & ! [X26 : $i] : ((mem @ X26 @ (ty_2Eoption_2Eoption @ X0)) => ((X26 = ((c_2Eoption_2ENONE @ X0))) <=> ~(p @ (ap @ (c_2Eoption_2EIS__SOME @ X0) @ X26)))) & ! [X23 : $i] : ((mem @ X23 @ (ty_2Eoption_2Eoption @ X0)) => ((p @ (ap @ (c_2Eoption_2EIS__NONE @ X0) @ X23)) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X0 @ X1) @ X23) @ X2) @ X3)) = X2))) & ! [X15 : $i] : ((mem @ X15 @ (arr @ X0 @ X1)) => ! [X16 : $i] : ((mem @ X16 @ X0) => (((ap @ (ap @ (c_2Eoption_2EOPTION__MAP @ X0 @ X1) @ X15) @ (ap @ (c_2Eoption_2ESOME @ X0) @ X16))) = ((ap @ (c_2Eoption_2ESOME @ X1) @ (ap @ X15 @ X16)))))) & ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X0) @ (c_2Eoption_2ENONE @ X0))) <=> $false) & ! [X24 : $i] : ((mem @ X24 @ (ty_2Eoption_2Eoption @ X0)) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X0 @ (ty_2Eoption_2Eoption @ X0)) @ X24) @ (c_2Eoption_2ENONE @ X0)) @ (c_2Eoption_2ESOME @ X0))) = X24)) & ! [X14 : $i] : ((mem @ X14 @ (ty_2Eoption_2Eoption @ X0)) => (((ap @ (c_2Eoption_2EOPTION__JOIN @ X0) @ (ap @ (c_2Eoption_2ESOME @ (ty_2Eoption_2Eoption @ X0)) @ X14))) = X14)) & ! [X10 : $i] : ((mem @ X10 @ (ty_2Eoption_2Eoption @ X0)) => ((X10 = ((c_2Eoption_2ENONE @ X0))) <=> (p @ (ap @ (c_2Eoption_2EIS__NONE @ X0) @ X10)))) & ! [X8 : $i] : ((mem @ X8 @ X0) => (((ap @ (c_2Eoption_2ESOME @ X0) @ X8)) != ((c_2Eoption_2ENONE @ X0)))) & (((ap @ (c_2Eoption_2EOPTION__JOIN @ X0) @ (c_2Eoption_2ENONE @ (ty_2Eoption_2Eoption @ X0)))) = ((c_2Eoption_2ENONE @ X0))) & ! [X25 : $i] : ((mem @ X25 @ (ty_2Eoption_2Eoption @ X0)) => ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X0) @ X25)) => (((ap @ (c_2Eoption_2ESOME @ X0) @ (ap @ (c_2Eoption_2ETHE @ X0) @ X25))) = X25))) & ! [X22 : $i] : ((mem @ X22 @ (ty_2Eoption_2Eoption @ X0)) => ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X0) @ X22)) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X0 @ X1) @ X22) @ X2) @ X3)) = ((ap @ X3 @ (ap @ (c_2Eoption_2ETHE @ X0) @ X22)))))) & ! [X12 : $i] : ((mem @ X12 @ (ty_2Eoption_2Eoption @ X0)) => ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X0) @ X12)) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X0 @ (ty_2Eoption_2Eoption @ X0)) @ X12) @ X4) @ (c_2Eoption_2ESOME @ X0))) = X12)))))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Eoption_2Eoption__CLAUSES)).
thf(f25,axiom,(
  ! [X0 : del] : (mem @ (c_2Eoption_2ESOME @ X0) @ (arr @ X0 @ (ty_2Eoption_2Eoption @ X0)))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Eoption_2ESOME)).
thf(f35,axiom,(
  ! [X0 : del] : (mem @ (c_2Eoption_2ENONE @ X0) @ (ty_2Eoption_2Eoption @ X0))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Eoption_2ENONE)).
thf(f39,conjecture,(
  ! [X1 : $i,X0 : del] : ((mem @ X1 @ (arr @ X0 @ (arr @ X0 @ bool))) => ! [X2 : $i] : ((mem @ X2 @ X0) => ! [X3 : $i] : ((mem @ X3 @ X0) => (($true <=> (p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X0 @ X0) @ X1) @ (c_2Eoption_2ENONE @ X0)) @ (c_2Eoption_2ENONE @ X0)))) & ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X0 @ X0) @ X1) @ (ap @ (c_2Eoption_2ESOME @ X0) @ X2)) @ (ap @ (c_2Eoption_2ESOME @ X0) @ X3))) <=> (p @ (ap @ (ap @ X1 @ X2) @ X3))) & ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X0 @ X0) @ X1) @ (c_2Eoption_2ENONE @ X0)) @ (ap @ (c_2Eoption_2ESOME @ X0) @ X3))) <=> $false) & ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X0 @ X0) @ X1) @ (ap @ (c_2Eoption_2ESOME @ X0) @ X2)) @ (c_2Eoption_2ENONE @ X0))) <=> $false)))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Equotient__option_2EOPTION__REL__def)).
thf(f40,negated_conjecture,(
  ~ ! [X1 : $i,X0 : del] : ((mem @ X1 @ (arr @ X0 @ (arr @ X0 @ bool))) => ! [X2 : $i] : ((mem @ X2 @ X0) => ! [X3 : $i] : ((mem @ X3 @ X0) => (($true <=> (p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X0 @ X0) @ X1) @ (c_2Eoption_2ENONE @ X0)) @ (c_2Eoption_2ENONE @ X0)))) & ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X0 @ X0) @ X1) @ (ap @ (c_2Eoption_2ESOME @ X0) @ X2)) @ (ap @ (c_2Eoption_2ESOME @ X0) @ X3))) <=> (p @ (ap @ (ap @ X1 @ X2) @ X3))) & ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X0 @ X0) @ X1) @ (c_2Eoption_2ENONE @ X0)) @ (ap @ (c_2Eoption_2ESOME @ X0) @ X3))) <=> $false) & ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X0 @ X0) @ X1) @ (ap @ (c_2Eoption_2ESOME @ X0) @ X2)) @ (c_2Eoption_2ENONE @ X0))) <=> $false)))))),
  inference(negated_conjecture,[status(cth)],[f39])).
thf(f46,axiom,(
  ! [X1 : del,X2 : $i,X0 : del] : ((mem @ X2 @ (arr @ X0 @ (arr @ X1 @ bool))) => ! [X3 : $i] : ((mem @ X3 @ (ty_2Eoption_2Eoption @ X0)) => ! [X4 : $i] : ((mem @ X4 @ (ty_2Eoption_2Eoption @ X1)) => ((((X3 = ((c_2Eoption_2ENONE @ X0))) & (X4 = ((c_2Eoption_2ENONE @ X1)))) | ? [X5 : $i] : (? [X6 : $i] : ((X4 = ((ap @ (c_2Eoption_2ESOME @ X1) @ X6))) & (X3 = ((ap @ (c_2Eoption_2ESOME @ X0) @ X5))) & (mem @ X6 @ X1) & (p @ (ap @ (ap @ X2 @ X5) @ X6))) & (mem @ X5 @ X0))) <=> (p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X0 @ X1) @ X2) @ X3) @ X4))))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Eoption_2EOPTREL__def)).
thf(f56,plain,(
  ~ ! [X0 : $i,X1 : del] : ((mem @ X0 @ (arr @ X1 @ (arr @ X1 @ bool))) => ! [X2 : $i] : ((mem @ X2 @ X1) => ! [X3 : $i] : ((mem @ X3 @ X1) => (($true <=> (p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X1 @ X1) @ X0) @ (c_2Eoption_2ENONE @ X1)) @ (c_2Eoption_2ENONE @ X1)))) & ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X1 @ X1) @ X0) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X2)) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X3))) <=> (p @ (ap @ (ap @ X0 @ X2) @ X3))) & ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X1 @ X1) @ X0) @ (c_2Eoption_2ENONE @ X1)) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X3))) <=> $false) & ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X1 @ X1) @ X0) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X2)) @ (c_2Eoption_2ENONE @ X1))) <=> $false)))))),
  inference(rectify,[],[f40])).
thf(f57,plain,(
  ~ ! [X0 : $i,X1 : del] : ((((mem @ X0 @ (arr @ X1 @ (arr @ X1 @ bool)))) = $true) => ! [X2 : $i] : ((((mem @ X2 @ X1)) = $true) => ! [X3 : $i] : ((((mem @ X3 @ X1)) = $true) => (($true <=> ($true = ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X1 @ X1) @ X0) @ (c_2Eoption_2ENONE @ X1)) @ (c_2Eoption_2ENONE @ X1)))))) & (((p @ (ap @ (ap @ X0 @ X2) @ X3))) = ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X1 @ X1) @ X0) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X2)) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X3))))) & ((((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X1 @ X1) @ X0) @ (c_2Eoption_2ENONE @ X1)) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X3)))) = $true) <=> $false) & ((((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X1 @ X1) @ X0) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X2)) @ (c_2Eoption_2ENONE @ X1)))) = $true) <=> $false)))))),
  inference(fool_elimination,[],[f56])).
thf(f84,plain,(
  ! [X0 : del,X1 : $i,X2 : del] : ((mem @ X1 @ (arr @ X0 @ X2)) => ! [X3 : $i] : ((mem @ X3 @ X0) => (mem @ (ap @ X1 @ X3) @ X2)))),
  inference(rectify,[],[f5])).
thf(f85,plain,(
  ! [X2 : del,X0 : del,X1 : $i] : ((((mem @ X1 @ (arr @ X0 @ X2))) = $true) => ! [X3 : $i] : ((((mem @ X3 @ X0)) = $true) => (((mem @ (ap @ X1 @ X3) @ X2)) = $true)))),
  inference(fool_elimination,[],[f84])).
thf(f86,plain,(
  ! [X0 : del] : (mem @ (c_2Eoption_2ESOME @ X0) @ (arr @ X0 @ (ty_2Eoption_2Eoption @ X0)))),
  inference(rectify,[],[f25])).
thf(f87,plain,(
  ! [X0 : del] : (((mem @ (c_2Eoption_2ESOME @ X0) @ (arr @ X0 @ (ty_2Eoption_2Eoption @ X0)))) = $true)),
  inference(fool_elimination,[],[f86])).
thf(f96,plain,(
  ! [X0 : del,X1 : $i,X2 : del] : ((mem @ X1 @ (arr @ X2 @ (arr @ X0 @ bool))) => ! [X3 : $i] : ((mem @ X3 @ (ty_2Eoption_2Eoption @ X2)) => ! [X4 : $i] : ((mem @ X4 @ (ty_2Eoption_2Eoption @ X0)) => ((((((c_2Eoption_2ENONE @ X2)) = X3) & (((c_2Eoption_2ENONE @ X0)) = X4)) | ? [X5 : $i] : (? [X6 : $i] : ((((ap @ (c_2Eoption_2ESOME @ X0) @ X6)) = X4) & (((ap @ (c_2Eoption_2ESOME @ X2) @ X5)) = X3) & (mem @ X6 @ X0) & (p @ (ap @ (ap @ X1 @ X5) @ X6))) & (mem @ X5 @ X2))) <=> (p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X0) @ X1) @ X3) @ X4))))))),
  inference(rectify,[],[f46])).
thf(f97,plain,(
  ! [X1 : $i,X2 : del,X0 : del] : ((((mem @ X1 @ (arr @ X2 @ (arr @ X0 @ bool)))) = $true) => ! [X3 : $i] : (($true = ((mem @ X3 @ (ty_2Eoption_2Eoption @ X2)))) => ! [X4 : $i] : ((((mem @ X4 @ (ty_2Eoption_2Eoption @ X0))) = $true) => ((? [X5 : $i] : ((((mem @ X5 @ X2)) = $true) & ? [X6 : $i] : ((((ap @ (c_2Eoption_2ESOME @ X2) @ X5)) = X3) & ($true = ((p @ (ap @ (ap @ X1 @ X5) @ X6)))) & (((mem @ X6 @ X0)) = $true) & (((ap @ (c_2Eoption_2ESOME @ X0) @ X6)) = X4))) | ((((c_2Eoption_2ENONE @ X0)) = X4) & (((c_2Eoption_2ENONE @ X2)) = X3))) <=> (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X0) @ X1) @ X3) @ X4))) = $true)))))),
  inference(fool_elimination,[],[f96])).
thf(f124,plain,(
  ! [X0 : del] : (mem @ (c_2Eoption_2ENONE @ X0) @ (ty_2Eoption_2Eoption @ X0))),
  inference(rectify,[],[f35])).
thf(f125,plain,(
  ! [X0 : del] : (((mem @ (c_2Eoption_2ENONE @ X0) @ (ty_2Eoption_2Eoption @ X0))) = $true)),
  inference(fool_elimination,[],[f124])).
thf(f134,plain,(
  ! [X0 : del,X1 : del,X2 : $i] : ((mem @ X2 @ X0) => ! [X3 : $i] : ((mem @ X3 @ (arr @ X1 @ X0)) => ! [X4 : $i] : ((mem @ X4 @ (ty_2Eoption_2Eoption @ X1)) => (! [X5 : $i] : ((mem @ X5 @ X1) => (((ap @ (c_2Eoption_2ETHE @ X1) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X5))) = X5)) & ! [X6 : $i] : ((mem @ X6 @ X1) => (((c_2Eoption_2ENONE @ X1)) != ((ap @ (c_2Eoption_2ESOME @ X1) @ X6)))) & ! [X7 : $i] : ((mem @ X7 @ X1) => ! [X8 : $i] : ((mem @ X8 @ X0) => ! [X9 : $i] : ((mem @ X9 @ (arr @ X1 @ X0)) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X7)) @ X8) @ X9)) = ((ap @ X9 @ X7)))))) & ! [X10 : $i] : ((mem @ X10 @ X1) => ! [X11 : $i] : ((mem @ X11 @ X1) => ((((ap @ (c_2Eoption_2ESOME @ X1) @ X11)) = ((ap @ (c_2Eoption_2ESOME @ X1) @ X10))) <=> (X10 = X11)))) & ! [X12 : $i] : ((mem @ X12 @ (ty_2Eoption_2Eoption @ X1)) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ (ty_2Eoption_2Eoption @ X1)) @ X12) @ X12) @ (c_2Eoption_2ESOME @ X1))) = X12)) & ! [X13 : $i] : ((mem @ X13 @ (arr @ X1 @ X0)) => (((c_2Eoption_2ENONE @ X0)) = ((ap @ (ap @ (c_2Eoption_2EOPTION__MAP @ X1 @ X0) @ X13) @ (c_2Eoption_2ENONE @ X1))))) & ! [X14 : $i] : ((mem @ X14 @ X0) => ! [X15 : $i] : ((mem @ X15 @ (arr @ X1 @ X0)) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ (c_2Eoption_2ENONE @ X1)) @ X14) @ X15)) = X14))) & ! [X16 : $i] : ((mem @ X16 @ X1) => ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X16))) <=> $true)) & ! [X17 : $i] : ((mem @ X17 @ (ty_2Eoption_2Eoption @ X1)) => ((((c_2Eoption_2ENONE @ X1)) = X17) <=> ~(p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X17)))) & ! [X18 : $i] : ((mem @ X18 @ (ty_2Eoption_2Eoption @ X1)) => ((p @ (ap @ (c_2Eoption_2EIS__NONE @ X1) @ X18)) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ X18) @ X2) @ X3)) = X2))) & ! [X19 : $i] : ((mem @ X19 @ (arr @ X1 @ X0)) => ! [X20 : $i] : ((mem @ X20 @ X1) => (((ap @ (ap @ (c_2Eoption_2EOPTION__MAP @ X1 @ X0) @ X19) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X20))) = ((ap @ (c_2Eoption_2ESOME @ X0) @ (ap @ X19 @ X20)))))) & ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ (c_2Eoption_2ENONE @ X1))) <=> $false) & ! [X21 : $i] : ((mem @ X21 @ (ty_2Eoption_2Eoption @ X1)) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ (ty_2Eoption_2Eoption @ X1)) @ X21) @ (c_2Eoption_2ENONE @ X1)) @ (c_2Eoption_2ESOME @ X1))) = X21)) & ! [X22 : $i] : ((mem @ X22 @ (ty_2Eoption_2Eoption @ X1)) => (((ap @ (c_2Eoption_2EOPTION__JOIN @ X1) @ (ap @ (c_2Eoption_2ESOME @ (ty_2Eoption_2Eoption @ X1)) @ X22))) = X22)) & ! [X23 : $i] : ((mem @ X23 @ (ty_2Eoption_2Eoption @ X1)) => ((((c_2Eoption_2ENONE @ X1)) = X23) <=> (p @ (ap @ (c_2Eoption_2EIS__NONE @ X1) @ X23)))) & ! [X24 : $i] : ((mem @ X24 @ X1) => (((c_2Eoption_2ENONE @ X1)) != ((ap @ (c_2Eoption_2ESOME @ X1) @ X24)))) & (((c_2Eoption_2ENONE @ X1)) = ((ap @ (c_2Eoption_2EOPTION__JOIN @ X1) @ (c_2Eoption_2ENONE @ (ty_2Eoption_2Eoption @ X1))))) & ! [X25 : $i] : ((mem @ X25 @ (ty_2Eoption_2Eoption @ X1)) => ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X25)) => (((ap @ (c_2Eoption_2ESOME @ X1) @ (ap @ (c_2Eoption_2ETHE @ X1) @ X25))) = X25))) & ! [X26 : $i] : ((mem @ X26 @ (ty_2Eoption_2Eoption @ X1)) => ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X26)) => (((ap @ X3 @ (ap @ (c_2Eoption_2ETHE @ X1) @ X26))) = ((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ X26) @ X2) @ X3))))) & ! [X27 : $i] : ((mem @ X27 @ (ty_2Eoption_2Eoption @ X1)) => ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X27)) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ (ty_2Eoption_2Eoption @ X1)) @ X27) @ X4) @ (c_2Eoption_2ESOME @ X1))) = X27)))))))),
  inference(rectify,[],[f21])).
thf(f135,plain,(
  ! [X0 : del,X1 : del,X2 : $i] : ((((mem @ X2 @ X0)) = $true) => ! [X3 : $i] : ((((mem @ X3 @ (arr @ X1 @ X0))) = $true) => ! [X4 : $i] : ((((mem @ X4 @ (ty_2Eoption_2Eoption @ X1))) = $true) => (! [X5 : $i] : ((((mem @ X5 @ X1)) = $true) => (((ap @ (c_2Eoption_2ETHE @ X1) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X5))) = X5)) & ! [X6 : $i] : ((((mem @ X6 @ X1)) = $true) => (((c_2Eoption_2ENONE @ X1)) != ((ap @ (c_2Eoption_2ESOME @ X1) @ X6)))) & ! [X7 : $i] : (($true = ((mem @ X7 @ X1))) => ! [X8 : $i] : ((((mem @ X8 @ X0)) = $true) => ! [X9 : $i] : ((((mem @ X9 @ (arr @ X1 @ X0))) = $true) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X7)) @ X8) @ X9)) = ((ap @ X9 @ X7)))))) & ! [X10 : $i] : (($true = ((mem @ X10 @ X1))) => ! [X11 : $i] : ((((mem @ X11 @ X1)) = $true) => ((X10 = X11) <=> (((ap @ (c_2Eoption_2ESOME @ X1) @ X11)) = ((ap @ (c_2Eoption_2ESOME @ X1) @ X10)))))) & ! [X12 : $i] : ((((mem @ X12 @ (ty_2Eoption_2Eoption @ X1))) = $true) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ (ty_2Eoption_2Eoption @ X1)) @ X12) @ X12) @ (c_2Eoption_2ESOME @ X1))) = X12)) & ! [X13 : $i] : ((((mem @ X13 @ (arr @ X1 @ X0))) = $true) => (((c_2Eoption_2ENONE @ X0)) = ((ap @ (ap @ (c_2Eoption_2EOPTION__MAP @ X1 @ X0) @ X13) @ (c_2Eoption_2ENONE @ X1))))) & ! [X14 : $i] : (($true = ((mem @ X14 @ X0))) => ! [X15 : $i] : ((((mem @ X15 @ (arr @ X1 @ X0))) = $true) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ (c_2Eoption_2ENONE @ X1)) @ X14) @ X15)) = X14))) & ! [X16 : $i] : (($true = ((mem @ X16 @ X1))) => ((((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X16)))) = $true) <=> $true)) & ! [X17 : $i] : ((((mem @ X17 @ (ty_2Eoption_2Eoption @ X1))) = $true) => ((((c_2Eoption_2ENONE @ X1)) = X17) <=> ~ ($true = ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X17)))))) & ! [X18 : $i] : ((((mem @ X18 @ (ty_2Eoption_2Eoption @ X1))) = $true) => (($true = ((p @ (ap @ (c_2Eoption_2EIS__NONE @ X1) @ X18)))) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ X18) @ X2) @ X3)) = X2))) & ! [X19 : $i] : (($true = ((mem @ X19 @ (arr @ X1 @ X0)))) => ! [X20 : $i] : ((((mem @ X20 @ X1)) = $true) => (((ap @ (ap @ (c_2Eoption_2EOPTION__MAP @ X1 @ X0) @ X19) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X20))) = ((ap @ (c_2Eoption_2ESOME @ X0) @ (ap @ X19 @ X20)))))) & ((((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ (c_2Eoption_2ENONE @ X1)))) = $true) <=> $false) & ! [X21 : $i] : (($true = ((mem @ X21 @ (ty_2Eoption_2Eoption @ X1)))) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ (ty_2Eoption_2Eoption @ X1)) @ X21) @ (c_2Eoption_2ENONE @ X1)) @ (c_2Eoption_2ESOME @ X1))) = X21)) & ! [X22 : $i] : ((((mem @ X22 @ (ty_2Eoption_2Eoption @ X1))) = $true) => (((ap @ (c_2Eoption_2EOPTION__JOIN @ X1) @ (ap @ (c_2Eoption_2ESOME @ (ty_2Eoption_2Eoption @ X1)) @ X22))) = X22)) & ! [X23 : $i] : (($true = ((mem @ X23 @ (ty_2Eoption_2Eoption @ X1)))) => ((((p @ (ap @ (c_2Eoption_2EIS__NONE @ X1) @ X23))) = $true) <=> (((c_2Eoption_2ENONE @ X1)) = X23))) & ! [X24 : $i] : (($true = ((mem @ X24 @ X1))) => (((c_2Eoption_2ENONE @ X1)) != ((ap @ (c_2Eoption_2ESOME @ X1) @ X24)))) & (((c_2Eoption_2ENONE @ X1)) = ((ap @ (c_2Eoption_2EOPTION__JOIN @ X1) @ (c_2Eoption_2ENONE @ (ty_2Eoption_2Eoption @ X1))))) & ! [X25 : $i] : ((((mem @ X25 @ (ty_2Eoption_2Eoption @ X1))) = $true) => (($true = ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X25)))) => (((ap @ (c_2Eoption_2ESOME @ X1) @ (ap @ (c_2Eoption_2ETHE @ X1) @ X25))) = X25))) & ! [X26 : $i] : ((((mem @ X26 @ (ty_2Eoption_2Eoption @ X1))) = $true) => (($true = ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X26)))) => (((ap @ X3 @ (ap @ (c_2Eoption_2ETHE @ X1) @ X26))) = ((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ X26) @ X2) @ X3))))) & ! [X27 : $i] : (($true = ((mem @ X27 @ (ty_2Eoption_2Eoption @ X1)))) => (($true = ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X27)))) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ (ty_2Eoption_2Eoption @ X1)) @ X27) @ X4) @ (c_2Eoption_2ESOME @ X1))) = X27)))))))),
  inference(fool_elimination,[],[f134])).
thf(f136,plain,(
  ~ ! [X0 : $i,X1 : del] : ((((mem @ X0 @ (arr @ X1 @ (arr @ X1 @ bool)))) = $true) => ! [X2 : $i] : ((((mem @ X2 @ X1)) = $true) => ! [X3 : $i] : ((((mem @ X3 @ X1)) = $true) => (($true = ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X1 @ X1) @ X0) @ (c_2Eoption_2ENONE @ X1)) @ (c_2Eoption_2ENONE @ X1))))) & (((p @ (ap @ (ap @ X0 @ X2) @ X3))) = ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X1 @ X1) @ X0) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X2)) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X3))))) & ~ (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X1 @ X1) @ X0) @ (c_2Eoption_2ENONE @ X1)) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X3)))) = $true) & ~ (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X1 @ X1) @ X0) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X2)) @ (c_2Eoption_2ENONE @ X1)))) = $true)))))),
  inference(true_and_false_elimination,[],[f57])).
thf(f137,plain,(
  ~ ! [X0 : $i,X1 : del] : ((((mem @ X0 @ (arr @ X1 @ (arr @ X1 @ bool)))) = $true) => ! [X2 : $i] : ((((mem @ X2 @ X1)) = $true) => ! [X3 : $i] : ((((mem @ X3 @ X1)) = $true) => ((((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X1 @ X1) @ X0) @ (c_2Eoption_2ENONE @ X1)) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X3)))) != $true) & (((p @ (ap @ (ap @ X0 @ X2) @ X3))) = ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X1 @ X1) @ X0) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X2)) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X3))))) & ($true = ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X1 @ X1) @ X0) @ (c_2Eoption_2ENONE @ X1)) @ (c_2Eoption_2ENONE @ X1))))) & (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X1 @ X1) @ X0) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X2)) @ (c_2Eoption_2ENONE @ X1)))) != $true)))))),
  inference(flattening,[],[f136])).
thf(f146,plain,(
  ! [X0 : del,X1 : del,X2 : $i] : ((((mem @ X2 @ X0)) = $true) => ! [X3 : $i] : ((((mem @ X3 @ (arr @ X1 @ X0))) = $true) => ! [X4 : $i] : ((((mem @ X4 @ (ty_2Eoption_2Eoption @ X1))) = $true) => (! [X5 : $i] : ((((mem @ X5 @ X1)) = $true) => (((ap @ (c_2Eoption_2ETHE @ X1) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X5))) = X5)) & ! [X6 : $i] : ((((mem @ X6 @ X1)) = $true) => (((c_2Eoption_2ENONE @ X1)) != ((ap @ (c_2Eoption_2ESOME @ X1) @ X6)))) & ! [X7 : $i] : (($true = ((mem @ X7 @ X1))) => ! [X8 : $i] : ((((mem @ X8 @ X0)) = $true) => ! [X9 : $i] : ((((mem @ X9 @ (arr @ X1 @ X0))) = $true) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X7)) @ X8) @ X9)) = ((ap @ X9 @ X7)))))) & ! [X10 : $i] : (($true = ((mem @ X10 @ X1))) => ! [X11 : $i] : ((((mem @ X11 @ X1)) = $true) => ((X10 = X11) <=> (((ap @ (c_2Eoption_2ESOME @ X1) @ X11)) = ((ap @ (c_2Eoption_2ESOME @ X1) @ X10)))))) & ! [X12 : $i] : ((((mem @ X12 @ (ty_2Eoption_2Eoption @ X1))) = $true) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ (ty_2Eoption_2Eoption @ X1)) @ X12) @ X12) @ (c_2Eoption_2ESOME @ X1))) = X12)) & ! [X13 : $i] : ((((mem @ X13 @ (arr @ X1 @ X0))) = $true) => (((c_2Eoption_2ENONE @ X0)) = ((ap @ (ap @ (c_2Eoption_2EOPTION__MAP @ X1 @ X0) @ X13) @ (c_2Eoption_2ENONE @ X1))))) & ! [X14 : $i] : (($true = ((mem @ X14 @ X0))) => ! [X15 : $i] : ((((mem @ X15 @ (arr @ X1 @ X0))) = $true) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ (c_2Eoption_2ENONE @ X1)) @ X14) @ X15)) = X14))) & ! [X16 : $i] : (($true = ((mem @ X16 @ X1))) => (((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X16)))) = $true)) & ! [X17 : $i] : ((((mem @ X17 @ (ty_2Eoption_2Eoption @ X1))) = $true) => ((((c_2Eoption_2ENONE @ X1)) = X17) <=> ~ ($true = ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X17)))))) & ! [X18 : $i] : ((((mem @ X18 @ (ty_2Eoption_2Eoption @ X1))) = $true) => (($true = ((p @ (ap @ (c_2Eoption_2EIS__NONE @ X1) @ X18)))) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ X18) @ X2) @ X3)) = X2))) & ! [X19 : $i] : (($true = ((mem @ X19 @ (arr @ X1 @ X0)))) => ! [X20 : $i] : ((((mem @ X20 @ X1)) = $true) => (((ap @ (ap @ (c_2Eoption_2EOPTION__MAP @ X1 @ X0) @ X19) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X20))) = ((ap @ (c_2Eoption_2ESOME @ X0) @ (ap @ X19 @ X20)))))) & ~ (((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ (c_2Eoption_2ENONE @ X1)))) = $true) & ! [X21 : $i] : (($true = ((mem @ X21 @ (ty_2Eoption_2Eoption @ X1)))) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ (ty_2Eoption_2Eoption @ X1)) @ X21) @ (c_2Eoption_2ENONE @ X1)) @ (c_2Eoption_2ESOME @ X1))) = X21)) & ! [X22 : $i] : ((((mem @ X22 @ (ty_2Eoption_2Eoption @ X1))) = $true) => (((ap @ (c_2Eoption_2EOPTION__JOIN @ X1) @ (ap @ (c_2Eoption_2ESOME @ (ty_2Eoption_2Eoption @ X1)) @ X22))) = X22)) & ! [X23 : $i] : (($true = ((mem @ X23 @ (ty_2Eoption_2Eoption @ X1)))) => ((((p @ (ap @ (c_2Eoption_2EIS__NONE @ X1) @ X23))) = $true) <=> (((c_2Eoption_2ENONE @ X1)) = X23))) & ! [X24 : $i] : (($true = ((mem @ X24 @ X1))) => (((c_2Eoption_2ENONE @ X1)) != ((ap @ (c_2Eoption_2ESOME @ X1) @ X24)))) & (((c_2Eoption_2ENONE @ X1)) = ((ap @ (c_2Eoption_2EOPTION__JOIN @ X1) @ (c_2Eoption_2ENONE @ (ty_2Eoption_2Eoption @ X1))))) & ! [X25 : $i] : ((((mem @ X25 @ (ty_2Eoption_2Eoption @ X1))) = $true) => (($true = ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X25)))) => (((ap @ (c_2Eoption_2ESOME @ X1) @ (ap @ (c_2Eoption_2ETHE @ X1) @ X25))) = X25))) & ! [X26 : $i] : ((((mem @ X26 @ (ty_2Eoption_2Eoption @ X1))) = $true) => (($true = ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X26)))) => (((ap @ X3 @ (ap @ (c_2Eoption_2ETHE @ X1) @ X26))) = ((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ X26) @ X2) @ X3))))) & ! [X27 : $i] : (($true = ((mem @ X27 @ (ty_2Eoption_2Eoption @ X1)))) => (($true = ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X27)))) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ (ty_2Eoption_2Eoption @ X1)) @ X27) @ X4) @ (c_2Eoption_2ESOME @ X1))) = X27)))))))),
  inference(true_and_false_elimination,[],[f135])).
thf(f147,plain,(
  ! [X0 : del,X1 : del,X2 : $i] : ((((mem @ X2 @ X0)) = $true) => ! [X3 : $i] : ((((mem @ X3 @ (arr @ X1 @ X0))) = $true) => ! [X4 : $i] : ((((mem @ X4 @ (ty_2Eoption_2Eoption @ X1))) = $true) => (! [X26 : $i] : ((((mem @ X26 @ (ty_2Eoption_2Eoption @ X1))) = $true) => (($true = ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X26)))) => (((ap @ X3 @ (ap @ (c_2Eoption_2ETHE @ X1) @ X26))) = ((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ X26) @ X2) @ X3))))) & ! [X10 : $i] : (($true = ((mem @ X10 @ X1))) => ! [X11 : $i] : ((((mem @ X11 @ X1)) = $true) => ((X10 = X11) <=> (((ap @ (c_2Eoption_2ESOME @ X1) @ X11)) = ((ap @ (c_2Eoption_2ESOME @ X1) @ X10)))))) & ! [X12 : $i] : ((((mem @ X12 @ (ty_2Eoption_2Eoption @ X1))) = $true) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ (ty_2Eoption_2Eoption @ X1)) @ X12) @ X12) @ (c_2Eoption_2ESOME @ X1))) = X12)) & ! [X25 : $i] : ((((mem @ X25 @ (ty_2Eoption_2Eoption @ X1))) = $true) => (($true = ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X25)))) => (((ap @ (c_2Eoption_2ESOME @ X1) @ (ap @ (c_2Eoption_2ETHE @ X1) @ X25))) = X25))) & ! [X17 : $i] : ((((mem @ X17 @ (ty_2Eoption_2Eoption @ X1))) = $true) => ((((c_2Eoption_2ENONE @ X1)) = X17) <=> ($true != ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X17)))))) & ! [X13 : $i] : ((((mem @ X13 @ (arr @ X1 @ X0))) = $true) => (((c_2Eoption_2ENONE @ X0)) = ((ap @ (ap @ (c_2Eoption_2EOPTION__MAP @ X1 @ X0) @ X13) @ (c_2Eoption_2ENONE @ X1))))) & ! [X6 : $i] : ((((mem @ X6 @ X1)) = $true) => (((c_2Eoption_2ENONE @ X1)) != ((ap @ (c_2Eoption_2ESOME @ X1) @ X6)))) & ! [X22 : $i] : ((((mem @ X22 @ (ty_2Eoption_2Eoption @ X1))) = $true) => (((ap @ (c_2Eoption_2EOPTION__JOIN @ X1) @ (ap @ (c_2Eoption_2ESOME @ (ty_2Eoption_2Eoption @ X1)) @ X22))) = X22)) & (((c_2Eoption_2ENONE @ X1)) = ((ap @ (c_2Eoption_2EOPTION__JOIN @ X1) @ (c_2Eoption_2ENONE @ (ty_2Eoption_2Eoption @ X1))))) & (((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ (c_2Eoption_2ENONE @ X1)))) != $true) & ! [X21 : $i] : (($true = ((mem @ X21 @ (ty_2Eoption_2Eoption @ X1)))) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ (ty_2Eoption_2Eoption @ X1)) @ X21) @ (c_2Eoption_2ENONE @ X1)) @ (c_2Eoption_2ESOME @ X1))) = X21)) & ! [X5 : $i] : ((((mem @ X5 @ X1)) = $true) => (((ap @ (c_2Eoption_2ETHE @ X1) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X5))) = X5)) & ! [X23 : $i] : (($true = ((mem @ X23 @ (ty_2Eoption_2Eoption @ X1)))) => ((((p @ (ap @ (c_2Eoption_2EIS__NONE @ X1) @ X23))) = $true) <=> (((c_2Eoption_2ENONE @ X1)) = X23))) & ! [X14 : $i] : (($true = ((mem @ X14 @ X0))) => ! [X15 : $i] : ((((mem @ X15 @ (arr @ X1 @ X0))) = $true) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ (c_2Eoption_2ENONE @ X1)) @ X14) @ X15)) = X14))) & ! [X16 : $i] : (($true = ((mem @ X16 @ X1))) => (((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X16)))) = $true)) & ! [X7 : $i] : (($true = ((mem @ X7 @ X1))) => ! [X8 : $i] : ((((mem @ X8 @ X0)) = $true) => ! [X9 : $i] : ((((mem @ X9 @ (arr @ X1 @ X0))) = $true) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X7)) @ X8) @ X9)) = ((ap @ X9 @ X7)))))) & ! [X27 : $i] : (($true = ((mem @ X27 @ (ty_2Eoption_2Eoption @ X1)))) => (($true = ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X27)))) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ (ty_2Eoption_2Eoption @ X1)) @ X27) @ X4) @ (c_2Eoption_2ESOME @ X1))) = X27))) & ! [X18 : $i] : ((((mem @ X18 @ (ty_2Eoption_2Eoption @ X1))) = $true) => (($true = ((p @ (ap @ (c_2Eoption_2EIS__NONE @ X1) @ X18)))) => (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ X18) @ X2) @ X3)) = X2))) & ! [X19 : $i] : (($true = ((mem @ X19 @ (arr @ X1 @ X0)))) => ! [X20 : $i] : ((((mem @ X20 @ X1)) = $true) => (((ap @ (ap @ (c_2Eoption_2EOPTION__MAP @ X1 @ X0) @ X19) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X20))) = ((ap @ (c_2Eoption_2ESOME @ X0) @ (ap @ X19 @ X20)))))) & ! [X24 : $i] : (($true = ((mem @ X24 @ X1))) => (((c_2Eoption_2ENONE @ X1)) != ((ap @ (c_2Eoption_2ESOME @ X1) @ X24))))))))),
  inference(flattening,[],[f146])).
thf(f148,plain,(
  ! [X0 : del,X1 : $i,X2 : del] : ((((mem @ X1 @ (arr @ X2 @ (arr @ X0 @ bool)))) != $true) | ! [X3 : $i] : (($true != ((mem @ X3 @ (ty_2Eoption_2Eoption @ X2)))) | ! [X4 : $i] : (((? [X5 : $i] : ((((mem @ X5 @ X2)) = $true) & ? [X6 : $i] : ((((ap @ (c_2Eoption_2ESOME @ X2) @ X5)) = X3) & ($true = ((p @ (ap @ (ap @ X1 @ X5) @ X6)))) & (((mem @ X6 @ X0)) = $true) & (((ap @ (c_2Eoption_2ESOME @ X0) @ X6)) = X4))) | ((((c_2Eoption_2ENONE @ X0)) = X4) & (((c_2Eoption_2ENONE @ X2)) = X3))) <=> (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X0) @ X1) @ X3) @ X4))) = $true)) | (((mem @ X4 @ (ty_2Eoption_2Eoption @ X0))) != $true))))),
  inference(ennf_transformation,[],[f97])).
thf(f149,plain,(
  ! [X2 : del,X0 : del,X1 : $i] : ((((mem @ X1 @ (arr @ X0 @ X2))) != $true) | ! [X3 : $i] : ((((mem @ X3 @ X0)) != $true) | (((mem @ (ap @ X1 @ X3) @ X2)) = $true)))),
  inference(ennf_transformation,[],[f85])).
thf(f153,plain,(
  ? [X1 : del,X0 : $i] : (? [X2 : $i] : ((((mem @ X2 @ X1)) = $true) & ? [X3 : $i] : (((((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X1 @ X1) @ X0) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X2)) @ (c_2Eoption_2ENONE @ X1)))) = $true) | (((p @ (ap @ (ap @ X0 @ X2) @ X3))) != ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X1 @ X1) @ X0) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X2)) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X3))))) | (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X1 @ X1) @ X0) @ (c_2Eoption_2ENONE @ X1)) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X3)))) = $true) | ($true != ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X1 @ X1) @ X0) @ (c_2Eoption_2ENONE @ X1)) @ (c_2Eoption_2ENONE @ X1)))))) & (((mem @ X3 @ X1)) = $true))) & (((mem @ X0 @ (arr @ X1 @ (arr @ X1 @ bool)))) = $true))),
  inference(ennf_transformation,[],[f137])).
thf(f159,plain,(
  ! [X0 : del,X1 : del,X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : ((! [X26 : $i] : (((((ap @ X3 @ (ap @ (c_2Eoption_2ETHE @ X1) @ X26))) = ((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ X26) @ X2) @ X3))) | ($true != ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X26))))) | (((mem @ X26 @ (ty_2Eoption_2Eoption @ X1))) != $true)) & ! [X10 : $i] : (($true != ((mem @ X10 @ X1))) | ! [X11 : $i] : (((X10 = X11) <=> (((ap @ (c_2Eoption_2ESOME @ X1) @ X11)) = ((ap @ (c_2Eoption_2ESOME @ X1) @ X10)))) | (((mem @ X11 @ X1)) != $true))) & ! [X12 : $i] : ((((mem @ X12 @ (ty_2Eoption_2Eoption @ X1))) != $true) | (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ (ty_2Eoption_2Eoption @ X1)) @ X12) @ X12) @ (c_2Eoption_2ESOME @ X1))) = X12)) & ! [X25 : $i] : (((((ap @ (c_2Eoption_2ESOME @ X1) @ (ap @ (c_2Eoption_2ETHE @ X1) @ X25))) = X25) | ($true != ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X25))))) | (((mem @ X25 @ (ty_2Eoption_2Eoption @ X1))) != $true)) & ! [X17 : $i] : ((((mem @ X17 @ (ty_2Eoption_2Eoption @ X1))) != $true) | ((((c_2Eoption_2ENONE @ X1)) = X17) <=> ($true != ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X17)))))) & ! [X13 : $i] : ((((mem @ X13 @ (arr @ X1 @ X0))) != $true) | (((c_2Eoption_2ENONE @ X0)) = ((ap @ (ap @ (c_2Eoption_2EOPTION__MAP @ X1 @ X0) @ X13) @ (c_2Eoption_2ENONE @ X1))))) & ! [X6 : $i] : ((((c_2Eoption_2ENONE @ X1)) != ((ap @ (c_2Eoption_2ESOME @ X1) @ X6))) | (((mem @ X6 @ X1)) != $true)) & ! [X22 : $i] : ((((ap @ (c_2Eoption_2EOPTION__JOIN @ X1) @ (ap @ (c_2Eoption_2ESOME @ (ty_2Eoption_2Eoption @ X1)) @ X22))) = X22) | (((mem @ X22 @ (ty_2Eoption_2Eoption @ X1))) != $true)) & (((c_2Eoption_2ENONE @ X1)) = ((ap @ (c_2Eoption_2EOPTION__JOIN @ X1) @ (c_2Eoption_2ENONE @ (ty_2Eoption_2Eoption @ X1))))) & (((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ (c_2Eoption_2ENONE @ X1)))) != $true) & ! [X21 : $i] : ((((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ (ty_2Eoption_2Eoption @ X1)) @ X21) @ (c_2Eoption_2ENONE @ X1)) @ (c_2Eoption_2ESOME @ X1))) = X21) | ($true != ((mem @ X21 @ (ty_2Eoption_2Eoption @ X1))))) & ! [X5 : $i] : ((((mem @ X5 @ X1)) != $true) | (((ap @ (c_2Eoption_2ETHE @ X1) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X5))) = X5)) & ! [X23 : $i] : (($true != ((mem @ X23 @ (ty_2Eoption_2Eoption @ X1)))) | ((((p @ (ap @ (c_2Eoption_2EIS__NONE @ X1) @ X23))) = $true) <=> (((c_2Eoption_2ENONE @ X1)) = X23))) & ! [X14 : $i] : (! [X15 : $i] : ((((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ (c_2Eoption_2ENONE @ X1)) @ X14) @ X15)) = X14) | (((mem @ X15 @ (arr @ X1 @ X0))) != $true)) | ($true != ((mem @ X14 @ X0)))) & ! [X16 : $i] : (($true != ((mem @ X16 @ X1))) | (((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X16)))) = $true)) & ! [X7 : $i] : (($true != ((mem @ X7 @ X1))) | ! [X8 : $i] : ((((mem @ X8 @ X0)) != $true) | ! [X9 : $i] : ((((mem @ X9 @ (arr @ X1 @ X0))) != $true) | (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X7)) @ X8) @ X9)) = ((ap @ X9 @ X7)))))) & ! [X27 : $i] : (((((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ (ty_2Eoption_2Eoption @ X1)) @ X27) @ X4) @ (c_2Eoption_2ESOME @ X1))) = X27) | ($true != ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X27))))) | ($true != ((mem @ X27 @ (ty_2Eoption_2Eoption @ X1))))) & ! [X18 : $i] : (((((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ X18) @ X2) @ X3)) = X2) | ($true != ((p @ (ap @ (c_2Eoption_2EIS__NONE @ X1) @ X18))))) | (((mem @ X18 @ (ty_2Eoption_2Eoption @ X1))) != $true)) & ! [X19 : $i] : (($true != ((mem @ X19 @ (arr @ X1 @ X0)))) | ! [X20 : $i] : ((((ap @ (ap @ (c_2Eoption_2EOPTION__MAP @ X1 @ X0) @ X19) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X20))) = ((ap @ (c_2Eoption_2ESOME @ X0) @ (ap @ X19 @ X20)))) | (((mem @ X20 @ X1)) != $true))) & ! [X24 : $i] : ((((c_2Eoption_2ENONE @ X1)) != ((ap @ (c_2Eoption_2ESOME @ X1) @ X24))) | ($true != ((mem @ X24 @ X1))))) | (((mem @ X4 @ (ty_2Eoption_2Eoption @ X1))) != $true)) | (((mem @ X3 @ (arr @ X1 @ X0))) != $true)) | (((mem @ X2 @ X0)) != $true))),
  inference(ennf_transformation,[],[f147])).
thf(f160,plain,(
  ! [X0 : del,X2 : $i,X1 : del] : (! [X3 : $i] : ((((mem @ X3 @ (arr @ X1 @ X0))) != $true) | ! [X4 : $i] : ((! [X13 : $i] : ((((mem @ X13 @ (arr @ X1 @ X0))) != $true) | (((c_2Eoption_2ENONE @ X0)) = ((ap @ (ap @ (c_2Eoption_2EOPTION__MAP @ X1 @ X0) @ X13) @ (c_2Eoption_2ENONE @ X1))))) & ! [X17 : $i] : ((((mem @ X17 @ (ty_2Eoption_2Eoption @ X1))) != $true) | ((((c_2Eoption_2ENONE @ X1)) = X17) <=> ($true != ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X17)))))) & ! [X23 : $i] : (($true != ((mem @ X23 @ (ty_2Eoption_2Eoption @ X1)))) | ((((p @ (ap @ (c_2Eoption_2EIS__NONE @ X1) @ X23))) = $true) <=> (((c_2Eoption_2ENONE @ X1)) = X23))) & ! [X6 : $i] : ((((c_2Eoption_2ENONE @ X1)) != ((ap @ (c_2Eoption_2ESOME @ X1) @ X6))) | (((mem @ X6 @ X1)) != $true)) & ! [X19 : $i] : (($true != ((mem @ X19 @ (arr @ X1 @ X0)))) | ! [X20 : $i] : ((((ap @ (ap @ (c_2Eoption_2EOPTION__MAP @ X1 @ X0) @ X19) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X20))) = ((ap @ (c_2Eoption_2ESOME @ X0) @ (ap @ X19 @ X20)))) | (((mem @ X20 @ X1)) != $true))) & ! [X24 : $i] : ((((c_2Eoption_2ENONE @ X1)) != ((ap @ (c_2Eoption_2ESOME @ X1) @ X24))) | ($true != ((mem @ X24 @ X1)))) & ! [X26 : $i] : (($true != ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X26)))) | (((mem @ X26 @ (ty_2Eoption_2Eoption @ X1))) != $true) | (((ap @ X3 @ (ap @ (c_2Eoption_2ETHE @ X1) @ X26))) = ((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ X26) @ X2) @ X3)))) & ! [X18 : $i] : (($true != ((p @ (ap @ (c_2Eoption_2EIS__NONE @ X1) @ X18)))) | (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ X18) @ X2) @ X3)) = X2) | (((mem @ X18 @ (ty_2Eoption_2Eoption @ X1))) != $true)) & ! [X22 : $i] : ((((ap @ (c_2Eoption_2EOPTION__JOIN @ X1) @ (ap @ (c_2Eoption_2ESOME @ (ty_2Eoption_2Eoption @ X1)) @ X22))) = X22) | (((mem @ X22 @ (ty_2Eoption_2Eoption @ X1))) != $true)) & (((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ (c_2Eoption_2ENONE @ X1)))) != $true) & ! [X27 : $i] : (($true != ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X27)))) | ($true != ((mem @ X27 @ (ty_2Eoption_2Eoption @ X1)))) | (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ (ty_2Eoption_2Eoption @ X1)) @ X27) @ X4) @ (c_2Eoption_2ESOME @ X1))) = X27)) & ! [X14 : $i] : (! [X15 : $i] : ((((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ (c_2Eoption_2ENONE @ X1)) @ X14) @ X15)) = X14) | (((mem @ X15 @ (arr @ X1 @ X0))) != $true)) | ($true != ((mem @ X14 @ X0)))) & ! [X10 : $i] : (($true != ((mem @ X10 @ X1))) | ! [X11 : $i] : (((X10 = X11) <=> (((ap @ (c_2Eoption_2ESOME @ X1) @ X11)) = ((ap @ (c_2Eoption_2ESOME @ X1) @ X10)))) | (((mem @ X11 @ X1)) != $true))) & ! [X5 : $i] : ((((mem @ X5 @ X1)) != $true) | (((ap @ (c_2Eoption_2ETHE @ X1) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X5))) = X5)) & ! [X25 : $i] : ((((ap @ (c_2Eoption_2ESOME @ X1) @ (ap @ (c_2Eoption_2ETHE @ X1) @ X25))) = X25) | ($true != ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X25)))) | (((mem @ X25 @ (ty_2Eoption_2Eoption @ X1))) != $true)) & ! [X21 : $i] : ((((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ (ty_2Eoption_2Eoption @ X1)) @ X21) @ (c_2Eoption_2ENONE @ X1)) @ (c_2Eoption_2ESOME @ X1))) = X21) | ($true != ((mem @ X21 @ (ty_2Eoption_2Eoption @ X1))))) & ! [X16 : $i] : (($true != ((mem @ X16 @ X1))) | (((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X16)))) = $true)) & ! [X7 : $i] : (($true != ((mem @ X7 @ X1))) | ! [X8 : $i] : ((((mem @ X8 @ X0)) != $true) | ! [X9 : $i] : ((((mem @ X9 @ (arr @ X1 @ X0))) != $true) | (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X7)) @ X8) @ X9)) = ((ap @ X9 @ X7)))))) & ! [X12 : $i] : ((((mem @ X12 @ (ty_2Eoption_2Eoption @ X1))) != $true) | (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ (ty_2Eoption_2Eoption @ X1)) @ X12) @ X12) @ (c_2Eoption_2ESOME @ X1))) = X12)) & (((c_2Eoption_2ENONE @ X1)) = ((ap @ (c_2Eoption_2EOPTION__JOIN @ X1) @ (c_2Eoption_2ENONE @ (ty_2Eoption_2Eoption @ X1)))))) | (((mem @ X4 @ (ty_2Eoption_2Eoption @ X1))) != $true))) | (((mem @ X2 @ X0)) != $true))),
  inference(flattening,[],[f159])).
thf(f163,definition,(
  ! [X2 : del,X3 : $i,X1 : $i,X0 : del,X4 : $i] : (($true = ((sP0 @ X4 @ X0 @ X1 @ X3 @ X2))) <=> ? [X5 : $i] : ((((mem @ X5 @ X2)) = $true) & ? [X6 : $i] : ((((ap @ (c_2Eoption_2ESOME @ X2) @ X5)) = X3) & ($true = ((p @ (ap @ (ap @ X1 @ X5) @ X6)))) & (((mem @ X6 @ X0)) = $true) & (((ap @ (c_2Eoption_2ESOME @ X0) @ X6)) = X4))))),
  introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
thf(f164,plain,(
  ! [X0 : del,X1 : $i,X2 : del] : ((((mem @ X1 @ (arr @ X2 @ (arr @ X0 @ bool)))) != $true) | ! [X3 : $i] : (($true != ((mem @ X3 @ (ty_2Eoption_2Eoption @ X2)))) | ! [X4 : $i] : (((($true = ((sP0 @ X4 @ X0 @ X1 @ X3 @ X2))) | ((((c_2Eoption_2ENONE @ X0)) = X4) & (((c_2Eoption_2ENONE @ X2)) = X3))) <=> (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X0) @ X1) @ X3) @ X4))) = $true)) | (((mem @ X4 @ (ty_2Eoption_2Eoption @ X0))) != $true))))),
  inference(definition_folding,[],[f148,f163])).
thf(f165,definition,(
  ! [X1 : del] : (! [X10 : $i] : (($true != ((mem @ X10 @ X1))) | ! [X11 : $i] : (((X10 = X11) <=> (((ap @ (c_2Eoption_2ESOME @ X1) @ X11)) = ((ap @ (c_2Eoption_2ESOME @ X1) @ X10)))) | (((mem @ X11 @ X1)) != $true))) | ~ (((sP1 @ X1)) = $true))),
  introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
thf(f166,definition,(
  ! [X1 : del] : (! [X23 : $i] : (($true != ((mem @ X23 @ (ty_2Eoption_2Eoption @ X1)))) | ((((p @ (ap @ (c_2Eoption_2EIS__NONE @ X1) @ X23))) = $true) <=> (((c_2Eoption_2ENONE @ X1)) = X23))) | ~ (((sP2 @ X1)) = $true))),
  introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
thf(f167,definition,(
  ! [X1 : del] : (! [X17 : $i] : ((((mem @ X17 @ (ty_2Eoption_2Eoption @ X1))) != $true) | ((((c_2Eoption_2ENONE @ X1)) = X17) <=> ($true != ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X17)))))) | ~ (((sP3 @ X1)) = $true))),
  introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
thf(f168,definition,(
  ! [X0 : del,X1 : del,X3 : $i,X2 : $i,X4 : $i] : ((! [X13 : $i] : ((((mem @ X13 @ (arr @ X1 @ X0))) != $true) | (((c_2Eoption_2ENONE @ X0)) = ((ap @ (ap @ (c_2Eoption_2EOPTION__MAP @ X1 @ X0) @ X13) @ (c_2Eoption_2ENONE @ X1))))) & (((sP3 @ X1)) = $true) & (((sP2 @ X1)) = $true) & ! [X6 : $i] : ((((c_2Eoption_2ENONE @ X1)) != ((ap @ (c_2Eoption_2ESOME @ X1) @ X6))) | (((mem @ X6 @ X1)) != $true)) & ! [X19 : $i] : (($true != ((mem @ X19 @ (arr @ X1 @ X0)))) | ! [X20 : $i] : ((((ap @ (ap @ (c_2Eoption_2EOPTION__MAP @ X1 @ X0) @ X19) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X20))) = ((ap @ (c_2Eoption_2ESOME @ X0) @ (ap @ X19 @ X20)))) | (((mem @ X20 @ X1)) != $true))) & ! [X24 : $i] : ((((c_2Eoption_2ENONE @ X1)) != ((ap @ (c_2Eoption_2ESOME @ X1) @ X24))) | ($true != ((mem @ X24 @ X1)))) & ! [X26 : $i] : (($true != ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X26)))) | (((mem @ X26 @ (ty_2Eoption_2Eoption @ X1))) != $true) | (((ap @ X3 @ (ap @ (c_2Eoption_2ETHE @ X1) @ X26))) = ((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ X26) @ X2) @ X3)))) & ! [X18 : $i] : (($true != ((p @ (ap @ (c_2Eoption_2EIS__NONE @ X1) @ X18)))) | (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ X18) @ X2) @ X3)) = X2) | (((mem @ X18 @ (ty_2Eoption_2Eoption @ X1))) != $true)) & ! [X22 : $i] : ((((ap @ (c_2Eoption_2EOPTION__JOIN @ X1) @ (ap @ (c_2Eoption_2ESOME @ (ty_2Eoption_2Eoption @ X1)) @ X22))) = X22) | (((mem @ X22 @ (ty_2Eoption_2Eoption @ X1))) != $true)) & (((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ (c_2Eoption_2ENONE @ X1)))) != $true) & ! [X27 : $i] : (($true != ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X27)))) | ($true != ((mem @ X27 @ (ty_2Eoption_2Eoption @ X1)))) | (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ (ty_2Eoption_2Eoption @ X1)) @ X27) @ X4) @ (c_2Eoption_2ESOME @ X1))) = X27)) & ! [X14 : $i] : (! [X15 : $i] : ((((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ (c_2Eoption_2ENONE @ X1)) @ X14) @ X15)) = X14) | (((mem @ X15 @ (arr @ X1 @ X0))) != $true)) | ($true != ((mem @ X14 @ X0)))) & (((sP1 @ X1)) = $true) & ! [X5 : $i] : ((((mem @ X5 @ X1)) != $true) | (((ap @ (c_2Eoption_2ETHE @ X1) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X5))) = X5)) & ! [X25 : $i] : ((((ap @ (c_2Eoption_2ESOME @ X1) @ (ap @ (c_2Eoption_2ETHE @ X1) @ X25))) = X25) | ($true != ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X25)))) | (((mem @ X25 @ (ty_2Eoption_2Eoption @ X1))) != $true)) & ! [X21 : $i] : ((((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ (ty_2Eoption_2Eoption @ X1)) @ X21) @ (c_2Eoption_2ENONE @ X1)) @ (c_2Eoption_2ESOME @ X1))) = X21) | ($true != ((mem @ X21 @ (ty_2Eoption_2Eoption @ X1))))) & ! [X16 : $i] : (($true != ((mem @ X16 @ X1))) | (((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X16)))) = $true)) & ! [X7 : $i] : (($true != ((mem @ X7 @ X1))) | ! [X8 : $i] : ((((mem @ X8 @ X0)) != $true) | ! [X9 : $i] : ((((mem @ X9 @ (arr @ X1 @ X0))) != $true) | (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X7)) @ X8) @ X9)) = ((ap @ X9 @ X7)))))) & ! [X12 : $i] : ((((mem @ X12 @ (ty_2Eoption_2Eoption @ X1))) != $true) | (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ (ty_2Eoption_2Eoption @ X1)) @ X12) @ X12) @ (c_2Eoption_2ESOME @ X1))) = X12)) & (((c_2Eoption_2ENONE @ X1)) = ((ap @ (c_2Eoption_2EOPTION__JOIN @ X1) @ (c_2Eoption_2ENONE @ (ty_2Eoption_2Eoption @ X1)))))) | ~ (((sP4 @ X4 @ X2 @ X3 @ X1 @ X0)) = $true))),
  introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
thf(f169,plain,(
  ! [X0 : del,X2 : $i,X1 : del] : (! [X3 : $i] : ((((mem @ X3 @ (arr @ X1 @ X0))) != $true) | ! [X4 : $i] : ((((sP4 @ X4 @ X2 @ X3 @ X1 @ X0)) = $true) | (((mem @ X4 @ (ty_2Eoption_2Eoption @ X1))) != $true))) | (((mem @ X2 @ X0)) != $true))),
  inference(definition_folding,[],[f160,f168,f167,f166,f165])).
thf(f170,plain,(
  ! [X2 : del,X3 : $i,X1 : $i,X0 : del,X4 : $i] : ((($true = ((sP0 @ X4 @ X0 @ X1 @ X3 @ X2))) | ! [X5 : $i] : ((((mem @ X5 @ X2)) != $true) | ! [X6 : $i] : ((((ap @ (c_2Eoption_2ESOME @ X2) @ X5)) != X3) | ($true != ((p @ (ap @ (ap @ X1 @ X5) @ X6)))) | (((mem @ X6 @ X0)) != $true) | (((ap @ (c_2Eoption_2ESOME @ X0) @ X6)) != X4)))) & (? [X5 : $i] : ((((mem @ X5 @ X2)) = $true) & ? [X6 : $i] : ((((ap @ (c_2Eoption_2ESOME @ X2) @ X5)) = X3) & ($true = ((p @ (ap @ (ap @ X1 @ X5) @ X6)))) & (((mem @ X6 @ X0)) = $true) & (((ap @ (c_2Eoption_2ESOME @ X0) @ X6)) = X4))) | ($true != ((sP0 @ X4 @ X0 @ X1 @ X3 @ X2)))))),
  inference(nnf_transformation,[],[f163])).
thf(f171,plain,(
  ! [X0 : del,X1 : $i,X2 : $i,X3 : del,X4 : $i] : (((((sP0 @ X4 @ X3 @ X2 @ X1 @ X0)) = $true) | ! [X5 : $i] : ((((mem @ X5 @ X0)) != $true) | ! [X6 : $i] : ((((ap @ (c_2Eoption_2ESOME @ X0) @ X5)) != X1) | (((p @ (ap @ (ap @ X2 @ X5) @ X6))) != $true) | ($true != ((mem @ X6 @ X3))) | (((ap @ (c_2Eoption_2ESOME @ X3) @ X6)) != X4)))) & (? [X7 : $i] : ((((mem @ X7 @ X0)) = $true) & ? [X8 : $i] : ((((ap @ (c_2Eoption_2ESOME @ X0) @ X7)) = X1) & (((p @ (ap @ (ap @ X2 @ X7) @ X8))) = $true) & (((mem @ X8 @ X3)) = $true) & (((ap @ (c_2Eoption_2ESOME @ X3) @ X8)) = X4))) | (((sP0 @ X4 @ X3 @ X2 @ X1 @ X0)) != $true)))),
  inference(rectify,[],[f170])).
thf(f172,plain,(
  ! [X0 : del,X1 : $i,X2 : $i,X3 : del,X4 : $i] : (((((sP0 @ X4 @ X3 @ X2 @ X1 @ X0)) = $true) | ! [X5 : $i] : ((((mem @ X5 @ X0)) != $true) | ! [X6 : $i] : ((((ap @ (c_2Eoption_2ESOME @ X0) @ X5)) != X1) | (((p @ (ap @ (ap @ X2 @ X5) @ X6))) != $true) | ($true != ((mem @ X6 @ X3))) | (((ap @ (c_2Eoption_2ESOME @ X3) @ X6)) != X4)))) & ((($true = ((mem @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0) @ X0))) & ((((ap @ (c_2Eoption_2ESOME @ X0) @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0))) = X1) & ($true = ((p @ (ap @ (ap @ X2 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0)) @ (sK6 @ X4 @ X3 @ X2 @ X1 @ X0))))) & ($true = ((mem @ (sK6 @ X4 @ X3 @ X2 @ X1 @ X0) @ X3))) & (((ap @ (c_2Eoption_2ESOME @ X3) @ (sK6 @ X4 @ X3 @ X2 @ X1 @ X0))) = X4))) | (((sP0 @ X4 @ X3 @ X2 @ X1 @ X0)) != $true)))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X8,$thf(sK6 @ X4 @ X3 @ X2 @ X1 @ X0)),skolemize(X8,$thf(sK6 @ X4 @ X3 @ X2 @ X1 @ X0))],[f171])).
thf(f173,plain,(
  ! [X0 : del,X1 : $i,X2 : del] : ((((mem @ X1 @ (arr @ X2 @ (arr @ X0 @ bool)))) != $true) | ! [X3 : $i] : (($true != ((mem @ X3 @ (ty_2Eoption_2Eoption @ X2)))) | ! [X4 : $i] : ((((($true = ((sP0 @ X4 @ X0 @ X1 @ X3 @ X2))) | ((((c_2Eoption_2ENONE @ X0)) = X4) & (((c_2Eoption_2ENONE @ X2)) = X3))) | (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X0) @ X1) @ X3) @ X4))) != $true)) & ((((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X0) @ X1) @ X3) @ X4))) = $true) | (($true != ((sP0 @ X4 @ X0 @ X1 @ X3 @ X2))) & ((((c_2Eoption_2ENONE @ X0)) != X4) | (((c_2Eoption_2ENONE @ X2)) != X3))))) | (((mem @ X4 @ (ty_2Eoption_2Eoption @ X0))) != $true))))),
  inference(nnf_transformation,[],[f164])).
thf(f174,plain,(
  ! [X0 : del,X1 : $i,X2 : del] : ((((mem @ X1 @ (arr @ X2 @ (arr @ X0 @ bool)))) != $true) | ! [X3 : $i] : (($true != ((mem @ X3 @ (ty_2Eoption_2Eoption @ X2)))) | ! [X4 : $i] : (((($true = ((sP0 @ X4 @ X0 @ X1 @ X3 @ X2))) | ((((c_2Eoption_2ENONE @ X0)) = X4) & (((c_2Eoption_2ENONE @ X2)) = X3)) | (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X0) @ X1) @ X3) @ X4))) != $true)) & ((((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X0) @ X1) @ X3) @ X4))) = $true) | (($true != ((sP0 @ X4 @ X0 @ X1 @ X3 @ X2))) & ((((c_2Eoption_2ENONE @ X0)) != X4) | (((c_2Eoption_2ENONE @ X2)) != X3))))) | (((mem @ X4 @ (ty_2Eoption_2Eoption @ X0))) != $true))))),
  inference(flattening,[],[f173])).
thf(f178,plain,(
  ! [X0 : del,X1 : del,X2 : $i] : (($true != ((mem @ X2 @ (arr @ X1 @ X0)))) | ! [X3 : $i] : ((((mem @ X3 @ X1)) != $true) | ($true = ((mem @ (ap @ X2 @ X3) @ X0)))))),
  inference(rectify,[],[f149])).
thf(f183,plain,(
  ? [X0 : del,X1 : $i] : (? [X2 : $i] : ((((mem @ X2 @ X0)) = $true) & ? [X3 : $i] : (((((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X0 @ X0) @ X1) @ (ap @ (c_2Eoption_2ESOME @ X0) @ X2)) @ (c_2Eoption_2ENONE @ X0)))) = $true) | (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X0 @ X0) @ X1) @ (ap @ (c_2Eoption_2ESOME @ X0) @ X2)) @ (ap @ (c_2Eoption_2ESOME @ X0) @ X3)))) != ((p @ (ap @ (ap @ X1 @ X2) @ X3)))) | (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X0 @ X0) @ X1) @ (c_2Eoption_2ENONE @ X0)) @ (ap @ (c_2Eoption_2ESOME @ X0) @ X3)))) = $true) | (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X0 @ X0) @ X1) @ (c_2Eoption_2ENONE @ X0)) @ (c_2Eoption_2ENONE @ X0)))) != $true)) & (((mem @ X3 @ X0)) = $true))) & (((mem @ X1 @ (arr @ X0 @ (arr @ X0 @ bool)))) = $true))),
  inference(rectify,[],[f153])).
thf(f184,plain,(
  ((((mem @ sK10 @ sK8)) = $true) & (((((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10)) @ (c_2Eoption_2ENONE @ sK8)))) = $true) | (((p @ (ap @ (ap @ sK9 @ sK10) @ sK11))) != ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10)) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11))))) | (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (c_2Eoption_2ENONE @ sK8)) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11)))) = $true) | (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (c_2Eoption_2ENONE @ sK8)) @ (c_2Eoption_2ENONE @ sK8)))) != $true)) & ($true = ((mem @ sK11 @ sK8))))) & ($true = ((mem @ sK9 @ (arr @ sK8 @ (arr @ sK8 @ bool)))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11]),skolemize(X0,$thf(sK8)),skolemize(X1,$thf(sK9)),skolemize(X2,$thf(sK10)),skolemize(X3,$thf(sK11))],[f183])).
thf(f190,plain,(
  ! [X0 : del,X1 : del,X3 : $i,X2 : $i,X4 : $i] : ((! [X13 : $i] : ((((mem @ X13 @ (arr @ X1 @ X0))) != $true) | (((c_2Eoption_2ENONE @ X0)) = ((ap @ (ap @ (c_2Eoption_2EOPTION__MAP @ X1 @ X0) @ X13) @ (c_2Eoption_2ENONE @ X1))))) & (((sP3 @ X1)) = $true) & (((sP2 @ X1)) = $true) & ! [X6 : $i] : ((((c_2Eoption_2ENONE @ X1)) != ((ap @ (c_2Eoption_2ESOME @ X1) @ X6))) | (((mem @ X6 @ X1)) != $true)) & ! [X19 : $i] : (($true != ((mem @ X19 @ (arr @ X1 @ X0)))) | ! [X20 : $i] : ((((ap @ (ap @ (c_2Eoption_2EOPTION__MAP @ X1 @ X0) @ X19) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X20))) = ((ap @ (c_2Eoption_2ESOME @ X0) @ (ap @ X19 @ X20)))) | (((mem @ X20 @ X1)) != $true))) & ! [X24 : $i] : ((((c_2Eoption_2ENONE @ X1)) != ((ap @ (c_2Eoption_2ESOME @ X1) @ X24))) | ($true != ((mem @ X24 @ X1)))) & ! [X26 : $i] : (($true != ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X26)))) | (((mem @ X26 @ (ty_2Eoption_2Eoption @ X1))) != $true) | (((ap @ X3 @ (ap @ (c_2Eoption_2ETHE @ X1) @ X26))) = ((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ X26) @ X2) @ X3)))) & ! [X18 : $i] : (($true != ((p @ (ap @ (c_2Eoption_2EIS__NONE @ X1) @ X18)))) | (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ X18) @ X2) @ X3)) = X2) | (((mem @ X18 @ (ty_2Eoption_2Eoption @ X1))) != $true)) & ! [X22 : $i] : ((((ap @ (c_2Eoption_2EOPTION__JOIN @ X1) @ (ap @ (c_2Eoption_2ESOME @ (ty_2Eoption_2Eoption @ X1)) @ X22))) = X22) | (((mem @ X22 @ (ty_2Eoption_2Eoption @ X1))) != $true)) & (((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ (c_2Eoption_2ENONE @ X1)))) != $true) & ! [X27 : $i] : (($true != ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X27)))) | ($true != ((mem @ X27 @ (ty_2Eoption_2Eoption @ X1)))) | (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ (ty_2Eoption_2Eoption @ X1)) @ X27) @ X4) @ (c_2Eoption_2ESOME @ X1))) = X27)) & ! [X14 : $i] : (! [X15 : $i] : ((((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ (c_2Eoption_2ENONE @ X1)) @ X14) @ X15)) = X14) | (((mem @ X15 @ (arr @ X1 @ X0))) != $true)) | ($true != ((mem @ X14 @ X0)))) & (((sP1 @ X1)) = $true) & ! [X5 : $i] : ((((mem @ X5 @ X1)) != $true) | (((ap @ (c_2Eoption_2ETHE @ X1) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X5))) = X5)) & ! [X25 : $i] : ((((ap @ (c_2Eoption_2ESOME @ X1) @ (ap @ (c_2Eoption_2ETHE @ X1) @ X25))) = X25) | ($true != ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X25)))) | (((mem @ X25 @ (ty_2Eoption_2Eoption @ X1))) != $true)) & ! [X21 : $i] : ((((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ (ty_2Eoption_2Eoption @ X1)) @ X21) @ (c_2Eoption_2ENONE @ X1)) @ (c_2Eoption_2ESOME @ X1))) = X21) | ($true != ((mem @ X21 @ (ty_2Eoption_2Eoption @ X1))))) & ! [X16 : $i] : (($true != ((mem @ X16 @ X1))) | (((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X16)))) = $true)) & ! [X7 : $i] : (($true != ((mem @ X7 @ X1))) | ! [X8 : $i] : ((((mem @ X8 @ X0)) != $true) | ! [X9 : $i] : ((((mem @ X9 @ (arr @ X1 @ X0))) != $true) | (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X7)) @ X8) @ X9)) = ((ap @ X9 @ X7)))))) & ! [X12 : $i] : ((((mem @ X12 @ (ty_2Eoption_2Eoption @ X1))) != $true) | (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ (ty_2Eoption_2Eoption @ X1)) @ X12) @ X12) @ (c_2Eoption_2ESOME @ X1))) = X12)) & (((c_2Eoption_2ENONE @ X1)) = ((ap @ (c_2Eoption_2EOPTION__JOIN @ X1) @ (c_2Eoption_2ENONE @ (ty_2Eoption_2Eoption @ X1)))))) | (((sP4 @ X4 @ X2 @ X3 @ X1 @ X0)) != $true))),
  inference(nnf_transformation,[],[f168])).
thf(f191,plain,(
  ! [X0 : del,X1 : del,X2 : $i,X3 : $i,X4 : $i] : ((! [X5 : $i] : ((((mem @ X5 @ (arr @ X1 @ X0))) != $true) | (((c_2Eoption_2ENONE @ X0)) = ((ap @ (ap @ (c_2Eoption_2EOPTION__MAP @ X1 @ X0) @ X5) @ (c_2Eoption_2ENONE @ X1))))) & (((sP3 @ X1)) = $true) & (((sP2 @ X1)) = $true) & ! [X6 : $i] : ((((c_2Eoption_2ENONE @ X1)) != ((ap @ (c_2Eoption_2ESOME @ X1) @ X6))) | (((mem @ X6 @ X1)) != $true)) & ! [X7 : $i] : ((((mem @ X7 @ (arr @ X1 @ X0))) != $true) | ! [X8 : $i] : ((((ap @ (ap @ (c_2Eoption_2EOPTION__MAP @ X1 @ X0) @ X7) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X8))) = ((ap @ (c_2Eoption_2ESOME @ X0) @ (ap @ X7 @ X8)))) | ($true != ((mem @ X8 @ X1))))) & ! [X9 : $i] : ((((c_2Eoption_2ENONE @ X1)) != ((ap @ (c_2Eoption_2ESOME @ X1) @ X9))) | ($true != ((mem @ X9 @ X1)))) & ! [X10 : $i] : (($true != ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X10)))) | (((mem @ X10 @ (ty_2Eoption_2Eoption @ X1))) != $true) | (((ap @ X2 @ (ap @ (c_2Eoption_2ETHE @ X1) @ X10))) = ((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ X10) @ X3) @ X2)))) & ! [X11 : $i] : (($true != ((p @ (ap @ (c_2Eoption_2EIS__NONE @ X1) @ X11)))) | (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ X11) @ X3) @ X2)) = X3) | (((mem @ X11 @ (ty_2Eoption_2Eoption @ X1))) != $true)) & ! [X12 : $i] : ((((ap @ (c_2Eoption_2EOPTION__JOIN @ X1) @ (ap @ (c_2Eoption_2ESOME @ (ty_2Eoption_2Eoption @ X1)) @ X12))) = X12) | (((mem @ X12 @ (ty_2Eoption_2Eoption @ X1))) != $true)) & (((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ (c_2Eoption_2ENONE @ X1)))) != $true) & ! [X13 : $i] : ((((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X13))) != $true) | (((mem @ X13 @ (ty_2Eoption_2Eoption @ X1))) != $true) | (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ (ty_2Eoption_2Eoption @ X1)) @ X13) @ X4) @ (c_2Eoption_2ESOME @ X1))) = X13)) & ! [X14 : $i] : (! [X15 : $i] : ((((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ (c_2Eoption_2ENONE @ X1)) @ X14) @ X15)) = X14) | (((mem @ X15 @ (arr @ X1 @ X0))) != $true)) | ($true != ((mem @ X14 @ X0)))) & (((sP1 @ X1)) = $true) & ! [X16 : $i] : (($true != ((mem @ X16 @ X1))) | (((ap @ (c_2Eoption_2ETHE @ X1) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X16))) = X16)) & ! [X17 : $i] : ((((ap @ (c_2Eoption_2ESOME @ X1) @ (ap @ (c_2Eoption_2ETHE @ X1) @ X17))) = X17) | ($true != ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ X17)))) | (((mem @ X17 @ (ty_2Eoption_2Eoption @ X1))) != $true)) & ! [X18 : $i] : ((((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ (ty_2Eoption_2Eoption @ X1)) @ X18) @ (c_2Eoption_2ENONE @ X1)) @ (c_2Eoption_2ESOME @ X1))) = X18) | (((mem @ X18 @ (ty_2Eoption_2Eoption @ X1))) != $true)) & ! [X19 : $i] : ((((mem @ X19 @ X1)) != $true) | ($true = ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X19)))))) & ! [X20 : $i] : ((((mem @ X20 @ X1)) != $true) | ! [X21 : $i] : ((((mem @ X21 @ X0)) != $true) | ! [X22 : $i] : ((((mem @ X22 @ (arr @ X1 @ X0))) != $true) | (((ap @ X22 @ X20)) = ((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ X0) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X20)) @ X21) @ X22)))))) & ! [X23 : $i] : (($true != ((mem @ X23 @ (ty_2Eoption_2Eoption @ X1)))) | (((ap @ (ap @ (ap @ (c_2Eoption_2Eoption__CASE @ X1 @ (ty_2Eoption_2Eoption @ X1)) @ X23) @ X23) @ (c_2Eoption_2ESOME @ X1))) = X23)) & (((c_2Eoption_2ENONE @ X1)) = ((ap @ (c_2Eoption_2EOPTION__JOIN @ X1) @ (c_2Eoption_2ENONE @ (ty_2Eoption_2Eoption @ X1)))))) | (((sP4 @ X4 @ X3 @ X2 @ X1 @ X0)) != $true))),
  inference(rectify,[],[f190])).
thf(f198,plain,(
  ! [X0 : del,X1 : $i,X2 : del] : (! [X3 : $i] : (($true != ((mem @ X3 @ (arr @ X2 @ X0)))) | ! [X4 : $i] : (($true = ((sP4 @ X4 @ X1 @ X3 @ X2 @ X0))) | ($true != ((mem @ X4 @ (ty_2Eoption_2Eoption @ X2)))))) | (((mem @ X1 @ X0)) != $true))),
  inference(rectify,[],[f169])).
thf(f201,plain,(
  ( ! [X2 : $i,X3 : del,X0 : del,X1 : $i,X4 : $i] : ((((sP0 @ X4 @ X3 @ X2 @ X1 @ X0)) != $true) | (((ap @ (c_2Eoption_2ESOME @ X3) @ (sK6 @ X4 @ X3 @ X2 @ X1 @ X0))) = X4)) )),
  inference(cnf_transformation,[],[f172])).
thf(f202,plain,(
  ( ! [X2 : $i,X3 : del,X0 : del,X1 : $i,X4 : $i] : ((((sP0 @ X4 @ X3 @ X2 @ X1 @ X0)) != $true) | ($true = ((mem @ (sK6 @ X4 @ X3 @ X2 @ X1 @ X0) @ X3)))) )),
  inference(cnf_transformation,[],[f172])).
thf(f203,plain,(
  ( ! [X2 : $i,X3 : del,X0 : del,X1 : $i,X4 : $i] : ((((sP0 @ X4 @ X3 @ X2 @ X1 @ X0)) != $true) | ($true = ((p @ (ap @ (ap @ X2 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0)) @ (sK6 @ X4 @ X3 @ X2 @ X1 @ X0)))))) )),
  inference(cnf_transformation,[],[f172])).
thf(f204,plain,(
  ( ! [X2 : $i,X3 : del,X0 : del,X1 : $i,X4 : $i] : ((((sP0 @ X4 @ X3 @ X2 @ X1 @ X0)) != $true) | (((ap @ (c_2Eoption_2ESOME @ X0) @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0))) = X1)) )),
  inference(cnf_transformation,[],[f172])).
thf(f205,plain,(
  ( ! [X2 : $i,X3 : del,X0 : del,X1 : $i,X4 : $i] : ((((sP0 @ X4 @ X3 @ X2 @ X1 @ X0)) != $true) | ($true = ((mem @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0) @ X0)))) )),
  inference(cnf_transformation,[],[f172])).
thf(f206,plain,(
  ( ! [X2 : $i,X3 : del,X0 : del,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : ((((sP0 @ X4 @ X3 @ X2 @ X1 @ X0)) = $true) | (((mem @ X5 @ X0)) != $true) | (((ap @ (c_2Eoption_2ESOME @ X0) @ X5)) != X1) | (((p @ (ap @ (ap @ X2 @ X5) @ X6))) != $true) | ($true != ((mem @ X6 @ X3))) | (((ap @ (c_2Eoption_2ESOME @ X3) @ X6)) != X4)) )),
  inference(cnf_transformation,[],[f172])).
thf(f207,plain,(
  ( ! [X2 : del,X3 : $i,X0 : del,X1 : $i,X4 : $i] : ((((mem @ X1 @ (arr @ X2 @ (arr @ X0 @ bool)))) != $true) | ($true != ((mem @ X3 @ (ty_2Eoption_2Eoption @ X2)))) | (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X0) @ X1) @ X3) @ X4))) = $true) | (((c_2Eoption_2ENONE @ X0)) != X4) | (((c_2Eoption_2ENONE @ X2)) != X3) | (((mem @ X4 @ (ty_2Eoption_2Eoption @ X0))) != $true)) )),
  inference(cnf_transformation,[],[f174])).
thf(f208,plain,(
  ( ! [X2 : del,X3 : $i,X0 : del,X1 : $i,X4 : $i] : (($true != ((sP0 @ X4 @ X0 @ X1 @ X3 @ X2))) | (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X0) @ X1) @ X3) @ X4))) = $true) | (((mem @ X4 @ (ty_2Eoption_2Eoption @ X0))) != $true) | (((mem @ X1 @ (arr @ X2 @ (arr @ X0 @ bool)))) != $true) | ($true != ((mem @ X3 @ (ty_2Eoption_2Eoption @ X2))))) )),
  inference(cnf_transformation,[],[f174])).
thf(f209,plain,(
  ( ! [X2 : del,X3 : $i,X0 : del,X1 : $i,X4 : $i] : ((((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X0) @ X1) @ X3) @ X4))) != $true) | (((mem @ X4 @ (ty_2Eoption_2Eoption @ X0))) != $true) | (((c_2Eoption_2ENONE @ X2)) = X3) | ($true != ((mem @ X3 @ (ty_2Eoption_2Eoption @ X2)))) | (((mem @ X1 @ (arr @ X2 @ (arr @ X0 @ bool)))) != $true) | ($true = ((sP0 @ X4 @ X0 @ X1 @ X3 @ X2)))) )),
  inference(cnf_transformation,[],[f174])).
thf(f210,plain,(
  ( ! [X2 : del,X3 : $i,X0 : del,X1 : $i,X4 : $i] : ((((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X0) @ X1) @ X3) @ X4))) != $true) | (((mem @ X1 @ (arr @ X2 @ (arr @ X0 @ bool)))) != $true) | ($true = ((sP0 @ X4 @ X0 @ X1 @ X3 @ X2))) | (((c_2Eoption_2ENONE @ X0)) = X4) | (((mem @ X4 @ (ty_2Eoption_2Eoption @ X0))) != $true) | ($true != ((mem @ X3 @ (ty_2Eoption_2Eoption @ X2))))) )),
  inference(cnf_transformation,[],[f174])).
thf(f221,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : del,X1 : del] : (($true != ((mem @ X2 @ (arr @ X1 @ X0)))) | (((mem @ X3 @ X1)) != $true) | ($true = ((mem @ (ap @ X2 @ X3) @ X0)))) )),
  inference(cnf_transformation,[],[f178])).
thf(f225,plain,(
  ( ! [X0 : del] : ((((mem @ (c_2Eoption_2ENONE @ X0) @ (ty_2Eoption_2Eoption @ X0))) = $true)) )),
  inference(cnf_transformation,[],[f125])).
thf(f227,plain,(
  ($true = ((mem @ sK9 @ (arr @ sK8 @ (arr @ sK8 @ bool)))))),
  inference(cnf_transformation,[],[f184])).
thf(f228,plain,(
  ($true = ((mem @ sK11 @ sK8)))),
  inference(cnf_transformation,[],[f184])).
thf(f229,plain,(
  (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10)) @ (c_2Eoption_2ENONE @ sK8)))) = $true) | (((p @ (ap @ (ap @ sK9 @ sK10) @ sK11))) != ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10)) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11))))) | (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (c_2Eoption_2ENONE @ sK8)) @ (c_2Eoption_2ENONE @ sK8)))) != $true) | (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (c_2Eoption_2ENONE @ sK8)) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11)))) = $true)),
  inference(cnf_transformation,[],[f184])).
thf(f230,plain,(
  (((mem @ sK10 @ sK8)) = $true)),
  inference(cnf_transformation,[],[f184])).
thf(f250,plain,(
  ( ! [X0 : del] : ((((mem @ (c_2Eoption_2ESOME @ X0) @ (arr @ X0 @ (ty_2Eoption_2Eoption @ X0)))) = $true)) )),
  inference(cnf_transformation,[],[f87])).
thf(f254,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : del,X1 : del,X19 : $i,X4 : $i] : ((((sP4 @ X4 @ X3 @ X2 @ X1 @ X0)) != $true) | (((mem @ X19 @ X1)) != $true) | ($true = ((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X19)))))) )),
  inference(cnf_transformation,[],[f191])).
thf(f257,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : del,X1 : del,X16 : $i,X4 : $i] : ((((sP4 @ X4 @ X3 @ X2 @ X1 @ X0)) != $true) | ($true != ((mem @ X16 @ X1))) | (((ap @ (c_2Eoption_2ETHE @ X1) @ (ap @ (c_2Eoption_2ESOME @ X1) @ X16))) = X16)) )),
  inference(cnf_transformation,[],[f191])).
thf(f261,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : del,X1 : del,X4 : $i] : ((((sP4 @ X4 @ X3 @ X2 @ X1 @ X0)) != $true) | (((p @ (ap @ (c_2Eoption_2EIS__SOME @ X1) @ (c_2Eoption_2ENONE @ X1)))) != $true)) )),
  inference(cnf_transformation,[],[f191])).
thf(f277,plain,(
  ( ! [X2 : del,X3 : $i,X0 : del,X1 : $i,X4 : $i] : (($true != ((mem @ X3 @ (arr @ X2 @ X0)))) | ($true = ((sP4 @ X4 @ X1 @ X3 @ X2 @ X0))) | ($true != ((mem @ X4 @ (ty_2Eoption_2Eoption @ X2)))) | (((mem @ X1 @ X0)) != $true)) )),
  inference(cnf_transformation,[],[f198])).
thf(f282,plain,(
  ( ! [X2 : $i,X3 : del,X0 : del,X6 : $i,X4 : $i,X5 : $i] : ((((sP0 @ X4 @ X3 @ X2 @ (ap @ (c_2Eoption_2ESOME @ X0) @ X5) @ X0)) = $true) | (((mem @ X5 @ X0)) != $true) | (((p @ (ap @ (ap @ X2 @ X5) @ X6))) != $true) | ($true != ((mem @ X6 @ X3))) | (((ap @ (c_2Eoption_2ESOME @ X3) @ X6)) != X4)) )),
  inference(equality_resolution,[],[f206])).
thf(f283,plain,(
  ( ! [X2 : $i,X3 : del,X0 : del,X6 : $i,X5 : $i] : ((((p @ (ap @ (ap @ X2 @ X5) @ X6))) != $true) | ($true = ((sP0 @ (ap @ (c_2Eoption_2ESOME @ X3) @ X6) @ X3 @ X2 @ (ap @ (c_2Eoption_2ESOME @ X0) @ X5) @ X0))) | ($true != ((mem @ X6 @ X3))) | (((mem @ X5 @ X0)) != $true)) )),
  inference(equality_resolution,[],[f282])).
thf(f284,plain,(
  ( ! [X2 : del,X3 : $i,X0 : del,X1 : $i] : ((((mem @ X1 @ (arr @ X2 @ (arr @ X0 @ bool)))) != $true) | ($true != ((mem @ X3 @ (ty_2Eoption_2Eoption @ X2)))) | (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X0) @ X1) @ X3) @ (c_2Eoption_2ENONE @ X0)))) = $true) | (((c_2Eoption_2ENONE @ X2)) != X3) | (((mem @ (c_2Eoption_2ENONE @ X0) @ (ty_2Eoption_2Eoption @ X0))) != $true)) )),
  inference(equality_resolution,[],[f207])).
thf(f285,plain,(
  ( ! [X2 : del,X0 : del,X1 : $i] : ((((mem @ X1 @ (arr @ X2 @ (arr @ X0 @ bool)))) != $true) | ($true = ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X0) @ X1) @ (c_2Eoption_2ENONE @ X2)) @ (c_2Eoption_2ENONE @ X0))))) | ($true != ((mem @ (c_2Eoption_2ENONE @ X2) @ (ty_2Eoption_2Eoption @ X2)))) | (((mem @ (c_2Eoption_2ENONE @ X0) @ (ty_2Eoption_2Eoption @ X0))) != $true)) )),
  inference(equality_resolution,[],[f284])).
thf(f303,plain,(
  (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (c_2Eoption_2ENONE @ sK8)) @ (c_2Eoption_2ENONE @ sK8)))) != $true) | (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10)) @ (c_2Eoption_2ENONE @ sK8)))) = $true) | ($true = ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10)) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11))))) | (((p @ (ap @ (ap @ sK9 @ sK10) @ sK11))) = $true) | (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (c_2Eoption_2ENONE @ sK8)) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11)))) = $true)),
  inference(xor_proxy_clausification,[],[f229])).
thf(f304,plain,(
  (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (c_2Eoption_2ENONE @ sK8)) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11)))) = $true) | (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10)) @ (c_2Eoption_2ENONE @ sK8)))) = $true) | (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (c_2Eoption_2ENONE @ sK8)) @ (c_2Eoption_2ENONE @ sK8)))) != $true) | ($false = ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10)) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11))))) | (((p @ (ap @ (ap @ sK9 @ sK10) @ sK11))) = $false)),
  inference(xor_proxy_clausification,[],[f229])).
thf(f307,definition,(
  spl13_1 <=> (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (c_2Eoption_2ENONE @ sK8)) @ (c_2Eoption_2ENONE @ sK8)))) = $true)),
  introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition])).
thf(f309,plain,(
  (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (c_2Eoption_2ENONE @ sK8)) @ (c_2Eoption_2ENONE @ sK8)))) != $true) | spl13_1),
  inference(avatar_component_clause,[],[f307])).
thf(f311,definition,(
  spl13_2 <=> (((p @ (ap @ (ap @ sK9 @ sK10) @ sK11))) = $false)),
  introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition])).
thf(f313,plain,(
  (((p @ (ap @ (ap @ sK9 @ sK10) @ sK11))) = $false) | ~spl13_2),
  inference(avatar_component_clause,[],[f311])).
thf(f315,definition,(
  spl13_3 <=> (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10)) @ (c_2Eoption_2ENONE @ sK8)))) = $true)),
  introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition])).
thf(f317,plain,(
  (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10)) @ (c_2Eoption_2ENONE @ sK8)))) = $true) | ~spl13_3),
  inference(avatar_component_clause,[],[f315])).
thf(f319,definition,(
  spl13_4 <=> (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (c_2Eoption_2ENONE @ sK8)) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11)))) = $true)),
  introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition])).
thf(f321,plain,(
  (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (c_2Eoption_2ENONE @ sK8)) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11)))) = $true) | ~spl13_4),
  inference(avatar_component_clause,[],[f319])).
thf(f323,definition,(
  spl13_5 <=> ($false = ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10)) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11)))))),
  introduced(definition,[new_symbols(definition,[spl13_5])],[avatar_definition])).
thf(f325,plain,(
  ($false = ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10)) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11))))) | ~spl13_5),
  inference(avatar_component_clause,[],[f323])).
thf(f326,plain,(
  ~spl13_1 | spl13_2 | spl13_3 | spl13_4 | spl13_5),
  inference(avatar_split_clause,[],[f304,f323,f319,f315,f311,f307])).
thf(f328,definition,(
  spl13_6 <=> ($true = ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10)) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11)))))),
  introduced(definition,[new_symbols(definition,[spl13_6])],[avatar_definition])).
thf(f329,plain,(
  ($true != ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10)) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11))))) | spl13_6),
  inference(avatar_component_clause,[],[f328])).
thf(f330,plain,(
  ($true = ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10)) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11))))) | ~spl13_6),
  inference(avatar_component_clause,[],[f328])).
thf(f332,definition,(
  spl13_7 <=> (((p @ (ap @ (ap @ sK9 @ sK10) @ sK11))) = $true)),
  introduced(definition,[new_symbols(definition,[spl13_7])],[avatar_definition])).
thf(f334,plain,(
  (((p @ (ap @ (ap @ sK9 @ sK10) @ sK11))) = $true) | ~spl13_7),
  inference(avatar_component_clause,[],[f332])).
thf(f335,plain,(
  spl13_3 | spl13_4 | spl13_6 | spl13_7 | ~spl13_1),
  inference(avatar_split_clause,[],[f303,f307,f332,f328,f319,f315])).
thf(f337,plain,(
  ( ! [X0 : $i] : (($true != $true) | (((mem @ (ap @ sK9 @ X0) @ (arr @ sK8 @ bool))) = $true) | ($true != ((mem @ X0 @ sK8)))) )),
  inference(constrained_superposition,[],[f221,f227])).
thf(f338,plain,(
  ( ! [X0 : del,X1 : $i] : ((((mem @ X1 @ X0)) != $true) | ($true != $true) | (((mem @ (ap @ (c_2Eoption_2ESOME @ X0) @ X1) @ (ty_2Eoption_2Eoption @ X0))) = $true)) )),
  inference(constrained_superposition,[],[f221,f250])).
thf(f339,plain,(
  ( ! [X0 : del,X1 : $i] : ((((mem @ X1 @ X0)) != $true) | (((mem @ (ap @ (c_2Eoption_2ESOME @ X0) @ X1) @ (ty_2Eoption_2Eoption @ X0))) = $true)) )),
  inference(trivial_inequality_removal,[],[f338])).
thf(f340,plain,(
  ( ! [X0 : $i] : (($true != ((mem @ X0 @ sK8))) | (((mem @ (ap @ sK9 @ X0) @ (arr @ sK8 @ bool))) = $true)) )),
  inference(trivial_inequality_removal,[],[f337])).
thf(f344,plain,(
  ($true != $true) | (((mem @ (ap @ sK9 @ sK10) @ (arr @ sK8 @ bool))) = $true)),
  inference(constrained_superposition,[],[f340,f230])).
thf(f345,plain,(
  (((mem @ (ap @ sK9 @ sK10) @ (arr @ sK8 @ bool))) = $true)),
  inference(trivial_inequality_removal,[],[f344])).
thf(f347,plain,(
  ( ! [X0 : $i] : (($true != ((mem @ X0 @ sK8))) | ($true != $true) | (((mem @ (ap @ (ap @ sK9 @ sK10) @ X0) @ bool)) = $true)) )),
  inference(constrained_superposition,[],[f221,f345])).
thf(f348,plain,(
  ( ! [X0 : $i] : (($true != ((mem @ X0 @ sK8))) | (((mem @ (ap @ (ap @ sK9 @ sK10) @ X0) @ bool)) = $true)) )),
  inference(trivial_inequality_removal,[],[f347])).
thf(f351,plain,(
  ($true != $true) | (((mem @ (ap @ (ap @ sK9 @ sK10) @ sK11) @ bool)) = $true)),
  inference(constrained_superposition,[],[f348,f228])).
thf(f354,plain,(
  (((mem @ (ap @ (ap @ sK9 @ sK10) @ sK11) @ bool)) = $true)),
  inference(trivial_inequality_removal,[],[f351])).
thf(f400,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((mem @ X0 @ (ty_2Eoption_2Eoption @ sK8)))) | ($true = ((sP4 @ X0 @ X1 @ (ap @ sK9 @ sK10) @ sK8 @ bool))) | ($true != $true) | (((mem @ X1 @ bool)) != $true)) )),
  inference(constrained_superposition,[],[f277,f345])).
thf(f402,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((mem @ X0 @ (ty_2Eoption_2Eoption @ sK8)))) | (((mem @ X1 @ bool)) != $true) | ($true = ((sP4 @ X0 @ X1 @ (ap @ sK9 @ sK10) @ sK8 @ bool)))) )),
  inference(trivial_inequality_removal,[],[f400])).
thf(f437,plain,(
  ( ! [X0 : $i] : (($true != $true) | (((mem @ X0 @ bool)) != $true) | (((sP4 @ (c_2Eoption_2ENONE @ sK8) @ X0 @ (ap @ sK9 @ sK10) @ sK8 @ bool)) = $true)) )),
  inference(constrained_superposition,[],[f402,f225])).
thf(f438,plain,(
  ( ! [X0 : $i] : ((((mem @ X0 @ bool)) != $true) | (((sP4 @ (c_2Eoption_2ENONE @ sK8) @ X0 @ (ap @ sK9 @ sK10) @ sK8 @ bool)) = $true)) )),
  inference(trivial_inequality_removal,[],[f437])).
thf(f440,plain,(
  ($true != $true) | ($true = ((sP4 @ (c_2Eoption_2ENONE @ sK8) @ (ap @ (ap @ sK9 @ sK10) @ sK11) @ (ap @ sK9 @ sK10) @ sK8 @ bool)))),
  inference(constrained_superposition,[],[f438,f354])).
thf(f444,plain,(
  ($true = ((sP4 @ (c_2Eoption_2ENONE @ sK8) @ (ap @ (ap @ sK9 @ sK10) @ sK11) @ (ap @ sK9 @ sK10) @ sK8 @ bool)))),
  inference(trivial_inequality_removal,[],[f440])).
thf(f451,plain,(
  ( ! [X0 : $i] : (($true != ((mem @ X0 @ sK8))) | (((p @ (ap @ (c_2Eoption_2EIS__SOME @ sK8) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ X0)))) = $true) | ($true != $true)) )),
  inference(constrained_superposition,[],[f254,f444])).
thf(f454,plain,(
  ( ! [X0 : $i] : (($true != ((mem @ X0 @ sK8))) | (((ap @ (c_2Eoption_2ETHE @ sK8) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ X0))) = X0) | ($true != $true)) )),
  inference(constrained_superposition,[],[f257,f444])).
thf(f456,plain,(
  (((p @ (ap @ (c_2Eoption_2EIS__SOME @ sK8) @ (c_2Eoption_2ENONE @ sK8)))) != $true) | ($true != $true)),
  inference(constrained_superposition,[],[f261,f444])).
thf(f464,plain,(
  ( ! [X0 : $i] : (($true != ((mem @ X0 @ sK8))) | (((ap @ (c_2Eoption_2ETHE @ sK8) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ X0))) = X0)) )),
  inference(trivial_inequality_removal,[],[f454])).
thf(f466,plain,(
  ( ! [X0 : $i] : (($true != ((mem @ X0 @ sK8))) | (((p @ (ap @ (c_2Eoption_2EIS__SOME @ sK8) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ X0)))) = $true)) )),
  inference(trivial_inequality_removal,[],[f451])).
thf(f471,plain,(
  (((p @ (ap @ (c_2Eoption_2EIS__SOME @ sK8) @ (c_2Eoption_2ENONE @ sK8)))) != $true)),
  inference(trivial_inequality_removal,[],[f456])).
thf(f480,plain,(
  (((mem @ (c_2Eoption_2ENONE @ sK8) @ (ty_2Eoption_2Eoption @ sK8))) != $true) | ($true != $true) | (((mem @ (c_2Eoption_2ENONE @ sK8) @ (ty_2Eoption_2Eoption @ sK8))) != $true) | (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (c_2Eoption_2ENONE @ sK8)) @ (c_2Eoption_2ENONE @ sK8)))) = $true)),
  inference(constrained_superposition,[],[f285,f227])).
thf(f481,plain,(
  (((mem @ (c_2Eoption_2ENONE @ sK8) @ (ty_2Eoption_2Eoption @ sK8))) != $true) | (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (c_2Eoption_2ENONE @ sK8)) @ (c_2Eoption_2ENONE @ sK8)))) = $true) | ($true != $true)),
  inference(duplicate_literal_removal,[],[f480])).
thf(f482,plain,(
  (((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (c_2Eoption_2ENONE @ sK8)) @ (c_2Eoption_2ENONE @ sK8)))) = $true) | (((mem @ (c_2Eoption_2ENONE @ sK8) @ (ty_2Eoption_2Eoption @ sK8))) != $true)),
  inference(trivial_inequality_removal,[],[f481])).
thf(f483,plain,(
  (((mem @ (c_2Eoption_2ENONE @ sK8) @ (ty_2Eoption_2Eoption @ sK8))) != $true) | spl13_1),
  inference(forward_subsumption_resolution,[],[f482,f309])).
thf(f484,plain,(
  $false | spl13_1),
  inference(forward_subsumption_resolution,[],[f483,f225])).
thf(f485,plain,(
  spl13_1),
  inference(avatar_contradiction_clause,[],[f484])).
thf(f495,plain,(
  (((ap @ (c_2Eoption_2ETHE @ sK8) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11))) = sK11) | ($true != $true)),
  inference(constrained_superposition,[],[f464,f228])).
thf(f496,plain,(
  (((ap @ (c_2Eoption_2ETHE @ sK8) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10))) = sK10) | ($true != $true)),
  inference(constrained_superposition,[],[f464,f230])).
thf(f497,plain,(
  (((ap @ (c_2Eoption_2ETHE @ sK8) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10))) = sK10)),
  inference(trivial_inequality_removal,[],[f496])).
thf(f498,plain,(
  (((ap @ (c_2Eoption_2ETHE @ sK8) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11))) = sK11)),
  inference(trivial_inequality_removal,[],[f495])).
thf(f503,plain,(
  ($true != $true) | (((p @ (ap @ (c_2Eoption_2EIS__SOME @ sK8) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11)))) = $true)),
  inference(constrained_superposition,[],[f466,f228])).
thf(f504,plain,(
  ($true = ((p @ (ap @ (c_2Eoption_2EIS__SOME @ sK8) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10))))) | ($true != $true)),
  inference(constrained_superposition,[],[f466,f230])).
thf(f505,plain,(
  ($true = ((p @ (ap @ (c_2Eoption_2EIS__SOME @ sK8) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10)))))),
  inference(trivial_inequality_removal,[],[f504])).
thf(f506,plain,(
  (((p @ (ap @ (c_2Eoption_2EIS__SOME @ sK8) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11)))) = $true)),
  inference(trivial_inequality_removal,[],[f503])).
thf(f510,plain,(
  ($true != ((mem @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ (ty_2Eoption_2Eoption @ sK8)))) | ($true != $true) | (((mem @ (c_2Eoption_2ENONE @ sK8) @ (ty_2Eoption_2Eoption @ sK8))) != $true) | (((c_2Eoption_2ENONE @ sK8)) = ((ap @ (c_2Eoption_2ESOME @ sK8) @ sK10))) | (((sP0 @ (c_2Eoption_2ENONE @ sK8) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8)) = $true) | ($true != ((mem @ sK9 @ (arr @ sK8 @ (arr @ sK8 @ bool))))) | ~spl13_3),
  inference(constrained_superposition,[],[f209,f317])).
thf(f511,plain,(
  (((c_2Eoption_2ENONE @ sK8)) = ((ap @ (c_2Eoption_2ESOME @ sK8) @ sK10))) | ($true != ((mem @ sK9 @ (arr @ sK8 @ (arr @ sK8 @ bool))))) | ($true != ((mem @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ (ty_2Eoption_2Eoption @ sK8)))) | (((mem @ (c_2Eoption_2ENONE @ sK8) @ (ty_2Eoption_2Eoption @ sK8))) != $true) | (((sP0 @ (c_2Eoption_2ENONE @ sK8) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8)) = $true) | ~spl13_3),
  inference(trivial_inequality_removal,[],[f510])).
thf(f513,plain,(
  (((mem @ (c_2Eoption_2ENONE @ sK8) @ (ty_2Eoption_2Eoption @ sK8))) != $true) | ($true != ((mem @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ (ty_2Eoption_2Eoption @ sK8)))) | (((c_2Eoption_2ENONE @ sK8)) = ((ap @ (c_2Eoption_2ESOME @ sK8) @ sK10))) | (((sP0 @ (c_2Eoption_2ENONE @ sK8) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8)) = $true) | ~spl13_3),
  inference(forward_subsumption_resolution,[],[f511,f227])).
thf(f514,plain,(
  ($true != ((mem @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ (ty_2Eoption_2Eoption @ sK8)))) | (((sP0 @ (c_2Eoption_2ENONE @ sK8) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8)) = $true) | (((c_2Eoption_2ENONE @ sK8)) = ((ap @ (c_2Eoption_2ESOME @ sK8) @ sK10))) | ~spl13_3),
  inference(forward_subsumption_resolution,[],[f513,f225])).
thf(f516,definition,(
  spl13_17 <=> ($true = ((mem @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ (ty_2Eoption_2Eoption @ sK8))))),
  introduced(definition,[new_symbols(definition,[spl13_17])],[avatar_definition])).
thf(f517,plain,(
  ($true = ((mem @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ (ty_2Eoption_2Eoption @ sK8)))) | ~spl13_17),
  inference(avatar_component_clause,[],[f516])).
thf(f518,plain,(
  ($true != ((mem @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ (ty_2Eoption_2Eoption @ sK8)))) | spl13_17),
  inference(avatar_component_clause,[],[f516])).
thf(f520,definition,(
  spl13_18 <=> (((c_2Eoption_2ENONE @ sK8)) = ((ap @ (c_2Eoption_2ESOME @ sK8) @ sK10)))),
  introduced(definition,[new_symbols(definition,[spl13_18])],[avatar_definition])).
thf(f521,plain,(
  (((c_2Eoption_2ENONE @ sK8)) != ((ap @ (c_2Eoption_2ESOME @ sK8) @ sK10))) | spl13_18),
  inference(avatar_component_clause,[],[f520])).
thf(f522,plain,(
  (((c_2Eoption_2ENONE @ sK8)) = ((ap @ (c_2Eoption_2ESOME @ sK8) @ sK10))) | ~spl13_18),
  inference(avatar_component_clause,[],[f520])).
thf(f524,definition,(
  spl13_19 <=> (((sP0 @ (c_2Eoption_2ENONE @ sK8) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8)) = $true)),
  introduced(definition,[new_symbols(definition,[spl13_19])],[avatar_definition])).
thf(f526,plain,(
  (((sP0 @ (c_2Eoption_2ENONE @ sK8) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8)) = $true) | ~spl13_19),
  inference(avatar_component_clause,[],[f524])).
thf(f527,plain,(
  ~spl13_17 | spl13_18 | spl13_19 | ~spl13_3),
  inference(avatar_split_clause,[],[f514,f315,f524,f520,f516])).
thf(f533,plain,(
  ($true != $true) | (((mem @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ (ty_2Eoption_2Eoption @ sK8))) = $true)),
  inference(constrained_superposition,[],[f339,f228])).
thf(f534,plain,(
  ($true != $true) | ($true = ((mem @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ (ty_2Eoption_2Eoption @ sK8))))),
  inference(constrained_superposition,[],[f339,f230])).
thf(f549,plain,(
  ($true = ((mem @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ (ty_2Eoption_2Eoption @ sK8))))),
  inference(trivial_inequality_removal,[],[f534])).
thf(f556,plain,(
  (((mem @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ (ty_2Eoption_2Eoption @ sK8))) = $true)),
  inference(trivial_inequality_removal,[],[f533])).
thf(f558,plain,(
  $false | spl13_17),
  inference(forward_subsumption_resolution,[],[f549,f518])).
thf(f559,plain,(
  spl13_17),
  inference(avatar_contradiction_clause,[],[f558])).
thf(f575,plain,(
  (((mem @ (c_2Eoption_2ENONE @ sK8) @ (ty_2Eoption_2Eoption @ sK8))) != $true) | (((ap @ (c_2Eoption_2ESOME @ sK8) @ sK11)) = ((c_2Eoption_2ENONE @ sK8))) | ($true != $true) | (((mem @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ (ty_2Eoption_2Eoption @ sK8))) != $true) | ($true != ((mem @ sK9 @ (arr @ sK8 @ (arr @ sK8 @ bool))))) | (((sP0 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (c_2Eoption_2ENONE @ sK8) @ sK8)) = $true) | ~spl13_4),
  inference(constrained_superposition,[],[f210,f321])).
thf(f577,plain,(
  (((ap @ (c_2Eoption_2ESOME @ sK8) @ sK11)) = ((c_2Eoption_2ENONE @ sK8))) | (((mem @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ (ty_2Eoption_2Eoption @ sK8))) != $true) | ($true != ((mem @ sK9 @ (arr @ sK8 @ (arr @ sK8 @ bool))))) | (((mem @ (c_2Eoption_2ENONE @ sK8) @ (ty_2Eoption_2Eoption @ sK8))) != $true) | (((sP0 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (c_2Eoption_2ENONE @ sK8) @ sK8)) = $true) | ~spl13_4),
  inference(trivial_inequality_removal,[],[f575])).
thf(f578,plain,(
  (((ap @ (c_2Eoption_2ESOME @ sK8) @ sK11)) = ((c_2Eoption_2ENONE @ sK8))) | (((mem @ (c_2Eoption_2ENONE @ sK8) @ (ty_2Eoption_2Eoption @ sK8))) != $true) | ($true != ((mem @ sK9 @ (arr @ sK8 @ (arr @ sK8 @ bool))))) | (((sP0 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (c_2Eoption_2ENONE @ sK8) @ sK8)) = $true) | ~spl13_4),
  inference(forward_subsumption_resolution,[],[f577,f556])).
thf(f579,plain,(
  (((ap @ (c_2Eoption_2ESOME @ sK8) @ sK11)) = ((c_2Eoption_2ENONE @ sK8))) | ($true != ((mem @ sK9 @ (arr @ sK8 @ (arr @ sK8 @ bool))))) | (((sP0 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (c_2Eoption_2ENONE @ sK8) @ sK8)) = $true) | ~spl13_4),
  inference(forward_subsumption_resolution,[],[f578,f225])).
thf(f580,plain,(
  (((ap @ (c_2Eoption_2ESOME @ sK8) @ sK11)) = ((c_2Eoption_2ENONE @ sK8))) | (((sP0 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (c_2Eoption_2ENONE @ sK8) @ sK8)) = $true) | ~spl13_4),
  inference(forward_subsumption_resolution,[],[f579,f227])).
thf(f582,definition,(
  spl13_20 <=> (((ap @ (c_2Eoption_2ESOME @ sK8) @ sK11)) = ((c_2Eoption_2ENONE @ sK8)))),
  introduced(definition,[new_symbols(definition,[spl13_20])],[avatar_definition])).
thf(f584,plain,(
  (((ap @ (c_2Eoption_2ESOME @ sK8) @ sK11)) = ((c_2Eoption_2ENONE @ sK8))) | ~spl13_20),
  inference(avatar_component_clause,[],[f582])).
thf(f586,definition,(
  spl13_21 <=> (((sP0 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (c_2Eoption_2ENONE @ sK8) @ sK8)) = $true)),
  introduced(definition,[new_symbols(definition,[spl13_21])],[avatar_definition])).
thf(f588,plain,(
  (((sP0 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (c_2Eoption_2ENONE @ sK8) @ sK8)) = $true) | ~spl13_21),
  inference(avatar_component_clause,[],[f586])).
thf(f589,plain,(
  spl13_20 | spl13_21 | ~spl13_4),
  inference(avatar_split_clause,[],[f580,f319,f586,f582])).
thf(f591,plain,(
  (((p @ (ap @ (c_2Eoption_2EIS__SOME @ sK8) @ (c_2Eoption_2ENONE @ sK8)))) = $true) | ~spl13_18),
  inference(constrained_superposition,[],[f505,f522])).
thf(f600,plain,(
  $false | ~spl13_18),
  inference(forward_subsumption_resolution,[],[f591,f471])).
thf(f601,plain,(
  ~spl13_18),
  inference(avatar_contradiction_clause,[],[f600])).
thf(f602,plain,(
  ($false = $true) | (~spl13_5 | ~spl13_6)),
  inference(forward_demodulation,[],[f330,f325])).
thf(f603,plain,(
  $false | (~spl13_5 | ~spl13_6)),
  inference(trivial_inequality_removal,[],[f602])).
thf(f604,plain,(
  ~spl13_5 | ~spl13_6),
  inference(avatar_contradiction_clause,[],[f603])).
thf(f756,plain,(
  (((ap @ (c_2Eoption_2ESOME @ sK8) @ (sK6 @ (c_2Eoption_2ENONE @ sK8) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8))) = ((c_2Eoption_2ENONE @ sK8))) | ($true != $true) | ~spl13_19),
  inference(constrained_superposition,[],[f201,f526])).
thf(f758,plain,(
  ($true != $true) | (((mem @ (sK6 @ (c_2Eoption_2ENONE @ sK8) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8) @ sK8)) = $true) | ~spl13_19),
  inference(constrained_superposition,[],[f202,f526])).
thf(f761,plain,(
  (((mem @ (sK6 @ (c_2Eoption_2ENONE @ sK8) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8) @ sK8)) = $true) | ~spl13_19),
  inference(trivial_inequality_removal,[],[f758])).
thf(f764,plain,(
  (((ap @ (c_2Eoption_2ESOME @ sK8) @ (sK6 @ (c_2Eoption_2ENONE @ sK8) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8))) = ((c_2Eoption_2ENONE @ sK8))) | ~spl13_19),
  inference(trivial_inequality_removal,[],[f756])).
thf(f974,plain,(
  (((p @ (ap @ (c_2Eoption_2EIS__SOME @ sK8) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ (sK6 @ (c_2Eoption_2ENONE @ sK8) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8))))) = $true) | ($true != $true) | ~spl13_19),
  inference(constrained_superposition,[],[f466,f761])).
thf(f982,plain,(
  (((p @ (ap @ (c_2Eoption_2EIS__SOME @ sK8) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ (sK6 @ (c_2Eoption_2ENONE @ sK8) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8))))) = $true) | ~spl13_19),
  inference(trivial_inequality_removal,[],[f974])).
thf(f987,plain,(
  (((p @ (ap @ (c_2Eoption_2EIS__SOME @ sK8) @ (c_2Eoption_2ENONE @ sK8)))) = $true) | ~spl13_19),
  inference(forward_demodulation,[],[f982,f764])).
thf(f990,plain,(
  $false | ~spl13_19),
  inference(forward_subsumption_resolution,[],[f987,f471])).
thf(f991,plain,(
  ~spl13_19),
  inference(avatar_contradiction_clause,[],[f990])).
thf(f995,plain,(
  ( ! [X0 : del,X1 : del] : (($true != ((mem @ sK10 @ X1))) | ($true != $true) | ($true = ((sP0 @ (ap @ (c_2Eoption_2ESOME @ X0) @ sK11) @ X0 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ X1) @ sK10) @ X1))) | ($true != ((mem @ sK11 @ X0)))) ) | ~spl13_7),
  inference(constrained_superposition,[],[f283,f334])).
thf(f996,plain,(
  ( ! [X0 : del,X1 : del] : (($true != ((mem @ sK11 @ X0))) | ($true != ((mem @ sK10 @ X1))) | ($true = ((sP0 @ (ap @ (c_2Eoption_2ESOME @ X0) @ sK11) @ X0 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ X1) @ sK10) @ X1)))) ) | ~spl13_7),
  inference(trivial_inequality_removal,[],[f995])).
thf(f1060,plain,(
  ( ! [X0 : del] : ((((mem @ sK10 @ X0)) != $true) | ($true != $true) | ($true = ((sP0 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ X0) @ sK10) @ X0)))) ) | ~spl13_7),
  inference(constrained_superposition,[],[f996,f228])).
thf(f1061,plain,(
  ( ! [X0 : del] : ((((mem @ sK10 @ X0)) != $true) | ($true = ((sP0 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ X0) @ sK10) @ X0)))) ) | ~spl13_7),
  inference(trivial_inequality_removal,[],[f1060])).
thf(f1184,plain,(
  ($true = ((sP0 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8))) | ($true != $true) | ~spl13_7),
  inference(constrained_superposition,[],[f1061,f230])).
thf(f1185,plain,(
  ($true = ((sP0 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8))) | ~spl13_7),
  inference(trivial_inequality_removal,[],[f1184])).
thf(f1750,plain,(
  ($true != ((mem @ sK9 @ (arr @ sK8 @ (arr @ sK8 @ bool))))) | (((mem @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ (ty_2Eoption_2Eoption @ sK8))) != $true) | ($true != ((mem @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ (ty_2Eoption_2Eoption @ sK8)))) | ($true != $true) | ($true = ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10)) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11))))) | ~spl13_7),
  inference(constrained_superposition,[],[f208,f1185])).
thf(f1761,plain,(
  (((mem @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ (ty_2Eoption_2Eoption @ sK8))) != $true) | ($true != ((mem @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ (ty_2Eoption_2Eoption @ sK8)))) | ($true != ((mem @ sK9 @ (arr @ sK8 @ (arr @ sK8 @ bool))))) | ($true = ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10)) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11))))) | ~spl13_7),
  inference(trivial_inequality_removal,[],[f1750])).
thf(f1762,plain,(
  ($true != ((mem @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ (ty_2Eoption_2Eoption @ sK8)))) | ($true != ((mem @ sK9 @ (arr @ sK8 @ (arr @ sK8 @ bool))))) | ($true = ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10)) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11))))) | ~spl13_7),
  inference(forward_subsumption_resolution,[],[f1761,f556])).
thf(f1763,plain,(
  ($true = ((p @ (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ sK8 @ sK8) @ sK9) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10)) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11))))) | ($true != ((mem @ sK9 @ (arr @ sK8 @ (arr @ sK8 @ bool))))) | (~spl13_7 | ~spl13_17)),
  inference(forward_subsumption_resolution,[],[f1762,f517])).
thf(f1764,plain,(
  ($true != ((mem @ sK9 @ (arr @ sK8 @ (arr @ sK8 @ bool))))) | (spl13_6 | ~spl13_7 | ~spl13_17)),
  inference(forward_subsumption_resolution,[],[f1763,f329])).
thf(f1765,plain,(
  $false | (spl13_6 | ~spl13_7 | ~spl13_17)),
  inference(forward_subsumption_resolution,[],[f1764,f227])).
thf(f1766,plain,(
  spl13_6 | ~spl13_7 | ~spl13_17),
  inference(avatar_contradiction_clause,[],[f1765])).
thf(f1771,plain,(
  (((p @ (ap @ (c_2Eoption_2EIS__SOME @ sK8) @ (c_2Eoption_2ENONE @ sK8)))) = $true) | ~spl13_20),
  inference(constrained_superposition,[],[f506,f584])).
thf(f1786,plain,(
  $false | ~spl13_20),
  inference(forward_subsumption_resolution,[],[f1771,f471])).
thf(f1787,plain,(
  ~spl13_20),
  inference(avatar_contradiction_clause,[],[f1786])).
thf(f1794,plain,(
  ($true != $true) | (((c_2Eoption_2ENONE @ sK8)) = ((ap @ (c_2Eoption_2ESOME @ sK8) @ (sK5 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (c_2Eoption_2ENONE @ sK8) @ sK8)))) | ~spl13_21),
  inference(constrained_superposition,[],[f204,f588])).
thf(f1796,plain,(
  (((mem @ (sK5 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (c_2Eoption_2ENONE @ sK8) @ sK8) @ sK8)) = $true) | ($true != $true) | ~spl13_21),
  inference(constrained_superposition,[],[f205,f588])).
thf(f1801,plain,(
  (((mem @ (sK5 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (c_2Eoption_2ENONE @ sK8) @ sK8) @ sK8)) = $true) | ~spl13_21),
  inference(trivial_inequality_removal,[],[f1796])).
thf(f1803,plain,(
  (((c_2Eoption_2ENONE @ sK8)) = ((ap @ (c_2Eoption_2ESOME @ sK8) @ (sK5 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (c_2Eoption_2ENONE @ sK8) @ sK8)))) | ~spl13_21),
  inference(trivial_inequality_removal,[],[f1794])).
thf(f1824,plain,(
  ($true != $true) | (((p @ (ap @ (c_2Eoption_2EIS__SOME @ sK8) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ (sK5 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (c_2Eoption_2ENONE @ sK8) @ sK8))))) = $true) | ~spl13_21),
  inference(constrained_superposition,[],[f466,f1801])).
thf(f1831,plain,(
  (((p @ (ap @ (c_2Eoption_2EIS__SOME @ sK8) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ (sK5 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (c_2Eoption_2ENONE @ sK8) @ sK8))))) = $true) | ~spl13_21),
  inference(trivial_inequality_removal,[],[f1824])).
thf(f1837,plain,(
  (((p @ (ap @ (c_2Eoption_2EIS__SOME @ sK8) @ (c_2Eoption_2ENONE @ sK8)))) = $true) | ~spl13_21),
  inference(forward_demodulation,[],[f1831,f1803])).
thf(f1840,plain,(
  $false | ~spl13_21),
  inference(forward_subsumption_resolution,[],[f1837,f471])).
thf(f1841,plain,(
  ~spl13_21),
  inference(avatar_contradiction_clause,[],[f1840])).
thf(f2049,plain,(
  (((mem @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ (ty_2Eoption_2Eoption @ sK8))) != $true) | ($true = ((sP0 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8))) | ($true != ((mem @ sK9 @ (arr @ sK8 @ (arr @ sK8 @ bool))))) | (((c_2Eoption_2ENONE @ sK8)) = ((ap @ (c_2Eoption_2ESOME @ sK8) @ sK10))) | ($true != ((mem @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ (ty_2Eoption_2Eoption @ sK8)))) | ($true != $true) | ~spl13_6),
  inference(constrained_superposition,[],[f209,f330])).
thf(f2050,plain,(
  ($true = ((sP0 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8))) | (((c_2Eoption_2ENONE @ sK8)) = ((ap @ (c_2Eoption_2ESOME @ sK8) @ sK10))) | ($true != ((mem @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ (ty_2Eoption_2Eoption @ sK8)))) | ($true != ((mem @ sK9 @ (arr @ sK8 @ (arr @ sK8 @ bool))))) | (((mem @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ (ty_2Eoption_2Eoption @ sK8))) != $true) | ~spl13_6),
  inference(trivial_inequality_removal,[],[f2049])).
thf(f2053,plain,(
  ($true != ((mem @ sK9 @ (arr @ sK8 @ (arr @ sK8 @ bool))))) | ($true != ((mem @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ (ty_2Eoption_2Eoption @ sK8)))) | ($true = ((sP0 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8))) | (((mem @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ (ty_2Eoption_2Eoption @ sK8))) != $true) | (~spl13_6 | spl13_18)),
  inference(forward_subsumption_resolution,[],[f2050,f521])).
thf(f2055,plain,(
  ($true != ((mem @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ (ty_2Eoption_2Eoption @ sK8)))) | (((mem @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ (ty_2Eoption_2Eoption @ sK8))) != $true) | ($true = ((sP0 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8))) | (~spl13_6 | spl13_18)),
  inference(forward_subsumption_resolution,[],[f2053,f227])).
thf(f2057,plain,(
  (((mem @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ (ty_2Eoption_2Eoption @ sK8))) != $true) | ($true = ((sP0 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8))) | (~spl13_6 | ~spl13_17 | spl13_18)),
  inference(forward_subsumption_resolution,[],[f2055,f517])).
thf(f2059,plain,(
  ($true = ((sP0 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8))) | (~spl13_6 | ~spl13_17 | spl13_18)),
  inference(forward_subsumption_resolution,[],[f2057,f556])).
thf(f2092,plain,(
  ($true != $true) | (((p @ (ap @ (ap @ sK9 @ (sK5 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8)) @ (sK6 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8)))) = $true) | (~spl13_6 | ~spl13_17 | spl13_18)),
  inference(constrained_superposition,[],[f203,f2059])).
thf(f2093,plain,(
  ($true != $true) | (((ap @ (c_2Eoption_2ESOME @ sK8) @ (sK5 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8))) = ((ap @ (c_2Eoption_2ESOME @ sK8) @ sK10))) | (~spl13_6 | ~spl13_17 | spl13_18)),
  inference(constrained_superposition,[],[f204,f2059])).
thf(f2094,plain,(
  (((ap @ (c_2Eoption_2ESOME @ sK8) @ sK11)) = ((ap @ (c_2Eoption_2ESOME @ sK8) @ (sK6 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8)))) | ($true != $true) | (~spl13_6 | ~spl13_17 | spl13_18)),
  inference(constrained_superposition,[],[f201,f2059])).
thf(f2095,plain,(
  ($true = ((mem @ (sK5 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8) @ sK8))) | ($true != $true) | (~spl13_6 | ~spl13_17 | spl13_18)),
  inference(constrained_superposition,[],[f205,f2059])).
thf(f2096,plain,(
  (((mem @ (sK6 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8) @ sK8)) = $true) | ($true != $true) | (~spl13_6 | ~spl13_17 | spl13_18)),
  inference(constrained_superposition,[],[f202,f2059])).
thf(f2098,plain,(
  ($true = ((mem @ (sK5 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8) @ sK8))) | (~spl13_6 | ~spl13_17 | spl13_18)),
  inference(trivial_inequality_removal,[],[f2095])).
thf(f2099,plain,(
  (((mem @ (sK6 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8) @ sK8)) = $true) | (~spl13_6 | ~spl13_17 | spl13_18)),
  inference(trivial_inequality_removal,[],[f2096])).
thf(f2100,plain,(
  (((ap @ (c_2Eoption_2ESOME @ sK8) @ sK11)) = ((ap @ (c_2Eoption_2ESOME @ sK8) @ (sK6 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8)))) | (~spl13_6 | ~spl13_17 | spl13_18)),
  inference(trivial_inequality_removal,[],[f2094])).
thf(f2101,plain,(
  (((p @ (ap @ (ap @ sK9 @ (sK5 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8)) @ (sK6 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8)))) = $true) | (~spl13_6 | ~spl13_17 | spl13_18)),
  inference(trivial_inequality_removal,[],[f2092])).
thf(f2102,plain,(
  (((ap @ (c_2Eoption_2ESOME @ sK8) @ (sK5 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8))) = ((ap @ (c_2Eoption_2ESOME @ sK8) @ sK10))) | (~spl13_6 | ~spl13_17 | spl13_18)),
  inference(trivial_inequality_removal,[],[f2093])).
thf(f2152,plain,(
  (((sK5 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8)) = ((ap @ (c_2Eoption_2ETHE @ sK8) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ (sK5 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8))))) | ($true != $true) | (~spl13_6 | ~spl13_17 | spl13_18)),
  inference(constrained_superposition,[],[f464,f2098])).
thf(f2161,plain,(
  (((sK5 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8)) = ((ap @ (c_2Eoption_2ETHE @ sK8) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ (sK5 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8))))) | (~spl13_6 | ~spl13_17 | spl13_18)),
  inference(trivial_inequality_removal,[],[f2152])).
thf(f2165,plain,(
  (((ap @ (c_2Eoption_2ETHE @ sK8) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10))) = ((sK5 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8))) | (~spl13_6 | ~spl13_17 | spl13_18)),
  inference(forward_demodulation,[],[f2161,f2102])).
thf(f2167,plain,(
  (((sK5 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8)) = sK10) | (~spl13_6 | ~spl13_17 | spl13_18)),
  inference(forward_demodulation,[],[f2165,f497])).
thf(f2197,plain,(
  (((ap @ (c_2Eoption_2ETHE @ sK8) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ (sK6 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8)))) = ((sK6 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8))) | ($true != $true) | (~spl13_6 | ~spl13_17 | spl13_18)),
  inference(constrained_superposition,[],[f464,f2099])).
thf(f2206,plain,(
  (((ap @ (c_2Eoption_2ETHE @ sK8) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ (sK6 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8)))) = ((sK6 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8))) | (~spl13_6 | ~spl13_17 | spl13_18)),
  inference(trivial_inequality_removal,[],[f2197])).
thf(f2211,plain,(
  (((sK6 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8)) = ((ap @ (c_2Eoption_2ETHE @ sK8) @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11)))) | (~spl13_6 | ~spl13_17 | spl13_18)),
  inference(forward_demodulation,[],[f2206,f2100])).
thf(f2212,plain,(
  (((sK6 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8)) = sK11) | (~spl13_6 | ~spl13_17 | spl13_18)),
  inference(forward_demodulation,[],[f2211,f498])).
thf(f3015,plain,(
  (((p @ (ap @ (ap @ sK9 @ sK10) @ (sK6 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK11) @ sK8 @ sK9 @ (ap @ (c_2Eoption_2ESOME @ sK8) @ sK10) @ sK8)))) = $true) | (~spl13_6 | ~spl13_17 | spl13_18)),
  inference(constrained_superposition,[],[f2101,f2167])).
thf(f3017,plain,(
  (((p @ (ap @ (ap @ sK9 @ sK10) @ sK11))) = $true) | (~spl13_6 | ~spl13_17 | spl13_18)),
  inference(forward_demodulation,[],[f3015,f2212])).
thf(f3018,plain,(
  ($false = $true) | (~spl13_2 | ~spl13_6 | ~spl13_17 | spl13_18)),
  inference(forward_demodulation,[],[f3017,f313])).
thf(f3019,plain,(
  $false | (~spl13_2 | ~spl13_6 | ~spl13_17 | spl13_18)),
  inference(trivial_inequality_removal,[],[f3018])).
thf(f3020,plain,(
  ~spl13_2 | ~spl13_6 | ~spl13_17 | spl13_18),
  inference(avatar_contradiction_clause,[],[f3019])).
cnf(s1, plain, ~spl13_1 | spl13_2 | spl13_3 | spl13_4 | spl13_5, inference(sat_conversion,[],[f326])).
cnf(s2, plain, ~spl13_1 | spl13_3 | spl13_4 | spl13_6 | spl13_7, inference(sat_conversion,[],[f335])).
cnf(s8, plain, spl13_1, inference(sat_conversion,[],[f485])).
cnf(s9, plain, ~spl13_3 | ~spl13_17 | spl13_18 | spl13_19, inference(sat_conversion,[],[f527])).
cnf(s10, plain, spl13_17, inference(sat_conversion,[],[f559])).
cnf(s11, plain, ~spl13_4 | spl13_20 | spl13_21, inference(sat_conversion,[],[f589])).
cnf(s13, plain, ~spl13_18, inference(sat_conversion,[],[f601])).
cnf(s14, plain, ~spl13_5 | ~spl13_6, inference(sat_conversion,[],[f604])).
cnf(s28, plain, ~spl13_19, inference(sat_conversion,[],[f991])).
cnf(s46, plain, spl13_6 | ~spl13_7 | ~spl13_17, inference(sat_conversion,[],[f1766])).
cnf(s48, plain, ~spl13_20, inference(sat_conversion,[],[f1787])).
cnf(s49, plain, ~spl13_21, inference(sat_conversion,[],[f1841])).
cnf(s81, plain, ~spl13_2 | ~spl13_6 | ~spl13_17 | spl13_18, inference(sat_conversion,[],[f3020])).
cnf(s88, plain, ~spl13_4, inference(rat,[],[s11,s49,s48])).
cnf(s91, plain, ~spl13_3, inference(rat,[],[s9,s28,s13,s10])).
cnf(s92, plain, spl13_6 | spl13_7, inference(rat,[],[s2,s88,s91,s8])).
cnf(s93, plain, spl13_2 | spl13_5, inference(rat,[],[s1,s88,s91,s8])).
cnf(s94, plain, spl13_6, inference(rat,[],[s92,s46,s10])).
cnf(s95, plain, ~spl13_2, inference(rat,[],[s81,s13,s10,s94])).
cnf(s96, plain, ~spl13_5, inference(rat,[],[s14,s94])).
cnf(s97, plain, $false, inference(rat,[],[s93,s96,s95])).
thf(f3021,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s97])).
% SZS output end Proof for theBenchmark