%----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(type_def_7, type, tp__ty_2Eextreal_2Eextreal: $tType).
thf(func_def_0, type, bool: del).
thf(func_def_1, type, ind: del).
thf(func_def_2, type, arr: (del > del > del)).
thf(func_def_3, type, mem: ($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_10, type, ty_2Eextreal_2Eextreal: del).
thf(func_def_11, type, inj__ty_2Eextreal_2Eextreal: (tp__ty_2Eextreal_2Eextreal > $i)).
thf(func_def_12, type, surj__ty_2Eextreal_2Eextreal: ($i > tp__ty_2Eextreal_2Eextreal)).
thf(func_def_14, type, c_2Ebool_2ECOND: (del > $i)).
thf(func_def_16, type, fo__c_2Eextreal_2Eextreal__max: (tp__ty_2Eextreal_2Eextreal > tp__ty_2Eextreal_2Eextreal > tp__ty_2Eextreal_2Eextreal)).
thf(func_def_22, type, c_2Emin_2E_3D: (del > $i)).
thf(func_def_23, type, c_2Ebool_2E_21: (del > $i)).
thf(func_def_26, type, sK0: (del > ($i > $i) > del > $i)).
thf(func_def_27, type, sK1: (del > $i > $i)).
thf(func_def_28, type, sK2: ($i > $i > del > $i)).
thf(func_def_29, type, sK3: tp__ty_2Eextreal_2Eextreal).
thf(func_def_30, type, sK4: tp__ty_2Eextreal_2Eextreal).
thf(func_def_31, type, sK5: tp__ty_2Eextreal_2Eextreal).
thf(func_def_36, type, sF10: $o).
thf(func_def_40, type, sF14: $o).
thf(func_def_45, type, sF19: $o).
thf(func_def_46, type, vNOT: ($o > $o)).
thf(func_def_48, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_49, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(f4,axiom,(
  ! [X0 : $i] : ((mem @ X0 @ bool) => (X0 = ((inj__o @ (p @ X0)))))),
  file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP001^2.ax',stp_iso_mem_o)).
thf(f5,axiom,(
  ! [X0 : del,X1 : del,X2 : $i] : ((mem @ X2 @ (arr @ X0 @ X1)) => ! [X3 : $i] : ((mem @ X3 @ X0) => (mem @ (ap @ X2 @ X3) @ X1)))),
  file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP001^2.ax',ap_tp)).
thf(f7,axiom,(
  ! [X0 : $o] : (mem @ (inj__o @ X0) @ bool)),
  file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP001^2.ax',stp_inj_mem_o)).
thf(f10,axiom,(
  (mem @ c_2Eextreal_2Eextreal__le @ (arr @ ty_2Eextreal_2Eextreal @ (arr @ ty_2Eextreal_2Eextreal @ bool)))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eextreal_2Eextreal__le)).
thf(f15,axiom,(
  ! [X0 : $i] : ((mem @ X0 @ ty_2Eextreal_2Eextreal) => (X0 = ((inj__ty_2Eextreal_2Eextreal @ (surj__ty_2Eextreal_2Eextreal @ X0)))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_iso_mem_ty_2Eextreal_2Eextreal)).
thf(f19,axiom,(
  (mem @ c_2Ebool_2ET @ bool)),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2ET)).
thf(f25,axiom,(
  ! [X0 : tp__ty_2Eextreal_2Eextreal] : (mem @ (inj__ty_2Eextreal_2Eextreal @ X0) @ ty_2Eextreal_2Eextreal)),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_mem_ty_2Eextreal_2Eextreal)).
thf(f29,axiom,(
  ! [X1 : tp__ty_2Eextreal_2Eextreal,X0 : tp__ty_2Eextreal_2Eextreal] : ((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X0))) | (p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ (inj__ty_2Eextreal_2Eextreal @ X1))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eextreal_2Ele__total)).
thf(f37,conjecture,(
  ! [X0 : tp__ty_2Eextreal_2Eextreal,X1 : tp__ty_2Eextreal_2Eextreal,X2 : tp__ty_2Eextreal_2Eextreal] : (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X2)) @ (inj__ty_2Eextreal_2Eextreal @ X0))) & (p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) <=> (p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (ap @ (ap @ c_2Eextreal_2Eextreal__max @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X2))) @ (inj__ty_2Eextreal_2Eextreal @ X0))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eextreal_2Emax__le)).
thf(f38,negated_conjecture,(
  ~ ! [X0 : tp__ty_2Eextreal_2Eextreal,X1 : tp__ty_2Eextreal_2Eextreal,X2 : tp__ty_2Eextreal_2Eextreal] : (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X2)) @ (inj__ty_2Eextreal_2Eextreal @ X0))) & (p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) <=> (p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (ap @ (ap @ c_2Eextreal_2Eextreal__max @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X2))) @ (inj__ty_2Eextreal_2Eextreal @ X0))))),
  inference(negated_conjecture,[status(cth)],[f37])).
thf(f39,axiom,(
  ~(p @ c_2Ebool_2EF)),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_false_p)).
thf(f42,axiom,(
  ! [X1 : tp__ty_2Eextreal_2Eextreal,X0 : tp__ty_2Eextreal_2Eextreal] : (((inj__ty_2Eextreal_2Eextreal @ (fo__c_2Eextreal_2Eextreal__max @ X0 @ X1))) = ((ap @ (ap @ c_2Eextreal_2Eextreal__max @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ (inj__ty_2Eextreal_2Eextreal @ X1))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Eextreal_2Eextreal__max)).
thf(f43,axiom,(
  (p @ c_2Ebool_2ET)),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_true_p)).
thf(f47,axiom,(
  ! [X1 : tp__ty_2Eextreal_2Eextreal,X0 : tp__ty_2Eextreal_2Eextreal] : (((surj__ty_2Eextreal_2Eextreal @ (ap @ (ap @ c_2Eextreal_2Eextreal__max @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ (inj__ty_2Eextreal_2Eextreal @ X1)))) = ((surj__ty_2Eextreal_2Eextreal @ (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ ty_2Eextreal_2Eextreal) @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ (inj__ty_2Eextreal_2Eextreal @ X1))) @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X0)))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Eextreal_2Eextreal__max__def)).
thf(f48,axiom,(
  ! [X1 : $i,X0 : del] : ((mem @ X1 @ X0) => ! [X2 : $i] : ((mem @ X2 @ X0) => ((((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X0) @ c_2Ebool_2ET) @ X1) @ X2)) = X1) & (((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X0) @ c_2Ebool_2EF) @ X1) @ X2)) = X2))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ECOND__CLAUSES)).
thf(f49,axiom,(
  ! [X0 : tp__ty_2Eextreal_2Eextreal,X1 : tp__ty_2Eextreal_2Eextreal,X2 : tp__ty_2Eextreal_2Eextreal] : (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ (inj__ty_2Eextreal_2Eextreal @ X1))) & (p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X2)))) => (p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ (inj__ty_2Eextreal_2Eextreal @ X2))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eextreal_2Ele__trans)).
thf(f51,axiom,(
  (mem @ c_2Ebool_2EF @ bool)),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2EF)).
thf(f52,axiom,(
  ! [X0 : tp__ty_2Eextreal_2Eextreal] : (((surj__ty_2Eextreal_2Eextreal @ (inj__ty_2Eextreal_2Eextreal @ X0))) = X0)),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_ty_2Eextreal_2Eextreal)).
thf(f53,axiom,(
  (mem @ c_2Ebool_2E_7E @ (arr @ bool @ bool))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_7E)).
thf(f56,axiom,(
  ! [X1 : $i,X0 : del] : ((mem @ X1 @ (arr @ X0 @ bool)) => (! [X2 : $i] : ((mem @ X2 @ X0) => (p @ (ap @ X1 @ X2))) <=> (p @ (ap @ (c_2Ebool_2E_21 @ X0) @ X1))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_all_p)).
thf(f57,axiom,(
  ! [X0 : $i] : ((mem @ X0 @ bool) => (~(p @ X0) <=> (p @ (ap @ c_2Ebool_2E_7E @ X0))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_neg_p)).
thf(f72,plain,(
  (mem @ c_2Ebool_2EF @ bool)),
  inference(rectify,[],[f51])).
thf(f73,plain,(
  (((mem @ c_2Ebool_2EF @ bool)) = $true)),
  inference(fool_elimination,[],[f72])).
thf(f76,plain,(
  (mem @ c_2Ebool_2ET @ bool)),
  inference(rectify,[],[f19])).
thf(f77,plain,(
  (((mem @ c_2Ebool_2ET @ bool)) = $true)),
  inference(fool_elimination,[],[f76])).
thf(f78,plain,(
  (mem @ c_2Eextreal_2Eextreal__le @ (arr @ ty_2Eextreal_2Eextreal @ (arr @ ty_2Eextreal_2Eextreal @ bool)))),
  inference(rectify,[],[f10])).
thf(f79,plain,(
  (((mem @ c_2Eextreal_2Eextreal__le @ (arr @ ty_2Eextreal_2Eextreal @ (arr @ ty_2Eextreal_2Eextreal @ bool)))) = $true)),
  inference(fool_elimination,[],[f78])).
thf(f80,plain,(
  (mem @ c_2Ebool_2E_7E @ (arr @ bool @ bool))),
  inference(rectify,[],[f53])).
thf(f81,plain,(
  (((mem @ c_2Ebool_2E_7E @ (arr @ bool @ bool))) = $true)),
  inference(fool_elimination,[],[f80])).
thf(f86,plain,(
  ! [X0 : tp__ty_2Eextreal_2Eextreal,X1 : tp__ty_2Eextreal_2Eextreal] : ((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ (inj__ty_2Eextreal_2Eextreal @ X1))) | (p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X0))))),
  inference(rectify,[],[f29])).
thf(f87,plain,(
  ! [X0 : tp__ty_2Eextreal_2Eextreal,X1 : tp__ty_2Eextreal_2Eextreal] : ((((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ (inj__ty_2Eextreal_2Eextreal @ X1)))) = $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) = $true))),
  inference(fool_elimination,[],[f86])).
thf(f96,plain,(
  ! [X0 : $i] : ((mem @ X0 @ bool) => (~(p @ X0) <=> (p @ (ap @ c_2Ebool_2E_7E @ X0))))),
  inference(rectify,[],[f57])).
thf(f97,plain,(
  ! [X0 : $i] : ((((mem @ X0 @ bool)) = $true) => (~ (((p @ X0)) = $true) <=> (((p @ (ap @ c_2Ebool_2E_7E @ X0))) = $true)))),
  inference(fool_elimination,[],[f96])).
thf(f98,plain,(
  ~(p @ c_2Ebool_2EF)),
  inference(rectify,[],[f39])).
thf(f99,plain,(
  ~ (((p @ c_2Ebool_2EF)) = $true)),
  inference(fool_elimination,[],[f98])).
thf(f104,plain,(
  ! [X0 : del,X1 : del,X2 : $i] : ((mem @ X2 @ (arr @ X0 @ X1)) => ! [X3 : $i] : ((mem @ X3 @ X0) => (mem @ (ap @ X2 @ X3) @ X1)))),
  inference(rectify,[],[f5])).
thf(f105,plain,(
  ! [X0 : del,X1 : del,X2 : $i] : ((((mem @ X2 @ (arr @ X0 @ X1))) = $true) => ! [X3 : $i] : ((((mem @ X3 @ X0)) = $true) => (((mem @ (ap @ X2 @ X3) @ X1)) = $true)))),
  inference(fool_elimination,[],[f104])).
thf(f112,plain,(
  ! [X0 : tp__ty_2Eextreal_2Eextreal] : (mem @ (inj__ty_2Eextreal_2Eextreal @ X0) @ ty_2Eextreal_2Eextreal)),
  inference(rectify,[],[f25])).
thf(f113,plain,(
  ! [X0 : tp__ty_2Eextreal_2Eextreal] : (((mem @ (inj__ty_2Eextreal_2Eextreal @ X0) @ ty_2Eextreal_2Eextreal)) = $true)),
  inference(fool_elimination,[],[f112])).
thf(f114,plain,(
  (p @ c_2Ebool_2ET)),
  inference(rectify,[],[f43])).
thf(f115,plain,(
  (((p @ c_2Ebool_2ET)) = $true)),
  inference(fool_elimination,[],[f114])).
thf(f120,plain,(
  ! [X0 : $o] : (mem @ (inj__o @ X0) @ bool)),
  inference(rectify,[],[f7])).
thf(f121,plain,(
  ! [X0 : $o] : (((mem @ (inj__o @ X0) @ bool)) = $true)),
  inference(fool_elimination,[],[f120])).
thf(f134,plain,(
  ! [X0 : $i] : ((mem @ X0 @ bool) => (X0 = ((inj__o @ (p @ X0)))))),
  inference(rectify,[],[f4])).
thf(f135,plain,(
  ! [X0 : $i] : ((((mem @ X0 @ bool)) = $true) => (((inj__o @ (p @ X0))) = X0))),
  inference(fool_elimination,[],[f134])).
thf(f142,plain,(
  ! [X0 : $i,X1 : del] : ((mem @ X0 @ (arr @ X1 @ bool)) => (! [X2 : $i] : ((mem @ X2 @ X1) => (p @ (ap @ X0 @ X2))) <=> (p @ (ap @ (c_2Ebool_2E_21 @ X1) @ X0))))),
  inference(rectify,[],[f56])).
thf(f143,plain,(
  ! [X1 : del,X0 : $i] : ((((mem @ X0 @ (arr @ X1 @ bool))) = $true) => (! [X2 : $i] : ((((mem @ X2 @ X1)) = $true) => (((p @ (ap @ X0 @ X2))) = $true)) <=> (((p @ (ap @ (c_2Ebool_2E_21 @ X1) @ X0))) = $true)))),
  inference(fool_elimination,[],[f142])).
thf(f144,plain,(
  ! [X0 : $i,X1 : del] : ((mem @ X0 @ X1) => ! [X2 : $i] : ((mem @ X2 @ X1) => ((((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X1) @ c_2Ebool_2ET) @ X0) @ X2)) = X0) & (((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X1) @ c_2Ebool_2EF) @ X0) @ X2)) = X2))))),
  inference(rectify,[],[f48])).
thf(f145,plain,(
  ! [X0 : $i,X1 : del] : ((((mem @ X0 @ X1)) = $true) => ! [X2 : $i] : ((((mem @ X2 @ X1)) = $true) => ((((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X1) @ c_2Ebool_2EF) @ X0) @ X2)) = X2) & (((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X1) @ c_2Ebool_2ET) @ X0) @ X2)) = X0))))),
  inference(fool_elimination,[],[f144])).
thf(f152,plain,(
  ~ ! [X0 : tp__ty_2Eextreal_2Eextreal,X1 : tp__ty_2Eextreal_2Eextreal,X2 : tp__ty_2Eextreal_2Eextreal] : (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X2)) @ (inj__ty_2Eextreal_2Eextreal @ X0))) & (p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) <=> (p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (ap @ (ap @ c_2Eextreal_2Eextreal__max @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X2))) @ (inj__ty_2Eextreal_2Eextreal @ X0))))),
  inference(rectify,[],[f38])).
thf(f153,plain,(
  ~ ! [X2 : tp__ty_2Eextreal_2Eextreal,X0 : tp__ty_2Eextreal_2Eextreal,X1 : tp__ty_2Eextreal_2Eextreal] : (((((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) = $true) & (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X2)) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) = $true)) <=> (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (ap @ (ap @ c_2Eextreal_2Eextreal__max @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X2))) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) = $true))),
  inference(fool_elimination,[],[f152])).
thf(f154,plain,(
  ! [X0 : $i] : ((mem @ X0 @ ty_2Eextreal_2Eextreal) => (X0 = ((inj__ty_2Eextreal_2Eextreal @ (surj__ty_2Eextreal_2Eextreal @ X0)))))),
  inference(rectify,[],[f15])).
thf(f155,plain,(
  ! [X0 : $i] : ((((mem @ X0 @ ty_2Eextreal_2Eextreal)) = $true) => (((inj__ty_2Eextreal_2Eextreal @ (surj__ty_2Eextreal_2Eextreal @ X0))) = X0))),
  inference(fool_elimination,[],[f154])).
thf(f162,plain,(
  ! [X0 : tp__ty_2Eextreal_2Eextreal,X1 : tp__ty_2Eextreal_2Eextreal,X2 : tp__ty_2Eextreal_2Eextreal] : (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ (inj__ty_2Eextreal_2Eextreal @ X1))) & (p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X2)))) => (p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ (inj__ty_2Eextreal_2Eextreal @ X2))))),
  inference(rectify,[],[f49])).
thf(f163,plain,(
  ! [X2 : tp__ty_2Eextreal_2Eextreal,X1 : tp__ty_2Eextreal_2Eextreal,X0 : tp__ty_2Eextreal_2Eextreal] : (((((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ (inj__ty_2Eextreal_2Eextreal @ X1)))) = $true) & (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X2)))) = $true)) => (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ (inj__ty_2Eextreal_2Eextreal @ X2)))) = $true))),
  inference(fool_elimination,[],[f162])).
thf(f172,plain,(
  ! [X0 : tp__ty_2Eextreal_2Eextreal,X1 : tp__ty_2Eextreal_2Eextreal] : (((inj__ty_2Eextreal_2Eextreal @ (fo__c_2Eextreal_2Eextreal__max @ X1 @ X0))) = ((ap @ (ap @ c_2Eextreal_2Eextreal__max @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X0))))),
  inference(rectify,[],[f42])).
thf(f181,plain,(
  ! [X0 : $i] : ((((mem @ X0 @ bool)) = $true) => ((((p @ X0)) != $true) <=> (((p @ (ap @ c_2Ebool_2E_7E @ X0))) = $true)))),
  inference(flattening,[],[f97])).
thf(f182,plain,(
  (((p @ c_2Ebool_2EF)) != $true)),
  inference(flattening,[],[f99])).
thf(f193,plain,(
  ! [X0 : tp__ty_2Eextreal_2Eextreal,X1 : tp__ty_2Eextreal_2Eextreal] : (((surj__ty_2Eextreal_2Eextreal @ (ap @ (ap @ c_2Eextreal_2Eextreal__max @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) = ((surj__ty_2Eextreal_2Eextreal @ (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ ty_2Eextreal_2Eextreal) @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X0))) @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ (inj__ty_2Eextreal_2Eextreal @ X1)))))),
  inference(rectify,[],[f47])).
thf(f203,plain,(
  ! [X2 : tp__ty_2Eextreal_2Eextreal,X1 : tp__ty_2Eextreal_2Eextreal,X0 : tp__ty_2Eextreal_2Eextreal] : ((((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ (inj__ty_2Eextreal_2Eextreal @ X2)))) = $true) | ((((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ (inj__ty_2Eextreal_2Eextreal @ X1)))) != $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X2)))) != $true)))),
  inference(ennf_transformation,[],[f163])).
thf(f204,plain,(
  ! [X2 : tp__ty_2Eextreal_2Eextreal,X0 : tp__ty_2Eextreal_2Eextreal,X1 : tp__ty_2Eextreal_2Eextreal] : ((((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ (inj__ty_2Eextreal_2Eextreal @ X1)))) != $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X2)))) != $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ (inj__ty_2Eextreal_2Eextreal @ X2)))) = $true))),
  inference(flattening,[],[f203])).
thf(f207,plain,(
  ! [X0 : $i] : (((((p @ X0)) != $true) <=> (((p @ (ap @ c_2Ebool_2E_7E @ X0))) = $true)) | (((mem @ X0 @ bool)) != $true))),
  inference(ennf_transformation,[],[f181])).
thf(f210,plain,(
  ! [X1 : del,X0 : $i] : ((((mem @ X0 @ X1)) != $true) | ! [X2 : $i] : (((((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X1) @ c_2Ebool_2EF) @ X0) @ X2)) = X2) & (((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X1) @ c_2Ebool_2ET) @ X0) @ X2)) = X0)) | (((mem @ X2 @ X1)) != $true)))),
  inference(ennf_transformation,[],[f145])).
thf(f221,plain,(
  ? [X2 : tp__ty_2Eextreal_2Eextreal,X0 : tp__ty_2Eextreal_2Eextreal,X1 : tp__ty_2Eextreal_2Eextreal] : ((((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (ap @ (ap @ c_2Eextreal_2Eextreal__max @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X2))) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) = $true) <~> ((((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) = $true) & (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X2)) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) = $true)))),
  inference(ennf_transformation,[],[f153])).
thf(f222,plain,(
  ! [X1 : del,X0 : del,X2 : $i] : ((((mem @ X2 @ (arr @ X0 @ X1))) != $true) | ! [X3 : $i] : ((((mem @ X3 @ X0)) != $true) | (((mem @ (ap @ X2 @ X3) @ X1)) = $true)))),
  inference(ennf_transformation,[],[f105])).
thf(f233,plain,(
  ! [X0 : $i,X1 : del] : ((((mem @ X0 @ (arr @ X1 @ bool))) != $true) | ((((p @ (ap @ (c_2Ebool_2E_21 @ X1) @ X0))) = $true) <=> ! [X2 : $i] : ((((mem @ X2 @ X1)) != $true) | (((p @ (ap @ X0 @ X2))) = $true))))),
  inference(ennf_transformation,[],[f143])).
thf(f236,plain,(
  ! [X0 : $i] : ((((inj__ty_2Eextreal_2Eextreal @ (surj__ty_2Eextreal_2Eextreal @ X0))) = X0) | (((mem @ X0 @ ty_2Eextreal_2Eextreal)) != $true))),
  inference(ennf_transformation,[],[f155])).
thf(f238,plain,(
  ! [X0 : $i] : ((((inj__o @ (p @ X0))) = X0) | (((mem @ X0 @ bool)) != $true))),
  inference(ennf_transformation,[],[f135])).
thf(f243,plain,(
  ! [X0 : $i] : ((((((p @ X0)) != $true) | (((p @ (ap @ c_2Ebool_2E_7E @ X0))) != $true)) & ((((p @ (ap @ c_2Ebool_2E_7E @ X0))) = $true) | (((p @ X0)) = $true))) | (((mem @ X0 @ bool)) != $true))),
  inference(nnf_transformation,[],[f207])).
thf(f264,plain,(
  ! [X0 : $i,X1 : del] : ((((mem @ X0 @ (arr @ X1 @ bool))) != $true) | (((((p @ (ap @ (c_2Ebool_2E_21 @ X1) @ X0))) = $true) | ? [X2 : $i] : ((((mem @ X2 @ X1)) = $true) & (((p @ (ap @ X0 @ X2))) != $true))) & (! [X2 : $i] : ((((mem @ X2 @ X1)) != $true) | (((p @ (ap @ X0 @ X2))) = $true)) | (((p @ (ap @ (c_2Ebool_2E_21 @ X1) @ X0))) != $true))))),
  inference(nnf_transformation,[],[f233])).
thf(f265,plain,(
  ! [X0 : $i,X1 : del] : ((((mem @ X0 @ (arr @ X1 @ bool))) != $true) | (((((p @ (ap @ (c_2Ebool_2E_21 @ X1) @ X0))) = $true) | ? [X2 : $i] : ((((mem @ X2 @ X1)) = $true) & (((p @ (ap @ X0 @ X2))) != $true))) & (! [X3 : $i] : (($true != ((mem @ X3 @ X1))) | (((p @ (ap @ X0 @ X3))) = $true)) | (((p @ (ap @ (c_2Ebool_2E_21 @ X1) @ X0))) != $true))))),
  inference(rectify,[],[f264])).
thf(f266,plain,(
  ! [X0 : $i,X1 : del] : ((((mem @ X0 @ (arr @ X1 @ bool))) != $true) | (((((p @ (ap @ (c_2Ebool_2E_21 @ X1) @ X0))) = $true) | ((((mem @ (sK1 @ X1 @ X0) @ X1)) = $true) & (((p @ (ap @ X0 @ (sK1 @ X1 @ X0)))) != $true))) & (! [X3 : $i] : (($true != ((mem @ X3 @ X1))) | (((p @ (ap @ X0 @ X3))) = $true)) | (((p @ (ap @ (c_2Ebool_2E_21 @ X1) @ X0))) != $true))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,$thf(sK0 @ X2 @ X1 @ X0))],[f265])).
thf(f269,plain,(
  ! [X0 : del,X1 : del,X2 : $i] : ((((mem @ X2 @ (arr @ X1 @ X0))) != $true) | ! [X3 : $i] : (($true != ((mem @ X3 @ X1))) | (((mem @ (ap @ X2 @ X3) @ X0)) = $true)))),
  inference(rectify,[],[f222])).
thf(f272,plain,(
  ! [X0 : del,X1 : $i] : ((((mem @ X1 @ X0)) != $true) | ! [X2 : $i] : (((((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X0) @ c_2Ebool_2EF) @ X1) @ X2)) = X2) & (((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X0) @ c_2Ebool_2ET) @ X1) @ X2)) = X1)) | (((mem @ X2 @ X0)) != $true)))),
  inference(rectify,[],[f210])).
thf(f279,plain,(
  ? [X2 : tp__ty_2Eextreal_2Eextreal,X0 : tp__ty_2Eextreal_2Eextreal,X1 : tp__ty_2Eextreal_2Eextreal] : ((((((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) != $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X2)) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) != $true)) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (ap @ (ap @ c_2Eextreal_2Eextreal__max @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X2))) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) != $true)) & (((((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) = $true) & (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X2)) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) = $true)) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (ap @ (ap @ c_2Eextreal_2Eextreal__max @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X2))) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) = $true)))),
  inference(nnf_transformation,[],[f221])).
thf(f280,plain,(
  ? [X2 : tp__ty_2Eextreal_2Eextreal,X0 : tp__ty_2Eextreal_2Eextreal,X1 : tp__ty_2Eextreal_2Eextreal] : (((((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) != $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X2)) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) != $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (ap @ (ap @ c_2Eextreal_2Eextreal__max @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X2))) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) != $true)) & (((((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) = $true) & (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X2)) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) = $true)) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (ap @ (ap @ c_2Eextreal_2Eextreal__max @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X2))) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) = $true)))),
  inference(flattening,[],[f279])).
thf(f281,plain,(
  ? [X0 : tp__ty_2Eextreal_2Eextreal,X1 : tp__ty_2Eextreal_2Eextreal,X2 : tp__ty_2Eextreal_2Eextreal] : (((((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X2)) @ (inj__ty_2Eextreal_2Eextreal @ X1)))) != $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ (inj__ty_2Eextreal_2Eextreal @ X1)))) != $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (ap @ (ap @ c_2Eextreal_2Eextreal__max @ (inj__ty_2Eextreal_2Eextreal @ X2)) @ (inj__ty_2Eextreal_2Eextreal @ X0))) @ (inj__ty_2Eextreal_2Eextreal @ X1)))) != $true)) & (((((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X2)) @ (inj__ty_2Eextreal_2Eextreal @ X1)))) = $true) & (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ (inj__ty_2Eextreal_2Eextreal @ X1)))) = $true)) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (ap @ (ap @ c_2Eextreal_2Eextreal__max @ (inj__ty_2Eextreal_2Eextreal @ X2)) @ (inj__ty_2Eextreal_2Eextreal @ X0))) @ (inj__ty_2Eextreal_2Eextreal @ X1)))) = $true)))),
  inference(rectify,[],[f280])).
thf(f282,plain,(
  (($true != ((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ sK5)) @ (inj__ty_2Eextreal_2Eextreal @ sK4))))) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ sK3)) @ (inj__ty_2Eextreal_2Eextreal @ sK4)))) != $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (ap @ (ap @ c_2Eextreal_2Eextreal__max @ (inj__ty_2Eextreal_2Eextreal @ sK5)) @ (inj__ty_2Eextreal_2Eextreal @ sK3))) @ (inj__ty_2Eextreal_2Eextreal @ sK4)))) != $true)) & ((($true = ((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ sK5)) @ (inj__ty_2Eextreal_2Eextreal @ sK4))))) & (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ sK3)) @ (inj__ty_2Eextreal_2Eextreal @ sK4)))) = $true)) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (ap @ (ap @ c_2Eextreal_2Eextreal__max @ (inj__ty_2Eextreal_2Eextreal @ sK5)) @ (inj__ty_2Eextreal_2Eextreal @ sK3))) @ (inj__ty_2Eextreal_2Eextreal @ sK4)))) = $true))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,$thf(sK3)),skolemize(X1,$thf(sK4)),skolemize(X2,$thf(sK5))],[f281])).
thf(f287,plain,(
  ! [X0 : tp__ty_2Eextreal_2Eextreal,X1 : tp__ty_2Eextreal_2Eextreal,X2 : tp__ty_2Eextreal_2Eextreal] : ((((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X2)))) != $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X2)) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) != $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) = $true))),
  inference(rectify,[],[f204])).
thf(f292,plain,(
  (((p @ c_2Ebool_2EF)) != $true)),
  inference(cnf_transformation,[],[f182])).
thf(f295,plain,(
  ( ! [X0 : $i] : ((((p @ (ap @ c_2Ebool_2E_7E @ X0))) = $true) | (((p @ X0)) = $true) | (((mem @ X0 @ bool)) != $true)) )),
  inference(cnf_transformation,[],[f243])).
thf(f296,plain,(
  ( ! [X0 : $i] : ((((p @ (ap @ c_2Ebool_2E_7E @ X0))) != $true) | (((mem @ X0 @ bool)) != $true) | (((p @ X0)) != $true)) )),
  inference(cnf_transformation,[],[f243])).
thf(f301,plain,(
  (((p @ c_2Ebool_2ET)) = $true)),
  inference(cnf_transformation,[],[f115])).
thf(f359,plain,(
  ( ! [X0 : $i] : ((((mem @ X0 @ bool)) != $true) | (((inj__o @ (p @ X0))) = X0)) )),
  inference(cnf_transformation,[],[f238])).
thf(f368,plain,(
  (((mem @ c_2Eextreal_2Eextreal__le @ (arr @ ty_2Eextreal_2Eextreal @ (arr @ ty_2Eextreal_2Eextreal @ bool)))) = $true)),
  inference(cnf_transformation,[],[f79])).
thf(f374,plain,(
  ( ! [X0 : $o] : ((((mem @ (inj__o @ X0) @ bool)) = $true)) )),
  inference(cnf_transformation,[],[f121])).
thf(f433,plain,(
  (((mem @ c_2Ebool_2EF @ bool)) = $true)),
  inference(cnf_transformation,[],[f73])).
thf(f434,plain,(
  ( ! [X3 : $i,X0 : $i,X1 : del] : ((((mem @ X0 @ (arr @ X1 @ bool))) != $true) | ($true != ((mem @ X3 @ X1))) | (((p @ (ap @ X0 @ X3))) = $true) | (((p @ (ap @ (c_2Ebool_2E_21 @ X1) @ X0))) != $true)) )),
  inference(cnf_transformation,[],[f266])).
thf(f435,plain,(
  ( ! [X0 : $i,X1 : del] : ((((p @ (ap @ X0 @ (sK1 @ X1 @ X0)))) != $true) | (((mem @ X0 @ (arr @ X1 @ bool))) != $true) | (((p @ (ap @ (c_2Ebool_2E_21 @ X1) @ X0))) = $true)) )),
  inference(cnf_transformation,[],[f266])).
thf(f436,plain,(
  ( ! [X0 : $i,X1 : del] : ((((mem @ X0 @ (arr @ X1 @ bool))) != $true) | (((mem @ (sK1 @ X1 @ X0) @ X1)) = $true) | (((p @ (ap @ (c_2Ebool_2E_21 @ X1) @ X0))) = $true)) )),
  inference(cnf_transformation,[],[f266])).
thf(f450,plain,(
  ( ! [X0 : tp__ty_2Eextreal_2Eextreal] : ((((surj__ty_2Eextreal_2Eextreal @ (inj__ty_2Eextreal_2Eextreal @ X0))) = X0)) )),
  inference(cnf_transformation,[],[f52])).
thf(f451,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : del,X1 : del] : ((((mem @ X2 @ (arr @ X1 @ X0))) != $true) | ($true != ((mem @ X3 @ X1))) | (((mem @ (ap @ X2 @ X3) @ X0)) = $true)) )),
  inference(cnf_transformation,[],[f269])).
thf(f454,plain,(
  ( ! [X0 : tp__ty_2Eextreal_2Eextreal,X1 : tp__ty_2Eextreal_2Eextreal] : ((((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) = $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ (inj__ty_2Eextreal_2Eextreal @ X1)))) = $true)) )),
  inference(cnf_transformation,[],[f87])).
thf(f455,plain,(
  (((mem @ c_2Ebool_2ET @ bool)) = $true)),
  inference(cnf_transformation,[],[f77])).
thf(f456,plain,(
  ( ! [X0 : tp__ty_2Eextreal_2Eextreal,X1 : tp__ty_2Eextreal_2Eextreal] : ((((inj__ty_2Eextreal_2Eextreal @ (fo__c_2Eextreal_2Eextreal__max @ X1 @ X0))) = ((ap @ (ap @ c_2Eextreal_2Eextreal__max @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X0))))) )),
  inference(cnf_transformation,[],[f172])).
thf(f457,plain,(
  ( ! [X2 : $i,X0 : del,X1 : $i] : ((((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X0) @ c_2Ebool_2ET) @ X1) @ X2)) = X1) | (((mem @ X1 @ X0)) != $true) | (((mem @ X2 @ X0)) != $true)) )),
  inference(cnf_transformation,[],[f272])).
thf(f458,plain,(
  ( ! [X2 : $i,X0 : del,X1 : $i] : ((((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X0) @ c_2Ebool_2EF) @ X1) @ X2)) = X2) | (((mem @ X1 @ X0)) != $true) | (((mem @ X2 @ X0)) != $true)) )),
  inference(cnf_transformation,[],[f272])).
thf(f460,plain,(
  ( ! [X0 : tp__ty_2Eextreal_2Eextreal] : ((((mem @ (inj__ty_2Eextreal_2Eextreal @ X0) @ ty_2Eextreal_2Eextreal)) = $true)) )),
  inference(cnf_transformation,[],[f113])).
thf(f476,plain,(
  ( ! [X0 : $i] : ((((mem @ X0 @ ty_2Eextreal_2Eextreal)) != $true) | (((inj__ty_2Eextreal_2Eextreal @ (surj__ty_2Eextreal_2Eextreal @ X0))) = X0)) )),
  inference(cnf_transformation,[],[f236])).
thf(f477,plain,(
  (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ sK3)) @ (inj__ty_2Eextreal_2Eextreal @ sK4)))) = $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (ap @ (ap @ c_2Eextreal_2Eextreal__max @ (inj__ty_2Eextreal_2Eextreal @ sK5)) @ (inj__ty_2Eextreal_2Eextreal @ sK3))) @ (inj__ty_2Eextreal_2Eextreal @ sK4)))) = $true)),
  inference(cnf_transformation,[],[f282])).
thf(f478,plain,(
  ($true = ((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ sK5)) @ (inj__ty_2Eextreal_2Eextreal @ sK4))))) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (ap @ (ap @ c_2Eextreal_2Eextreal__max @ (inj__ty_2Eextreal_2Eextreal @ sK5)) @ (inj__ty_2Eextreal_2Eextreal @ sK3))) @ (inj__ty_2Eextreal_2Eextreal @ sK4)))) = $true)),
  inference(cnf_transformation,[],[f282])).
thf(f479,plain,(
  ($true != ((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ sK5)) @ (inj__ty_2Eextreal_2Eextreal @ sK4))))) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ sK3)) @ (inj__ty_2Eextreal_2Eextreal @ sK4)))) != $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (ap @ (ap @ c_2Eextreal_2Eextreal__max @ (inj__ty_2Eextreal_2Eextreal @ sK5)) @ (inj__ty_2Eextreal_2Eextreal @ sK3))) @ (inj__ty_2Eextreal_2Eextreal @ sK4)))) != $true)),
  inference(cnf_transformation,[],[f282])).
thf(f525,plain,(
  (((mem @ c_2Ebool_2E_7E @ (arr @ bool @ bool))) = $true)),
  inference(cnf_transformation,[],[f81])).
thf(f532,plain,(
  ( ! [X2 : tp__ty_2Eextreal_2Eextreal,X0 : tp__ty_2Eextreal_2Eextreal,X1 : tp__ty_2Eextreal_2Eextreal] : ((((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X2)) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) != $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X2)))) != $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) = $true)) )),
  inference(cnf_transformation,[],[f287])).
thf(f704,plain,(
  ( ! [X0 : tp__ty_2Eextreal_2Eextreal,X1 : tp__ty_2Eextreal_2Eextreal] : ((((surj__ty_2Eextreal_2Eextreal @ (ap @ (ap @ c_2Eextreal_2Eextreal__max @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) = ((surj__ty_2Eextreal_2Eextreal @ (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ ty_2Eextreal_2Eextreal) @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X0))) @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ (inj__ty_2Eextreal_2Eextreal @ X1)))))) )),
  inference(cnf_transformation,[],[f193])).
thf(f714,definition,(
  ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
  introduced(theory,[fool_exhaustiveness_axiom])).
thf(f718,definition,(
  (sF6 = ((inj__ty_2Eextreal_2Eextreal @ sK5)))),
  introduced(definition,[new_symbols(definition,[sF6])],[function_definition])).
thf(f719,plain,(
  (((inj__ty_2Eextreal_2Eextreal @ sK5)) = sF6)),
  inference(reorient_equations,[],[f718])).
thf(f720,definition,(
  (sF7 = ((ap @ c_2Eextreal_2Eextreal__le @ sF6)))),
  introduced(definition,[new_symbols(definition,[sF7])],[function_definition])).
thf(f721,plain,(
  (((ap @ c_2Eextreal_2Eextreal__le @ sF6)) = sF7)),
  inference(reorient_equations,[],[f720])).
thf(f722,definition,(
  (sF8 = ((inj__ty_2Eextreal_2Eextreal @ sK4)))),
  introduced(definition,[new_symbols(definition,[sF8])],[function_definition])).
thf(f723,plain,(
  (((inj__ty_2Eextreal_2Eextreal @ sK4)) = sF8)),
  inference(reorient_equations,[],[f722])).
thf(f724,definition,(
  (sF9 = ((ap @ sF7 @ sF8)))),
  introduced(definition,[new_symbols(definition,[sF9])],[function_definition])).
thf(f725,definition,(
  (sF10 = ((p @ sF9)))),
  introduced(definition,[new_symbols(definition,[sF10])],[function_definition])).
thf(f726,definition,(
  (sF11 = ((inj__ty_2Eextreal_2Eextreal @ sK3)))),
  introduced(definition,[new_symbols(definition,[sF11])],[function_definition])).
thf(f727,plain,(
  (((inj__ty_2Eextreal_2Eextreal @ sK3)) = sF11)),
  inference(reorient_equations,[],[f726])).
thf(f728,definition,(
  (sF12 = ((ap @ c_2Eextreal_2Eextreal__le @ sF11)))),
  introduced(definition,[new_symbols(definition,[sF12])],[function_definition])).
thf(f729,definition,(
  (sF13 = ((ap @ sF12 @ sF8)))),
  introduced(definition,[new_symbols(definition,[sF13])],[function_definition])).
thf(f730,plain,(
  (((ap @ sF12 @ sF8)) = sF13)),
  inference(reorient_equations,[],[f729])).
thf(f731,definition,(
  (sF14 = ((p @ sF13)))),
  introduced(definition,[new_symbols(definition,[sF14])],[function_definition])).
thf(f732,definition,(
  (sF15 = ((ap @ c_2Eextreal_2Eextreal__max @ sF6)))),
  introduced(definition,[new_symbols(definition,[sF15])],[function_definition])).
thf(f733,plain,(
  (((ap @ c_2Eextreal_2Eextreal__max @ sF6)) = sF15)),
  inference(reorient_equations,[],[f732])).
thf(f734,definition,(
  (sF16 = ((ap @ sF15 @ sF11)))),
  introduced(definition,[new_symbols(definition,[sF16])],[function_definition])).
thf(f735,plain,(
  (((ap @ sF15 @ sF11)) = sF16)),
  inference(reorient_equations,[],[f734])).
thf(f736,definition,(
  (sF17 = ((ap @ c_2Eextreal_2Eextreal__le @ sF16)))),
  introduced(definition,[new_symbols(definition,[sF17])],[function_definition])).
thf(f737,plain,(
  (((ap @ c_2Eextreal_2Eextreal__le @ sF16)) = sF17)),
  inference(reorient_equations,[],[f736])).
thf(f738,definition,(
  (sF18 = ((ap @ sF17 @ sF8)))),
  introduced(definition,[new_symbols(definition,[sF18])],[function_definition])).
thf(f739,plain,(
  (((ap @ sF17 @ sF8)) = sF18)),
  inference(reorient_equations,[],[f738])).
thf(f740,definition,(
  (sF19 = ((p @ sF18)))),
  introduced(definition,[new_symbols(definition,[sF19])],[function_definition])).
thf(f741,plain,(
  (sF14 != $true) | (sF19 != $true) | (sF10 != $true)),
  inference(definition_folding,[],[f479,f740,f739,f723,f737,f735,f727,f733,f719,f731,f730,f723,f728,f727,f725,f724,f723,f721,f719])).
thf(f742,plain,(
  (sF10 = $true) | (sF19 = $true)),
  inference(definition_folding,[],[f478,f740,f739,f723,f737,f735,f727,f733,f719,f725,f724,f723,f721,f719])).
thf(f743,plain,(
  (sF19 = $true) | (sF14 = $true)),
  inference(definition_folding,[],[f477,f740,f739,f723,f737,f735,f727,f733,f719,f731,f730,f723,f728,f727])).
thf(f1267,plain,(
  (((p @ sF13)) = $false) | (sF14 = $true)),
  inference(iff_proxy_clausification,[],[f731])).
thf(f1268,plain,(
  (sF14 = $false) | (((p @ sF13)) = $true)),
  inference(iff_proxy_clausification,[],[f731])).
thf(f1297,plain,(
  ($false = ((p @ sF9))) | (sF10 = $true)),
  inference(iff_proxy_clausification,[],[f725])).
thf(f1298,plain,(
  ($false = sF10) | ($true = ((p @ sF9)))),
  inference(iff_proxy_clausification,[],[f725])).
thf(f1416,plain,(
  (sF19 = $true) | ($false = ((p @ sF18)))),
  inference(iff_proxy_clausification,[],[f740])).
thf(f1417,plain,(
  ($false = sF19) | (((p @ sF18)) = $true)),
  inference(iff_proxy_clausification,[],[f740])).
thf(f1563,definition,(
  spl20_4 <=> ! [X0 : $i] : ((((mem @ X0 @ bool)) != $true) | (((p @ X0)) != $true))),
  introduced(definition,[new_symbols(definition,[spl20_4])],[avatar_definition])).
thf(f1564,plain,(
  ( ! [X0 : $i] : ((((mem @ X0 @ bool)) != $true) | (((p @ X0)) != $true)) ) | ~spl20_4),
  inference(avatar_component_clause,[],[f1563])).
thf(f1567,definition,(
  spl20_5 <=> (sF14 = $true)),
  introduced(definition,[new_symbols(definition,[spl20_5])],[avatar_definition])).
thf(f1568,plain,(
  (sF14 = $true) | ~spl20_5),
  inference(avatar_component_clause,[],[f1567])).
thf(f1571,definition,(
  spl20_6 <=> (sF10 = $true)),
  introduced(definition,[new_symbols(definition,[spl20_6])],[avatar_definition])).
thf(f1572,plain,(
  (sF10 = $true) | ~spl20_6),
  inference(avatar_component_clause,[],[f1571])).
thf(f1575,definition,(
  spl20_7 <=> (sF19 = $true)),
  introduced(definition,[new_symbols(definition,[spl20_7])],[avatar_definition])).
thf(f1576,plain,(
  (sF19 = $true) | ~spl20_7),
  inference(avatar_component_clause,[],[f1575])).
thf(f1578,plain,(
  ~spl20_5 | ~spl20_6 | ~spl20_7),
  inference(avatar_split_clause,[],[f741,f1575,f1571,f1567])).
thf(f1587,plain,(
  spl20_7 | spl20_5),
  inference(avatar_split_clause,[],[f743,f1567,f1575])).
thf(f1589,definition,(
  spl20_8 <=> (((p @ sF13)) = $true)),
  introduced(definition,[new_symbols(definition,[spl20_8])],[avatar_definition])).
thf(f1591,plain,(
  (((p @ sF13)) = $true) | ~spl20_8),
  inference(avatar_component_clause,[],[f1589])).
thf(f1593,definition,(
  spl20_9 <=> (sF14 = $false)),
  introduced(definition,[new_symbols(definition,[spl20_9])],[avatar_definition])).
thf(f1595,plain,(
  (sF14 = $false) | ~spl20_9),
  inference(avatar_component_clause,[],[f1593])).
thf(f1596,plain,(
  spl20_8 | spl20_9),
  inference(avatar_split_clause,[],[f1268,f1593,f1589])).
thf(f1598,definition,(
  spl20_10 <=> (((p @ sF13)) = $false)),
  introduced(definition,[new_symbols(definition,[spl20_10])],[avatar_definition])).
thf(f1600,plain,(
  (((p @ sF13)) = $false) | ~spl20_10),
  inference(avatar_component_clause,[],[f1598])).
thf(f1601,plain,(
  spl20_10 | spl20_5),
  inference(avatar_split_clause,[],[f1267,f1567,f1598])).
thf(f1603,definition,(
  spl20_11 <=> ($true = ((p @ sF9)))),
  introduced(definition,[new_symbols(definition,[spl20_11])],[avatar_definition])).
thf(f1604,plain,(
  ($true != ((p @ sF9))) | spl20_11),
  inference(avatar_component_clause,[],[f1603])).
thf(f1605,plain,(
  ($true = ((p @ sF9))) | ~spl20_11),
  inference(avatar_component_clause,[],[f1603])).
thf(f1607,definition,(
  spl20_12 <=> ($false = sF10)),
  introduced(definition,[new_symbols(definition,[spl20_12])],[avatar_definition])).
thf(f1609,plain,(
  ($false = sF10) | ~spl20_12),
  inference(avatar_component_clause,[],[f1607])).
thf(f1610,plain,(
  spl20_11 | spl20_12),
  inference(avatar_split_clause,[],[f1298,f1607,f1603])).
thf(f1612,definition,(
  spl20_13 <=> ($false = ((p @ sF9)))),
  introduced(definition,[new_symbols(definition,[spl20_13])],[avatar_definition])).
thf(f1614,plain,(
  ($false = ((p @ sF9))) | ~spl20_13),
  inference(avatar_component_clause,[],[f1612])).
thf(f1615,plain,(
  spl20_6 | spl20_13),
  inference(avatar_split_clause,[],[f1297,f1612,f1571])).
thf(f1621,definition,(
  spl20_14 <=> ($false = sF19)),
  introduced(definition,[new_symbols(definition,[spl20_14])],[avatar_definition])).
thf(f1623,plain,(
  ($false = sF19) | ~spl20_14),
  inference(avatar_component_clause,[],[f1621])).
thf(f1625,definition,(
  spl20_15 <=> (((p @ sF18)) = $true)),
  introduced(definition,[new_symbols(definition,[spl20_15])],[avatar_definition])).
thf(f1626,plain,(
  (((p @ sF18)) != $true) | spl20_15),
  inference(avatar_component_clause,[],[f1625])).
thf(f1627,plain,(
  (((p @ sF18)) = $true) | ~spl20_15),
  inference(avatar_component_clause,[],[f1625])).
thf(f1628,plain,(
  spl20_14 | spl20_15),
  inference(avatar_split_clause,[],[f1417,f1625,f1621])).
thf(f1630,definition,(
  spl20_16 <=> ($false = ((p @ sF18)))),
  introduced(definition,[new_symbols(definition,[spl20_16])],[avatar_definition])).
thf(f1632,plain,(
  ($false = ((p @ sF18))) | ~spl20_16),
  inference(avatar_component_clause,[],[f1630])).
thf(f1633,plain,(
  spl20_7 | spl20_16),
  inference(avatar_split_clause,[],[f1416,f1630,f1575])).
thf(f1635,plain,(
  spl20_6 | spl20_7),
  inference(avatar_split_clause,[],[f742,f1575,f1571])).
thf(f1638,plain,(
  ($false = $true) | (~spl20_7 | ~spl20_14)),
  inference(backward_demodulation,[],[f1576,f1623])).
thf(f1639,plain,(
  $false | (~spl20_7 | ~spl20_14)),
  inference(trivial_inequality_removal,[],[f1638])).
thf(f1640,plain,(
  ~spl20_7 | ~spl20_14),
  inference(avatar_contradiction_clause,[],[f1639])).
thf(f1655,plain,(
  ($true != $true) | (((p @ c_2Ebool_2EF)) = $false)),
  inference(constrained_superposition,[],[f292,f714])).
thf(f1656,plain,(
  (((p @ c_2Ebool_2EF)) = $false)),
  inference(trivial_inequality_removal,[],[f1655])).
thf(f1657,plain,(
  (((surj__ty_2Eextreal_2Eextreal @ sF6)) = sK5)),
  inference(constrained_superposition,[],[f450,f719])).
thf(f1659,plain,(
  (sK3 = ((surj__ty_2Eextreal_2Eextreal @ sF11)))),
  inference(constrained_superposition,[],[f450,f727])).
thf(f1660,plain,(
  ($false = $true) | (~spl20_8 | ~spl20_10)),
  inference(backward_demodulation,[],[f1591,f1600])).
thf(f1662,plain,(
  $false | (~spl20_8 | ~spl20_10)),
  inference(trivial_inequality_removal,[],[f1660])).
thf(f1663,plain,(
  ~spl20_8 | ~spl20_10),
  inference(avatar_contradiction_clause,[],[f1662])).
thf(f1665,plain,(
  ($false = $true) | (~spl20_5 | ~spl20_9)),
  inference(forward_demodulation,[],[f1568,f1595])).
thf(f1666,plain,(
  $false | (~spl20_5 | ~spl20_9)),
  inference(trivial_inequality_removal,[],[f1665])).
thf(f1667,plain,(
  ~spl20_5 | ~spl20_9),
  inference(avatar_contradiction_clause,[],[f1666])).
thf(f1685,plain,(
  ($false = $true) | (~spl20_6 | ~spl20_12)),
  inference(backward_demodulation,[],[f1572,f1609])).
thf(f1687,plain,(
  $false | (~spl20_6 | ~spl20_12)),
  inference(trivial_inequality_removal,[],[f1685])).
thf(f1688,plain,(
  ~spl20_6 | ~spl20_12),
  inference(avatar_contradiction_clause,[],[f1687])).
thf(f1692,plain,(
  ($false = $true) | (~spl20_15 | ~spl20_16)),
  inference(backward_demodulation,[],[f1627,f1632])).
thf(f1694,plain,(
  $false | (~spl20_15 | ~spl20_16)),
  inference(trivial_inequality_removal,[],[f1692])).
thf(f1695,plain,(
  ~spl20_15 | ~spl20_16),
  inference(avatar_contradiction_clause,[],[f1694])).
thf(f1698,plain,(
  (((mem @ sF6 @ ty_2Eextreal_2Eextreal)) = $true)),
  inference(constrained_superposition,[],[f460,f719])).
thf(f1699,plain,(
  (((mem @ sF8 @ ty_2Eextreal_2Eextreal)) = $true)),
  inference(constrained_superposition,[],[f460,f723])).
thf(f1700,plain,(
  (((mem @ sF11 @ ty_2Eextreal_2Eextreal)) = $true)),
  inference(constrained_superposition,[],[f460,f727])).
thf(f1704,plain,(
  ( ! [X0 : $i] : ((((mem @ X0 @ bool)) = $false) | ($true != $true) | (((inj__o @ (p @ X0))) = X0)) )),
  inference(constrained_superposition,[],[f359,f714])).
thf(f1705,plain,(
  ($true != $true) | (c_2Ebool_2EF = ((inj__o @ (p @ c_2Ebool_2EF))))),
  inference(constrained_superposition,[],[f359,f433])).
thf(f1706,plain,(
  ($true != $true) | (c_2Ebool_2ET = ((inj__o @ (p @ c_2Ebool_2ET))))),
  inference(constrained_superposition,[],[f359,f455])).
thf(f1707,plain,(
  ( ! [X0 : $o] : ((((inj__o @ X0)) = ((inj__o @ (p @ (inj__o @ X0))))) | ($true != $true)) )),
  inference(constrained_superposition,[],[f359,f374])).
thf(f1708,plain,(
  (c_2Ebool_2EF = ((inj__o @ (p @ c_2Ebool_2EF))))),
  inference(trivial_inequality_removal,[],[f1705])).
thf(f1709,plain,(
  (c_2Ebool_2ET = ((inj__o @ (p @ c_2Ebool_2ET))))),
  inference(trivial_inequality_removal,[],[f1706])).
thf(f1710,plain,(
  ( ! [X0 : $o] : ((((inj__o @ X0)) = ((inj__o @ (p @ (inj__o @ X0)))))) )),
  inference(trivial_inequality_removal,[],[f1707])).
thf(f1711,plain,(
  ( ! [X0 : $i] : ((((inj__o @ (p @ X0))) = X0) | (((mem @ X0 @ bool)) = $false)) )),
  inference(trivial_inequality_removal,[],[f1704])).
thf(f1712,plain,(
  (c_2Ebool_2EF = ((inj__o @ $false)))),
  inference(forward_demodulation,[],[f1708,f1656])).
thf(f1713,plain,(
  (c_2Ebool_2ET = ((inj__o @ $true)))),
  inference(forward_demodulation,[],[f1709,f301])).
thf(f1752,plain,(
  ( ! [X0 : $o] : ((((inj__o @ X0)) = ((inj__o @ $true))) | (((p @ (inj__o @ X0))) = $false)) )),
  inference(constrained_superposition,[],[f1710,f714])).
thf(f1761,plain,(
  ( ! [X0 : $o] : ((((p @ (inj__o @ X0))) = $false) | (((inj__o @ X0)) = c_2Ebool_2ET)) )),
  inference(forward_demodulation,[],[f1752,f1713])).
thf(f1781,plain,(
  ( ! [X0 : $o] : ((((inj__o @ X0)) = c_2Ebool_2ET) | (((inj__o @ X0)) = ((inj__o @ $false)))) )),
  inference(constrained_superposition,[],[f1710,f1761])).
thf(f1786,plain,(
  ( ! [X0 : $o] : ((((inj__o @ X0)) = c_2Ebool_2EF) | (((inj__o @ X0)) = c_2Ebool_2ET)) )),
  inference(forward_demodulation,[],[f1781,f1712])).
thf(f1790,plain,(
  ( ! [X0 : tp__ty_2Eextreal_2Eextreal] : ((((ap @ (ap @ c_2Eextreal_2Eextreal__max @ sF6) @ (inj__ty_2Eextreal_2Eextreal @ X0))) = ((inj__ty_2Eextreal_2Eextreal @ (fo__c_2Eextreal_2Eextreal__max @ sK5 @ X0))))) )),
  inference(constrained_superposition,[],[f456,f719])).
thf(f1793,plain,(
  ( ! [X0 : tp__ty_2Eextreal_2Eextreal] : ((((inj__ty_2Eextreal_2Eextreal @ (fo__c_2Eextreal_2Eextreal__max @ sK5 @ X0))) = ((ap @ sF15 @ (inj__ty_2Eextreal_2Eextreal @ X0))))) )),
  inference(forward_demodulation,[],[f1790,f733])).
thf(f1805,definition,(
  spl20_17 <=> (c_2Ebool_2ET = c_2Ebool_2EF)),
  introduced(definition,[new_symbols(definition,[spl20_17])],[avatar_definition])).
thf(f1807,plain,(
  (c_2Ebool_2ET != c_2Ebool_2EF) | spl20_17),
  inference(avatar_component_clause,[],[f1805])).
thf(f1814,plain,(
  ( ! [X2 : del,X3 : $i,X0 : $i,X1 : del] : (($true != $true) | (((mem @ (ap @ X0 @ X3) @ X2)) = $true) | ($false = ((mem @ X0 @ (arr @ X1 @ X2)))) | ($true != ((mem @ X3 @ X1)))) )),
  inference(constrained_superposition,[],[f451,f714])).
thf(f1822,plain,(
  ( ! [X0 : $i] : (($true != $true) | (((mem @ X0 @ ty_2Eextreal_2Eextreal)) != $true) | (((mem @ (ap @ c_2Eextreal_2Eextreal__le @ X0) @ (arr @ ty_2Eextreal_2Eextreal @ bool))) = $true)) )),
  inference(constrained_superposition,[],[f451,f368])).
thf(f1826,plain,(
  ( ! [X2 : del,X3 : $i,X0 : $i,X1 : del] : (($true != ((mem @ X3 @ X1))) | (((mem @ (ap @ X0 @ X3) @ X2)) = $true) | ($false = ((mem @ X0 @ (arr @ X1 @ X2))))) )),
  inference(trivial_inequality_removal,[],[f1814])).
thf(f1828,plain,(
  ( ! [X0 : $i] : ((((mem @ (ap @ c_2Eextreal_2Eextreal__le @ X0) @ (arr @ ty_2Eextreal_2Eextreal @ bool))) = $true) | (((mem @ X0 @ ty_2Eextreal_2Eextreal)) != $true)) )),
  inference(trivial_inequality_removal,[],[f1822])).
thf(f1861,plain,(
  ($false = ((mem @ sF9 @ bool))) | (sF9 = ((inj__o @ $false))) | ~spl20_13),
  inference(constrained_superposition,[],[f1711,f1614])).
thf(f1862,plain,(
  (((inj__o @ $true)) = sF13) | ($false = ((mem @ sF13 @ bool))) | ~spl20_8),
  inference(constrained_superposition,[],[f1711,f1591])).
thf(f1864,plain,(
  ( ! [X0 : $i] : ((((inj__o @ (p @ X0))) = c_2Ebool_2ET) | (((mem @ X0 @ bool)) = $false) | (c_2Ebool_2EF = X0)) )),
  inference(constrained_superposition,[],[f1711,f1786])).
thf(f1875,plain,(
  ( ! [X0 : $i] : ((((mem @ X0 @ bool)) = $false) | (c_2Ebool_2EF = X0) | (c_2Ebool_2ET = X0)) )),
  inference(constrained_superposition,[],[f1786,f1711])).
thf(f1883,plain,(
  (c_2Ebool_2EF = sF9) | ($false = ((mem @ sF9 @ bool))) | ~spl20_13),
  inference(forward_demodulation,[],[f1861,f1712])).
thf(f1890,plain,(
  ($false = ((mem @ sF13 @ bool))) | (c_2Ebool_2ET = sF13) | ~spl20_8),
  inference(forward_demodulation,[],[f1862,f1713])).
thf(f1894,definition,(
  spl20_19 <=> ($false = ((mem @ sF9 @ bool)))),
  introduced(definition,[new_symbols(definition,[spl20_19])],[avatar_definition])).
thf(f1896,plain,(
  ($false = ((mem @ sF9 @ bool))) | ~spl20_19),
  inference(avatar_component_clause,[],[f1894])).
thf(f1898,definition,(
  spl20_20 <=> (c_2Ebool_2EF = sF9)),
  introduced(definition,[new_symbols(definition,[spl20_20])],[avatar_definition])).
thf(f1900,plain,(
  (c_2Ebool_2EF = sF9) | ~spl20_20),
  inference(avatar_component_clause,[],[f1898])).
thf(f1901,plain,(
  spl20_19 | spl20_20 | ~spl20_13),
  inference(avatar_split_clause,[],[f1883,f1612,f1898,f1894])).
thf(f1903,definition,(
  spl20_21 <=> (c_2Ebool_2ET = sF18)),
  introduced(definition,[new_symbols(definition,[spl20_21])],[avatar_definition])).
thf(f1905,plain,(
  (c_2Ebool_2ET = sF18) | ~spl20_21),
  inference(avatar_component_clause,[],[f1903])).
thf(f1912,definition,(
  spl20_23 <=> ($false = ((mem @ sF13 @ bool)))),
  introduced(definition,[new_symbols(definition,[spl20_23])],[avatar_definition])).
thf(f1914,plain,(
  ($false = ((mem @ sF13 @ bool))) | ~spl20_23),
  inference(avatar_component_clause,[],[f1912])).
thf(f1916,definition,(
  spl20_24 <=> (c_2Ebool_2ET = sF13)),
  introduced(definition,[new_symbols(definition,[spl20_24])],[avatar_definition])).
thf(f1918,plain,(
  (c_2Ebool_2ET = sF13) | ~spl20_24),
  inference(avatar_component_clause,[],[f1916])).
thf(f1919,plain,(
  spl20_23 | spl20_24 | ~spl20_8),
  inference(avatar_split_clause,[],[f1890,f1589,f1916,f1912])).
thf(f1955,definition,(
  spl20_26 <=> (c_2Ebool_2EF = sF18)),
  introduced(definition,[new_symbols(definition,[spl20_26])],[avatar_definition])).
thf(f1956,plain,(
  (c_2Ebool_2EF != sF18) | spl20_26),
  inference(avatar_component_clause,[],[f1955])).
thf(f1957,plain,(
  (c_2Ebool_2EF = sF18) | ~spl20_26),
  inference(avatar_component_clause,[],[f1955])).
thf(f1971,plain,(
  ($true = ((p @ (ap @ (c_2Ebool_2E_21 @ bool) @ c_2Ebool_2E_7E)))) | (((mem @ (sK1 @ bool @ c_2Ebool_2E_7E) @ bool)) = $true) | ($true != $true)),
  inference(constrained_superposition,[],[f436,f525])).
thf(f1975,plain,(
  (((mem @ (sK1 @ bool @ c_2Ebool_2E_7E) @ bool)) = $true) | ($true = ((p @ (ap @ (c_2Ebool_2E_21 @ bool) @ c_2Ebool_2E_7E))))),
  inference(trivial_inequality_removal,[],[f1971])).
thf(f1977,definition,(
  spl20_27 <=> (((mem @ (sK1 @ bool @ c_2Ebool_2E_7E) @ bool)) = $true)),
  introduced(definition,[new_symbols(definition,[spl20_27])],[avatar_definition])).
thf(f1979,plain,(
  (((mem @ (sK1 @ bool @ c_2Ebool_2E_7E) @ bool)) = $true) | ~spl20_27),
  inference(avatar_component_clause,[],[f1977])).
thf(f1981,definition,(
  spl20_28 <=> ($true = ((p @ (ap @ (c_2Ebool_2E_21 @ bool) @ c_2Ebool_2E_7E))))),
  introduced(definition,[new_symbols(definition,[spl20_28])],[avatar_definition])).
thf(f1982,plain,(
  ($true != ((p @ (ap @ (c_2Ebool_2E_21 @ bool) @ c_2Ebool_2E_7E)))) | spl20_28),
  inference(avatar_component_clause,[],[f1981])).
thf(f1984,plain,(
  spl20_27 | spl20_28),
  inference(avatar_split_clause,[],[f1975,f1981,f1977])).
thf(f1993,plain,(
  ($false = ((p @ sF9))) | ($true != $true) | spl20_11),
  inference(constrained_superposition,[],[f1604,f714])).
thf(f1994,plain,(
  ($false = ((p @ sF9))) | spl20_11),
  inference(trivial_inequality_removal,[],[f1993])).
thf(f1995,plain,(
  spl20_13 | spl20_11),
  inference(avatar_split_clause,[],[f1994,f1603,f1612])).
thf(f1997,plain,(
  ( ! [X0 : tp__ty_2Eextreal_2Eextreal] : ((((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ sF8) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) = $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ sF8))) = $true)) )),
  inference(constrained_superposition,[],[f454,f723])).
thf(f2026,plain,(
  (sF9 = ((inj__o @ $false))) | ($false = ((mem @ sF9 @ bool))) | ~spl20_13),
  inference(constrained_superposition,[],[f1711,f1614])).
thf(f2028,plain,(
  ($false = ((mem @ sF9 @ bool))) | (c_2Ebool_2EF = sF9) | ~spl20_13),
  inference(forward_demodulation,[],[f2026,f1712])).
thf(f2029,plain,(
  spl20_20 | spl20_19 | ~spl20_13),
  inference(avatar_split_clause,[],[f2028,f1612,f1894,f1898])).
thf(f2056,plain,(
  ( ! [X0 : $i] : (($true != ((p @ (ap @ (c_2Ebool_2E_21 @ bool) @ c_2Ebool_2E_7E)))) | (((mem @ X0 @ bool)) != $true) | ($true != $true) | (((p @ (ap @ c_2Ebool_2E_7E @ X0))) = $true)) )),
  inference(constrained_superposition,[],[f434,f525])).
thf(f2060,plain,(
  ( ! [X0 : $i] : ((((mem @ X0 @ bool)) != $true) | (((p @ (ap @ c_2Ebool_2E_7E @ X0))) = $true) | ($true != ((p @ (ap @ (c_2Ebool_2E_21 @ bool) @ c_2Ebool_2E_7E))))) )),
  inference(trivial_inequality_removal,[],[f2056])).
thf(f2063,definition,(
  spl20_29 <=> ! [X0 : $i] : ((((mem @ X0 @ bool)) != $true) | (((p @ (ap @ c_2Ebool_2E_7E @ X0))) = $true))),
  introduced(definition,[new_symbols(definition,[spl20_29])],[avatar_definition])).
thf(f2064,plain,(
  ( ! [X0 : $i] : ((((p @ (ap @ c_2Ebool_2E_7E @ X0))) = $true) | (((mem @ X0 @ bool)) != $true)) ) | ~spl20_29),
  inference(avatar_component_clause,[],[f2063])).
thf(f2065,plain,(
  ~spl20_28 | spl20_29),
  inference(avatar_split_clause,[],[f2060,f2063,f1981])).
thf(f2109,plain,(
  ( ! [X0 : tp__ty_2Eextreal_2Eextreal,X1 : tp__ty_2Eextreal_2Eextreal] : ((((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) != $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ sF11))) != $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ sF11))) = $true)) )),
  inference(constrained_superposition,[],[f532,f727])).
thf(f2112,plain,(
  ( ! [X0 : tp__ty_2Eextreal_2Eextreal,X1 : tp__ty_2Eextreal_2Eextreal] : ((((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) = $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ sF11) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) != $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ sF11))) != $true)) )),
  inference(constrained_superposition,[],[f532,f727])).
thf(f2120,plain,(
  ( ! [X0 : tp__ty_2Eextreal_2Eextreal,X1 : tp__ty_2Eextreal_2Eextreal] : ((((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ sF11))) != $true) | (((p @ (ap @ sF12 @ (inj__ty_2Eextreal_2Eextreal @ X0)))) != $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) = $true)) )),
  inference(forward_demodulation,[],[f2112,f728])).
thf(f2145,plain,(
  ( ! [X0 : tp__ty_2Eextreal_2Eextreal,X1 : tp__ty_2Eextreal_2Eextreal] : ((((surj__ty_2Eextreal_2Eextreal @ (inj__ty_2Eextreal_2Eextreal @ (fo__c_2Eextreal_2Eextreal__max @ X1 @ X0)))) = ((surj__ty_2Eextreal_2Eextreal @ (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ ty_2Eextreal_2Eextreal) @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X0))) @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ (inj__ty_2Eextreal_2Eextreal @ X1)))))) )),
  inference(forward_demodulation,[],[f704,f456])).
thf(f2146,plain,(
  ( ! [X0 : tp__ty_2Eextreal_2Eextreal,X1 : tp__ty_2Eextreal_2Eextreal] : ((((fo__c_2Eextreal_2Eextreal__max @ X1 @ X0)) = ((surj__ty_2Eextreal_2Eextreal @ (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ ty_2Eextreal_2Eextreal) @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X1)) @ (inj__ty_2Eextreal_2Eextreal @ X0))) @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ (inj__ty_2Eextreal_2Eextreal @ X1)))))) )),
  inference(forward_demodulation,[],[f2145,f450])).
thf(f2157,plain,(
  ( ! [X0 : tp__ty_2Eextreal_2Eextreal] : ((((fo__c_2Eextreal_2Eextreal__max @ sK5 @ X0)) = ((surj__ty_2Eextreal_2Eextreal @ (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ ty_2Eextreal_2Eextreal) @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ sF6) @ (inj__ty_2Eextreal_2Eextreal @ X0))) @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ sF6))))) )),
  inference(constrained_superposition,[],[f2146,f719])).
thf(f2161,plain,(
  ( ! [X0 : tp__ty_2Eextreal_2Eextreal] : ((((fo__c_2Eextreal_2Eextreal__max @ sK5 @ X0)) = ((surj__ty_2Eextreal_2Eextreal @ (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ ty_2Eextreal_2Eextreal) @ (ap @ sF7 @ (inj__ty_2Eextreal_2Eextreal @ X0))) @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ sF6))))) )),
  inference(forward_demodulation,[],[f2157,f721])).
thf(f2172,definition,(
  spl20_33 <=> (c_2Ebool_2EF = ((sK1 @ bool @ c_2Ebool_2E_7E)))),
  introduced(definition,[new_symbols(definition,[spl20_33])],[avatar_definition])).
thf(f2173,plain,(
  (c_2Ebool_2EF != ((sK1 @ bool @ c_2Ebool_2E_7E))) | spl20_33),
  inference(avatar_component_clause,[],[f2172])).
thf(f2174,plain,(
  (c_2Ebool_2EF = ((sK1 @ bool @ c_2Ebool_2E_7E))) | ~spl20_33),
  inference(avatar_component_clause,[],[f2172])).
thf(f2176,definition,(
  spl20_34 <=> (c_2Ebool_2ET = ((sK1 @ bool @ c_2Ebool_2E_7E)))),
  introduced(definition,[new_symbols(definition,[spl20_34])],[avatar_definition])).
thf(f2178,plain,(
  (c_2Ebool_2ET = ((sK1 @ bool @ c_2Ebool_2E_7E))) | ~spl20_34),
  inference(avatar_component_clause,[],[f2176])).
thf(f2225,plain,(
  ( ! [X0 : $i] : ((((mem @ X0 @ bool)) != $true) | ($true != $true) | (((p @ X0)) != $true) | (((mem @ X0 @ bool)) != $true)) ) | ~spl20_29),
  inference(constrained_superposition,[],[f296,f2064])).
thf(f2227,plain,(
  ( ! [X0 : $i] : ((((mem @ X0 @ bool)) != $true) | (((p @ X0)) != $true) | ($true != $true)) ) | ~spl20_29),
  inference(duplicate_literal_removal,[],[f2225])).
thf(f2228,plain,(
  ( ! [X0 : $i] : ((((mem @ X0 @ bool)) != $true) | (((p @ X0)) != $true)) ) | ~spl20_29),
  inference(trivial_inequality_removal,[],[f2227])).
thf(f2231,plain,(
  spl20_4 | ~spl20_29),
  inference(avatar_split_clause,[],[f2228,f2063,f1563])).
thf(f2237,plain,(
  (((p @ c_2Ebool_2ET)) != $true) | ($true != $true) | ~spl20_4),
  inference(constrained_superposition,[],[f1564,f455])).
thf(f2243,plain,(
  (((p @ c_2Ebool_2ET)) != $true) | ~spl20_4),
  inference(trivial_inequality_removal,[],[f2237])).
thf(f2245,plain,(
  $false | ~spl20_4),
  inference(forward_subsumption_resolution,[],[f2243,f301])).
thf(f2246,plain,(
  ~spl20_4),
  inference(avatar_contradiction_clause,[],[f2245])).
thf(f2250,plain,(
  ($true = ((p @ (ap @ (c_2Ebool_2E_21 @ bool) @ c_2Ebool_2E_7E)))) | (((p @ (ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF))) != $true) | (((mem @ c_2Ebool_2E_7E @ (arr @ bool @ bool))) != $true) | ~spl20_33),
  inference(constrained_superposition,[],[f435,f2174])).
thf(f2251,plain,(
  (((mem @ c_2Ebool_2E_7E @ (arr @ bool @ bool))) != $true) | (((p @ (ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF))) != $true) | (spl20_28 | ~spl20_33)),
  inference(forward_subsumption_resolution,[],[f2250,f1982])).
thf(f2252,plain,(
  (((p @ (ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF))) != $true) | (spl20_28 | ~spl20_33)),
  inference(forward_subsumption_resolution,[],[f2251,f525])).
thf(f2255,plain,(
  (((p @ c_2Ebool_2EF)) = $true) | ($true != $true) | (((mem @ c_2Ebool_2EF @ bool)) != $true) | (spl20_28 | ~spl20_33)),
  inference(constrained_superposition,[],[f2252,f295])).
thf(f2256,plain,(
  (((p @ c_2Ebool_2EF)) = $true) | (((mem @ c_2Ebool_2EF @ bool)) != $true) | (spl20_28 | ~spl20_33)),
  inference(trivial_inequality_removal,[],[f2255])).
thf(f2258,plain,(
  (((p @ c_2Ebool_2EF)) = $true) | (spl20_28 | ~spl20_33)),
  inference(forward_subsumption_resolution,[],[f2256,f433])).
thf(f2259,plain,(
  ($false = $true) | (spl20_28 | ~spl20_33)),
  inference(forward_demodulation,[],[f2258,f1656])).
thf(f2260,plain,(
  $false | (spl20_28 | ~spl20_33)),
  inference(trivial_inequality_removal,[],[f2259])).
thf(f2261,plain,(
  spl20_28 | ~spl20_33),
  inference(avatar_contradiction_clause,[],[f2260])).
thf(f2265,plain,(
  (c_2Ebool_2ET = ((sK1 @ bool @ c_2Ebool_2E_7E))) | ($false = $true) | (c_2Ebool_2EF = ((sK1 @ bool @ c_2Ebool_2E_7E))) | ~spl20_27),
  inference(constrained_superposition,[],[f1875,f1979])).
thf(f2269,plain,(
  (c_2Ebool_2EF = ((sK1 @ bool @ c_2Ebool_2E_7E))) | (c_2Ebool_2ET = ((sK1 @ bool @ c_2Ebool_2E_7E))) | ~spl20_27),
  inference(trivial_inequality_removal,[],[f2265])).
thf(f2278,plain,(
  spl20_33 | spl20_34 | ~spl20_27),
  inference(avatar_split_clause,[],[f2269,f1977,f2176,f2172])).
thf(f2280,plain,(
  ( ! [X0 : tp__ty_2Eextreal_2Eextreal] : ((((fo__c_2Eextreal_2Eextreal__max @ sK5 @ X0)) = ((surj__ty_2Eextreal_2Eextreal @ (ap @ sF15 @ (inj__ty_2Eextreal_2Eextreal @ X0)))))) )),
  inference(constrained_superposition,[],[f450,f1793])).
thf(f2287,plain,(
  ( ! [X0 : tp__ty_2Eextreal_2Eextreal] : ((((mem @ (ap @ sF15 @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ ty_2Eextreal_2Eextreal)) = $true)) )),
  inference(constrained_superposition,[],[f460,f1793])).
thf(f2292,plain,(
  (c_2Ebool_2ET != c_2Ebool_2EF) | (spl20_33 | ~spl20_34)),
  inference(backward_demodulation,[],[f2173,f2178])).
thf(f2450,plain,(
  (((mem @ sF7 @ (arr @ ty_2Eextreal_2Eextreal @ bool))) = $true) | (((mem @ sF6 @ ty_2Eextreal_2Eextreal)) != $true)),
  inference(constrained_superposition,[],[f1828,f721])).
thf(f2451,plain,(
  ($true = ((mem @ sF12 @ (arr @ ty_2Eextreal_2Eextreal @ bool)))) | (((mem @ sF11 @ ty_2Eextreal_2Eextreal)) != $true)),
  inference(constrained_superposition,[],[f1828,f728])).
thf(f2468,definition,(
  spl20_43 <=> (((mem @ sF16 @ ty_2Eextreal_2Eextreal)) = $true)),
  introduced(definition,[new_symbols(definition,[spl20_43])],[avatar_definition])).
thf(f2469,plain,(
  (((mem @ sF16 @ ty_2Eextreal_2Eextreal)) = $true) | ~spl20_43),
  inference(avatar_component_clause,[],[f2468])).
thf(f2472,plain,(
  (((mem @ sF7 @ (arr @ ty_2Eextreal_2Eextreal @ bool))) = $true)),
  inference(forward_subsumption_resolution,[],[f2450,f1698])).
thf(f2473,plain,(
  ($true = ((mem @ sF12 @ (arr @ ty_2Eextreal_2Eextreal @ bool))))),
  inference(forward_subsumption_resolution,[],[f2451,f1700])).
thf(f2499,plain,(
  ( ! [X0 : $i] : ((((mem @ X0 @ ty_2Eextreal_2Eextreal)) != $true) | (((mem @ (ap @ sF7 @ X0) @ bool)) = $true) | ($true != $true)) )),
  inference(constrained_superposition,[],[f451,f2472])).
thf(f2505,plain,(
  ( ! [X0 : $i] : ((((mem @ (ap @ sF7 @ X0) @ bool)) = $true) | (((mem @ X0 @ ty_2Eextreal_2Eextreal)) != $true)) )),
  inference(trivial_inequality_removal,[],[f2499])).
thf(f2590,definition,(
  spl20_50 <=> (((p @ (ap @ sF7 @ sF11))) = $true)),
  introduced(definition,[new_symbols(definition,[spl20_50])],[avatar_definition])).
thf(f2591,plain,(
  (((p @ (ap @ sF7 @ sF11))) != $true) | spl20_50),
  inference(avatar_component_clause,[],[f2590])).
thf(f2592,plain,(
  (((p @ (ap @ sF7 @ sF11))) = $true) | ~spl20_50),
  inference(avatar_component_clause,[],[f2590])).
thf(f2601,definition,(
  spl20_52 <=> (c_2Ebool_2ET = ((ap @ sF7 @ sF11)))),
  introduced(definition,[new_symbols(definition,[spl20_52])],[avatar_definition])).
thf(f2603,plain,(
  (c_2Ebool_2ET = ((ap @ sF7 @ sF11))) | ~spl20_52),
  inference(avatar_component_clause,[],[f2601])).
thf(f2605,definition,(
  spl20_53 <=> ($false = ((mem @ (ap @ sF7 @ sF11) @ bool)))),
  introduced(definition,[new_symbols(definition,[spl20_53])],[avatar_definition])).
thf(f2607,plain,(
  ($false = ((mem @ (ap @ sF7 @ sF11) @ bool))) | ~spl20_53),
  inference(avatar_component_clause,[],[f2605])).
thf(f2711,plain,(
  ( ! [X0 : $i,X1 : del] : ((((mem @ X0 @ (arr @ ty_2Eextreal_2Eextreal @ X1))) = $false) | (((mem @ (ap @ X0 @ sF8) @ X1)) = $true) | ($true != $true)) )),
  inference(constrained_superposition,[],[f1826,f1699])).
thf(f2736,plain,(
  ( ! [X0 : $i,X1 : del] : ((((mem @ X0 @ (arr @ ty_2Eextreal_2Eextreal @ X1))) = $false) | (((mem @ (ap @ X0 @ sF8) @ X1)) = $true)) )),
  inference(trivial_inequality_removal,[],[f2711])).
thf(f2799,plain,(
  (((mem @ (ap @ sF15 @ sF11) @ ty_2Eextreal_2Eextreal)) = $true)),
  inference(constrained_superposition,[],[f2287,f727])).
thf(f2806,plain,(
  (((mem @ sF16 @ ty_2Eextreal_2Eextreal)) = $true)),
  inference(forward_demodulation,[],[f2799,f735])).
thf(f2810,plain,(
  spl20_43),
  inference(avatar_split_clause,[],[f2806,f2468])).
thf(f2818,plain,(
  (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ sF8) @ sF11))) = $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ sF11) @ sF8))) = $true)),
  inference(constrained_superposition,[],[f1997,f727])).
thf(f2828,plain,(
  (((p @ (ap @ sF12 @ sF8))) = $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ sF8) @ sF11))) = $true)),
  inference(forward_demodulation,[],[f2818,f728])).
thf(f2833,plain,(
  (((p @ sF13)) = $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ sF8) @ sF11))) = $true)),
  inference(forward_demodulation,[],[f2828,f730])).
thf(f2840,plain,(
  (sF16 = ((inj__ty_2Eextreal_2Eextreal @ (surj__ty_2Eextreal_2Eextreal @ sF16)))) | ($true != $true) | ~spl20_43),
  inference(constrained_superposition,[],[f476,f2469])).
thf(f2842,plain,(
  (sF16 = ((inj__ty_2Eextreal_2Eextreal @ (surj__ty_2Eextreal_2Eextreal @ sF16)))) | ~spl20_43),
  inference(trivial_inequality_removal,[],[f2840])).
thf(f3601,plain,(
  (((p @ c_2Ebool_2ET)) != $true) | (spl20_15 | ~spl20_21)),
  inference(forward_demodulation,[],[f1626,f1905])).
thf(f3605,plain,(
  $false | (spl20_15 | ~spl20_21)),
  inference(forward_subsumption_resolution,[],[f3601,f301])).
thf(f3606,plain,(
  spl20_15 | ~spl20_21),
  inference(avatar_contradiction_clause,[],[f3605])).
thf(f3718,plain,(
  (((surj__ty_2Eextreal_2Eextreal @ (ap @ sF15 @ sF11))) = ((fo__c_2Eextreal_2Eextreal__max @ sK5 @ sK3)))),
  inference(constrained_superposition,[],[f2280,f727])).
thf(f3722,plain,(
  (((surj__ty_2Eextreal_2Eextreal @ sF16)) = ((fo__c_2Eextreal_2Eextreal__max @ sK5 @ sK3)))),
  inference(forward_demodulation,[],[f3718,f735])).
thf(f3794,plain,(
  (((surj__ty_2Eextreal_2Eextreal @ (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ ty_2Eextreal_2Eextreal) @ (ap @ sF7 @ sF11)) @ sF11) @ sF6))) = ((fo__c_2Eextreal_2Eextreal__max @ sK5 @ sK3)))),
  inference(constrained_superposition,[],[f2161,f727])).
thf(f3800,plain,(
  (((surj__ty_2Eextreal_2Eextreal @ sF16)) = ((surj__ty_2Eextreal_2Eextreal @ (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ ty_2Eextreal_2Eextreal) @ (ap @ sF7 @ sF11)) @ sF11) @ sF6))))),
  inference(forward_demodulation,[],[f3794,f3722])).
thf(f4382,plain,(
  ( ! [X0 : tp__ty_2Eextreal_2Eextreal] : ((((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ sF6) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) = $true) | (((p @ (ap @ sF12 @ (inj__ty_2Eextreal_2Eextreal @ X0)))) != $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ sF6) @ sF11))) != $true)) )),
  inference(constrained_superposition,[],[f2120,f719])).
thf(f4388,plain,(
  ( ! [X0 : tp__ty_2Eextreal_2Eextreal] : ((((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ sF6) @ sF11))) != $true) | (((p @ (ap @ sF7 @ (inj__ty_2Eextreal_2Eextreal @ X0)))) = $true) | (((p @ (ap @ sF12 @ (inj__ty_2Eextreal_2Eextreal @ X0)))) != $true)) )),
  inference(forward_demodulation,[],[f4382,f721])).
thf(f4391,definition,(
  spl20_123 <=> (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ sF8) @ sF11))) = $true)),
  introduced(definition,[new_symbols(definition,[spl20_123])],[avatar_definition])).
thf(f4392,plain,(
  (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ sF8) @ sF11))) = $true) | ~spl20_123),
  inference(avatar_component_clause,[],[f4391])).
thf(f4399,plain,(
  ( ! [X0 : tp__ty_2Eextreal_2Eextreal] : ((((p @ (ap @ sF7 @ (inj__ty_2Eextreal_2Eextreal @ X0)))) = $true) | (((p @ (ap @ sF7 @ sF11))) != $true) | (((p @ (ap @ sF12 @ (inj__ty_2Eextreal_2Eextreal @ X0)))) != $true)) )),
  inference(forward_demodulation,[],[f4388,f721])).
thf(f4538,plain,(
  ( ! [X0 : tp__ty_2Eextreal_2Eextreal] : ((((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ sF6) @ (inj__ty_2Eextreal_2Eextreal @ X0)))) != $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ sF6) @ sF11))) = $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ sF11))) != $true)) )),
  inference(constrained_superposition,[],[f2109,f719])).
thf(f4551,plain,(
  ( ! [X0 : tp__ty_2Eextreal_2Eextreal] : ((((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ sF11))) != $true) | (((p @ (ap @ sF7 @ (inj__ty_2Eextreal_2Eextreal @ X0)))) != $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ sF6) @ sF11))) = $true)) )),
  inference(forward_demodulation,[],[f4538,f721])).
thf(f4556,plain,(
  ( ! [X0 : tp__ty_2Eextreal_2Eextreal] : ((((p @ (ap @ sF7 @ sF11))) = $true) | (((p @ (ap @ sF7 @ (inj__ty_2Eextreal_2Eextreal @ X0)))) != $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ sF11))) != $true)) )),
  inference(forward_demodulation,[],[f4551,f721])).
thf(f5896,plain,(
  (((mem @ sF8 @ ty_2Eextreal_2Eextreal)) != $true) | (((mem @ sF9 @ bool)) = $true)),
  inference(constrained_superposition,[],[f2505,f724])).
thf(f5930,plain,(
  (((mem @ sF9 @ bool)) = $true)),
  inference(forward_subsumption_resolution,[],[f5896,f1699])).
thf(f5931,plain,(
  ($false = $true) | ~spl20_19),
  inference(forward_demodulation,[],[f5930,f1896])).
thf(f5932,plain,(
  $false | ~spl20_19),
  inference(trivial_inequality_removal,[],[f5931])).
thf(f5933,plain,(
  ~spl20_19),
  inference(avatar_contradiction_clause,[],[f5932])).
thf(f6018,definition,(
  spl20_220 <=> ! [X0 : tp__ty_2Eextreal_2Eextreal] : ((((p @ (ap @ sF7 @ (inj__ty_2Eextreal_2Eextreal @ X0)))) != $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ sF11))) != $true))),
  introduced(definition,[new_symbols(definition,[spl20_220])],[avatar_definition])).
thf(f6019,plain,(
  ( ! [X0 : tp__ty_2Eextreal_2Eextreal] : ((((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ sF11))) != $true) | (((p @ (ap @ sF7 @ (inj__ty_2Eextreal_2Eextreal @ X0)))) != $true)) ) | ~spl20_220),
  inference(avatar_component_clause,[],[f6018])).
thf(f6020,plain,(
  spl20_220 | spl20_50),
  inference(avatar_split_clause,[],[f4556,f2590,f6018])).
thf(f6026,definition,(
  spl20_222 <=> ! [X0 : tp__ty_2Eextreal_2Eextreal] : ((((p @ (ap @ sF7 @ (inj__ty_2Eextreal_2Eextreal @ X0)))) = $true) | (((p @ (ap @ sF12 @ (inj__ty_2Eextreal_2Eextreal @ X0)))) != $true))),
  introduced(definition,[new_symbols(definition,[spl20_222])],[avatar_definition])).
thf(f6027,plain,(
  ( ! [X0 : tp__ty_2Eextreal_2Eextreal] : ((((p @ (ap @ sF7 @ (inj__ty_2Eextreal_2Eextreal @ X0)))) = $true) | (((p @ (ap @ sF12 @ (inj__ty_2Eextreal_2Eextreal @ X0)))) != $true)) ) | ~spl20_222),
  inference(avatar_component_clause,[],[f6026])).
thf(f6028,plain,(
  spl20_222 | ~spl20_50),
  inference(avatar_split_clause,[],[f4399,f2590,f6026])).
thf(f6466,plain,(
  ($false = $true) | (((mem @ (ap @ sF12 @ sF8) @ bool)) = $true)),
  inference(constrained_superposition,[],[f2736,f2473])).
thf(f6525,plain,(
  (((mem @ (ap @ sF12 @ sF8) @ bool)) = $true)),
  inference(trivial_inequality_removal,[],[f6466])).
thf(f6556,plain,(
  ($true = ((mem @ sF13 @ bool)))),
  inference(forward_demodulation,[],[f6525,f730])).
thf(f6569,plain,(
  ($false = $true) | ~spl20_23),
  inference(forward_demodulation,[],[f6556,f1914])).
thf(f6570,plain,(
  $false | ~spl20_23),
  inference(trivial_inequality_removal,[],[f6569])).
thf(f6571,plain,(
  ~spl20_23),
  inference(avatar_contradiction_clause,[],[f6570])).
thf(f6572,plain,(
  (c_2Ebool_2ET = ((ap @ sF12 @ sF8))) | ~spl20_24),
  inference(backward_demodulation,[],[f730,f1918])).
thf(f7111,plain,(
  (((mem @ sF11 @ ty_2Eextreal_2Eextreal)) != $true) | ($false = $true) | ~spl20_53),
  inference(constrained_superposition,[],[f2607,f2505])).
thf(f7117,plain,(
  (((mem @ sF11 @ ty_2Eextreal_2Eextreal)) != $true) | ~spl20_53),
  inference(trivial_inequality_removal,[],[f7111])).
thf(f7120,plain,(
  $false | ~spl20_53),
  inference(forward_subsumption_resolution,[],[f7117,f1700])).
thf(f7121,plain,(
  ~spl20_53),
  inference(avatar_contradiction_clause,[],[f7120])).
thf(f7586,plain,(
  (((surj__ty_2Eextreal_2Eextreal @ sF16)) = ((surj__ty_2Eextreal_2Eextreal @ (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ ty_2Eextreal_2Eextreal) @ c_2Ebool_2ET) @ sF11) @ sF6)))) | ~spl20_52),
  inference(forward_demodulation,[],[f3800,f2603])).
thf(f7588,plain,(
  (((mem @ sF11 @ ty_2Eextreal_2Eextreal)) != $true) | (((surj__ty_2Eextreal_2Eextreal @ sF11)) = ((surj__ty_2Eextreal_2Eextreal @ sF16))) | (((mem @ sF6 @ ty_2Eextreal_2Eextreal)) != $true) | ~spl20_52),
  inference(constrained_superposition,[],[f7586,f457])).
thf(f7609,plain,(
  (((mem @ sF6 @ ty_2Eextreal_2Eextreal)) != $true) | (((surj__ty_2Eextreal_2Eextreal @ sF11)) = ((surj__ty_2Eextreal_2Eextreal @ sF16))) | ~spl20_52),
  inference(forward_subsumption_resolution,[],[f7588,f1700])).
thf(f7626,plain,(
  (((surj__ty_2Eextreal_2Eextreal @ sF11)) = ((surj__ty_2Eextreal_2Eextreal @ sF16))) | ~spl20_52),
  inference(forward_subsumption_resolution,[],[f7609,f1698])).
thf(f7632,plain,(
  (sK3 = ((surj__ty_2Eextreal_2Eextreal @ sF16))) | ~spl20_52),
  inference(forward_demodulation,[],[f7626,f1659])).
thf(f7665,plain,(
  ($true != $true) | (((p @ (ap @ sF7 @ sF11))) = $false) | spl20_50),
  inference(constrained_superposition,[],[f2591,f714])).
thf(f7666,plain,(
  (((p @ (ap @ sF7 @ sF11))) = $false) | spl20_50),
  inference(trivial_inequality_removal,[],[f7665])).
thf(f7696,plain,(
  (c_2Ebool_2ET = ((inj__o @ $false))) | (c_2Ebool_2EF = ((ap @ sF7 @ sF11))) | ($false = ((mem @ (ap @ sF7 @ sF11) @ bool))) | spl20_50),
  inference(constrained_superposition,[],[f1864,f7666])).
thf(f7697,plain,(
  ($false = ((mem @ (ap @ sF7 @ sF11) @ bool))) | (((ap @ sF7 @ sF11)) = ((inj__o @ $false))) | spl20_50),
  inference(constrained_superposition,[],[f1711,f7666])).
thf(f7699,plain,(
  ($false = ((mem @ (ap @ sF7 @ sF11) @ bool))) | (c_2Ebool_2EF = ((ap @ sF7 @ sF11))) | (c_2Ebool_2ET = c_2Ebool_2EF) | spl20_50),
  inference(forward_demodulation,[],[f7696,f1712])).
thf(f7700,plain,(
  ($false = ((mem @ (ap @ sF7 @ sF11) @ bool))) | (c_2Ebool_2EF = ((ap @ sF7 @ sF11))) | spl20_50),
  inference(forward_demodulation,[],[f7697,f1712])).
thf(f7701,plain,(
  ($false = ((mem @ (ap @ sF7 @ sF11) @ bool))) | (c_2Ebool_2EF = ((ap @ sF7 @ sF11))) | (spl20_17 | spl20_50)),
  inference(forward_subsumption_resolution,[],[f7699,f1807])).
thf(f7703,definition,(
  spl20_271 <=> (c_2Ebool_2EF = ((ap @ sF7 @ sF11)))),
  introduced(definition,[new_symbols(definition,[spl20_271])],[avatar_definition])).
thf(f7705,plain,(
  (c_2Ebool_2EF = ((ap @ sF7 @ sF11))) | ~spl20_271),
  inference(avatar_component_clause,[],[f7703])).
thf(f7706,plain,(
  spl20_271 | spl20_53 | spl20_50),
  inference(avatar_split_clause,[],[f7700,f2590,f2605,f7703])).
thf(f7707,plain,(
  spl20_53 | spl20_271 | spl20_17 | spl20_50),
  inference(avatar_split_clause,[],[f7701,f2590,f1805,f7703,f2605])).
thf(f7720,plain,(
  (((p @ (ap @ sF7 @ sF8))) != $true) | (((p @ (ap @ (ap @ c_2Eextreal_2Eextreal__le @ sF8) @ sF11))) != $true) | ~spl20_220),
  inference(constrained_superposition,[],[f6019,f723])).
thf(f7754,plain,(
  (((surj__ty_2Eextreal_2Eextreal @ (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ ty_2Eextreal_2Eextreal) @ c_2Ebool_2EF) @ sF11) @ sF6))) = ((surj__ty_2Eextreal_2Eextreal @ sF16))) | ~spl20_271),
  inference(forward_demodulation,[],[f3800,f7705])).
thf(f7757,plain,(
  (((surj__ty_2Eextreal_2Eextreal @ sF6)) = ((surj__ty_2Eextreal_2Eextreal @ sF16))) | (((mem @ sF11 @ ty_2Eextreal_2Eextreal)) != $true) | (((mem @ sF6 @ ty_2Eextreal_2Eextreal)) != $true) | ~spl20_271),
  inference(constrained_superposition,[],[f7754,f458])).
thf(f7794,plain,(
  (((mem @ sF6 @ ty_2Eextreal_2Eextreal)) != $true) | (((surj__ty_2Eextreal_2Eextreal @ sF6)) = ((surj__ty_2Eextreal_2Eextreal @ sF16))) | ~spl20_271),
  inference(forward_subsumption_resolution,[],[f7757,f1700])).
thf(f7800,plain,(
  (((surj__ty_2Eextreal_2Eextreal @ sF6)) = ((surj__ty_2Eextreal_2Eextreal @ sF16))) | ~spl20_271),
  inference(forward_subsumption_resolution,[],[f7794,f1698])).
thf(f7801,plain,(
  (((surj__ty_2Eextreal_2Eextreal @ sF16)) = sK5) | ~spl20_271),
  inference(forward_demodulation,[],[f7800,f1657])).
thf(f7818,plain,(
  (((inj__ty_2Eextreal_2Eextreal @ sK3)) = sF16) | (~spl20_43 | ~spl20_52)),
  inference(backward_demodulation,[],[f2842,f7632])).
thf(f7834,plain,(
  (sF16 = sF11) | (~spl20_43 | ~spl20_52)),
  inference(forward_demodulation,[],[f7818,f727])).
thf(f7846,plain,(
  (((ap @ c_2Eextreal_2Eextreal__le @ sF11)) = sF17) | (~spl20_43 | ~spl20_52)),
  inference(backward_demodulation,[],[f737,f7834])).
thf(f7859,plain,(
  (sF12 = sF17) | (~spl20_43 | ~spl20_52)),
  inference(forward_demodulation,[],[f7846,f728])).
thf(f7896,plain,(
  ~spl20_17 | spl20_33 | ~spl20_34),
  inference(avatar_split_clause,[],[f2292,f2176,f2172,f1805])).
thf(f7967,plain,(
  (sF18 = ((ap @ sF12 @ sF8))) | (~spl20_43 | ~spl20_52)),
  inference(forward_demodulation,[],[f739,f7859])).
thf(f7977,plain,(
  (c_2Ebool_2ET = sF18) | (~spl20_24 | ~spl20_43 | ~spl20_52)),
  inference(forward_demodulation,[],[f7967,f6572])).
thf(f7983,plain,(
  spl20_21 | ~spl20_24 | ~spl20_43 | ~spl20_52),
  inference(avatar_split_clause,[],[f7977,f2601,f2468,f1916,f1903])).
thf(f8057,plain,(
  (c_2Ebool_2EF = ((ap @ sF7 @ sF8))) | ~spl20_20),
  inference(backward_demodulation,[],[f724,f1900])).
thf(f8232,plain,(
  ($false = ((mem @ (ap @ sF7 @ sF11) @ bool))) | (((ap @ sF7 @ sF11)) = ((inj__o @ $true))) | ~spl20_50),
  inference(constrained_superposition,[],[f1711,f2592])).
thf(f8252,plain,(
  ($false = ((mem @ (ap @ sF7 @ sF11) @ bool))) | (c_2Ebool_2ET = ((ap @ sF7 @ sF11))) | ~spl20_50),
  inference(forward_demodulation,[],[f8232,f1713])).
thf(f8274,plain,(
  spl20_52 | spl20_53 | ~spl20_50),
  inference(avatar_split_clause,[],[f8252,f2590,f2605,f2601])).
thf(f8343,plain,(
  (((p @ (ap @ sF12 @ sF8))) != $true) | (((p @ (ap @ sF7 @ sF8))) = $true) | ~spl20_222),
  inference(constrained_superposition,[],[f6027,f723])).
thf(f8348,plain,(
  (((p @ (ap @ sF12 @ sF8))) != $true) | (((p @ c_2Ebool_2EF)) = $true) | (~spl20_20 | ~spl20_222)),
  inference(forward_demodulation,[],[f8343,f8057])).
thf(f8354,plain,(
  (((p @ c_2Ebool_2EF)) = $true) | (((p @ c_2Ebool_2ET)) != $true) | (~spl20_20 | ~spl20_24 | ~spl20_222)),
  inference(forward_demodulation,[],[f8348,f6572])).
thf(f8356,plain,(
  (((p @ c_2Ebool_2EF)) = $true) | (~spl20_20 | ~spl20_24 | ~spl20_222)),
  inference(forward_subsumption_resolution,[],[f8354,f301])).
thf(f8358,plain,(
  ($false = $true) | (~spl20_20 | ~spl20_24 | ~spl20_222)),
  inference(forward_demodulation,[],[f8356,f1656])).
thf(f8359,plain,(
  $false | (~spl20_20 | ~spl20_24 | ~spl20_222)),
  inference(trivial_inequality_removal,[],[f8358])).
thf(f8360,plain,(
  ~spl20_20 | ~spl20_24 | ~spl20_222),
  inference(avatar_contradiction_clause,[],[f8359])).
thf(f8372,plain,(
  (((p @ (ap @ sF7 @ sF8))) != $true) | (~spl20_123 | ~spl20_220)),
  inference(forward_subsumption_resolution,[],[f7720,f4392])).
thf(f8521,plain,(
  ($true != ((p @ sF9))) | (~spl20_123 | ~spl20_220)),
  inference(forward_demodulation,[],[f8372,f724])).
thf(f8550,plain,(
  ~spl20_11 | ~spl20_123 | ~spl20_220),
  inference(avatar_split_clause,[],[f8521,f6018,f4391,f1603])).
thf(f8563,plain,(
  (c_2Ebool_2EF = ((ap @ sF7 @ sF8))) | ~spl20_20),
  inference(backward_demodulation,[],[f724,f1900])).
thf(f8583,plain,(
  (((inj__o @ $false)) = sF13) | ($false = ((mem @ sF13 @ bool))) | ~spl20_10),
  inference(constrained_superposition,[],[f1711,f1600])).
thf(f8585,plain,(
  (c_2Ebool_2EF = sF13) | ($false = ((mem @ sF13 @ bool))) | ~spl20_10),
  inference(forward_demodulation,[],[f8583,f1712])).
thf(f8587,definition,(
  spl20_299 <=> (c_2Ebool_2EF = sF13)),
  introduced(definition,[new_symbols(definition,[spl20_299])],[avatar_definition])).
thf(f8590,plain,(
  spl20_299 | spl20_23 | ~spl20_10),
  inference(avatar_split_clause,[],[f8585,f1598,f1912,f8587])).
thf(f8619,definition,(
  spl20_302 <=> (sF6 = sF16)),
  introduced(definition,[new_symbols(definition,[spl20_302])],[avatar_definition])).
thf(f8621,plain,(
  (sF6 = sF16) | ~spl20_302),
  inference(avatar_component_clause,[],[f8619])).
thf(f8644,plain,(
  (((ap @ c_2Eextreal_2Eextreal__le @ sF6)) = sF17) | ~spl20_302),
  inference(backward_demodulation,[],[f737,f8621])).
thf(f8646,plain,(
  (sF7 = sF17) | ~spl20_302),
  inference(forward_demodulation,[],[f8644,f721])).
thf(f8679,plain,(
  (((inj__ty_2Eextreal_2Eextreal @ sK5)) = sF16) | (~spl20_43 | ~spl20_271)),
  inference(forward_demodulation,[],[f2842,f7801])).
thf(f8680,plain,(
  (sF6 = sF16) | (~spl20_43 | ~spl20_271)),
  inference(forward_demodulation,[],[f8679,f719])).
thf(f8686,plain,(
  spl20_302 | ~spl20_43 | ~spl20_271),
  inference(avatar_split_clause,[],[f8680,f7703,f2468,f8619])).
thf(f8694,plain,(
  (((ap @ sF7 @ sF8)) = sF18) | ~spl20_302),
  inference(forward_demodulation,[],[f739,f8646])).
thf(f8700,plain,(
  (c_2Ebool_2EF = sF18) | (~spl20_20 | ~spl20_302)),
  inference(forward_demodulation,[],[f8694,f8563])).
thf(f8704,plain,(
  spl20_26 | ~spl20_20 | ~spl20_302),
  inference(avatar_split_clause,[],[f8700,f8619,f1898,f1955])).
thf(f8717,plain,(
  (((p @ c_2Ebool_2EF)) = $true) | (~spl20_15 | ~spl20_26)),
  inference(forward_demodulation,[],[f1627,f1957])).
thf(f8718,plain,(
  ($false = $true) | (~spl20_15 | ~spl20_26)),
  inference(forward_demodulation,[],[f8717,f1656])).
thf(f8719,plain,(
  $false | (~spl20_15 | ~spl20_26)),
  inference(trivial_inequality_removal,[],[f8718])).
thf(f8720,plain,(
  ~spl20_15 | ~spl20_26),
  inference(avatar_contradiction_clause,[],[f8719])).
thf(f8742,plain,(
  (sF9 = sF18) | ~spl20_302),
  inference(backward_demodulation,[],[f724,f8694])).
thf(f8745,plain,(
  (((p @ sF18)) = $true) | (~spl20_11 | ~spl20_302)),
  inference(forward_demodulation,[],[f1605,f8742])).
thf(f8746,plain,(
  spl20_15 | ~spl20_11 | ~spl20_302),
  inference(avatar_split_clause,[],[f8745,f8619,f1603,f1625])).
thf(f8773,plain,(
  spl20_123 | spl20_8),
  inference(avatar_split_clause,[],[f2833,f1589,f4391])).
thf(f8847,plain,(
  (sF18 = ((ap @ sF12 @ sF8))) | (~spl20_43 | ~spl20_52)),
  inference(forward_demodulation,[],[f739,f7859])).
thf(f8848,plain,(
  (sF18 = sF13) | (~spl20_43 | ~spl20_52)),
  inference(forward_demodulation,[],[f8847,f730])).
thf(f8856,plain,(
  (c_2Ebool_2EF != sF13) | (spl20_26 | ~spl20_43 | ~spl20_52)),
  inference(forward_demodulation,[],[f1956,f8848])).
thf(f8857,plain,(
  ~spl20_299 | spl20_26 | ~spl20_43 | ~spl20_52),
  inference(avatar_split_clause,[],[f8856,f2601,f2468,f1955,f8587])).
cnf(s4, plain, ~spl20_5 | ~spl20_6 | ~spl20_7, inference(sat_conversion,[],[f1578])).
cnf(s13, plain, spl20_5 | spl20_7, inference(sat_conversion,[],[f1587])).
cnf(s14, plain, spl20_8 | spl20_9, inference(sat_conversion,[],[f1596])).
cnf(s15, plain, spl20_5 | spl20_10, inference(sat_conversion,[],[f1601])).
cnf(s16, plain, spl20_11 | spl20_12, inference(sat_conversion,[],[f1610])).
cnf(s17, plain, spl20_6 | spl20_13, inference(sat_conversion,[],[f1615])).
cnf(s22, plain, spl20_14 | spl20_15, inference(sat_conversion,[],[f1628])).
cnf(s23, plain, spl20_7 | spl20_16, inference(sat_conversion,[],[f1633])).
cnf(s25, plain, spl20_6 | spl20_7, inference(sat_conversion,[],[f1635])).
cnf(s30, plain, ~spl20_7 | ~spl20_14, inference(sat_conversion,[],[f1640])).
cnf(s32, plain, ~spl20_8 | ~spl20_10, inference(sat_conversion,[],[f1663])).
cnf(s33, plain, ~spl20_5 | ~spl20_9, inference(sat_conversion,[],[f1667])).
cnf(s37, plain, ~spl20_6 | ~spl20_12, inference(sat_conversion,[],[f1688])).
cnf(s38, plain, ~spl20_15 | ~spl20_16, inference(sat_conversion,[],[f1695])).
cnf(s40, plain, ~spl20_13 | spl20_19 | spl20_20, inference(sat_conversion,[],[f1901])).
cnf(s42, plain, ~spl20_8 | spl20_23 | spl20_24, inference(sat_conversion,[],[f1919])).
cnf(s50, plain, spl20_27 | spl20_28, inference(sat_conversion,[],[f1984])).
cnf(s51, plain, spl20_11 | spl20_13, inference(sat_conversion,[],[f1995])).
cnf(s52, plain, ~spl20_13 | spl20_19 | spl20_20, inference(sat_conversion,[],[f2029])).
cnf(s53, plain, ~spl20_28 | spl20_29, inference(sat_conversion,[],[f2065])).
cnf(s60, plain, spl20_4 | ~spl20_29, inference(sat_conversion,[],[f2231])).
cnf(s61, plain, ~spl20_4, inference(sat_conversion,[],[f2246])).
cnf(s62, plain, spl20_28 | ~spl20_33, inference(sat_conversion,[],[f2261])).
cnf(s65, plain, ~spl20_27 | spl20_33 | spl20_34, inference(sat_conversion,[],[f2278])).
cnf(s82, plain, spl20_43, inference(sat_conversion,[],[f2810])).
cnf(s131, plain, spl20_15 | ~spl20_21, inference(sat_conversion,[],[f3606])).
cnf(s300, plain, ~spl20_19, inference(sat_conversion,[],[f5933])).
cnf(s313, plain, spl20_50 | spl20_220, inference(sat_conversion,[],[f6020])).
cnf(s315, plain, ~spl20_50 | spl20_222, inference(sat_conversion,[],[f6028])).
cnf(s343, plain, ~spl20_23, inference(sat_conversion,[],[f6571])).
cnf(s365, plain, ~spl20_53, inference(sat_conversion,[],[f7121])).
cnf(s401, plain, spl20_50 | spl20_53 | spl20_271, inference(sat_conversion,[],[f7706])).
cnf(s402, plain, spl20_17 | spl20_50 | spl20_53 | spl20_271, inference(sat_conversion,[],[f7707])).
cnf(s433, plain, ~spl20_17 | spl20_33 | ~spl20_34, inference(sat_conversion,[],[f7896])).
cnf(s460, plain, spl20_21 | ~spl20_24 | ~spl20_43 | ~spl20_52, inference(sat_conversion,[],[f7983])).
cnf(s491, plain, ~spl20_50 | spl20_52 | spl20_53, inference(sat_conversion,[],[f8274])).
cnf(s501, plain, ~spl20_20 | ~spl20_24 | ~spl20_222, inference(sat_conversion,[],[f8360])).
cnf(s571, plain, ~spl20_11 | ~spl20_123 | ~spl20_220, inference(sat_conversion,[],[f8550])).
cnf(s589, plain, ~spl20_10 | spl20_23 | spl20_299, inference(sat_conversion,[],[f8590])).
cnf(s607, plain, ~spl20_43 | ~spl20_271 | spl20_302, inference(sat_conversion,[],[f8686])).
cnf(s612, plain, ~spl20_20 | spl20_26 | ~spl20_302, inference(sat_conversion,[],[f8704])).
cnf(s614, plain, ~spl20_15 | ~spl20_26, inference(sat_conversion,[],[f8720])).
cnf(s624, plain, ~spl20_11 | spl20_15 | ~spl20_302, inference(sat_conversion,[],[f8746])).
cnf(s655, plain, spl20_8 | spl20_123, inference(sat_conversion,[],[f8773])).
cnf(s695, plain, spl20_26 | ~spl20_43 | ~spl20_52 | ~spl20_299, inference(sat_conversion,[],[f8857])).
cnf(s718, plain, ~spl20_29, inference(rat,[],[s60,s61])).
cnf(s722, plain, ~spl20_28, inference(rat,[],[s53,s718])).
cnf(s724, plain, ~spl20_33, inference(rat,[],[s62,s722])).
cnf(s725, plain, ~spl20_13 | spl20_20, inference(rat,[],[s52,s300])).
cnf(s726, plain, spl20_27, inference(rat,[],[s50,s722])).
cnf(s727, plain, spl20_34, inference(rat,[],[s65,s724,s726])).
cnf(s728, plain, ~spl20_17, inference(rat,[],[s433,s724,s727])).
cnf(s731, plain, ~spl20_8 | spl20_24, inference(rat,[],[s42,s343])).
cnf(s732, plain, ~spl20_13 | spl20_20, inference(rat,[],[s40,s300])).
cnf(s734, plain, spl20_5, inference(rat,[],[s732,s51,s612,s571,s607,s313,s402,s491,s695,s614,s22,s655,s30,s32,s589,s13,s15,s82,s365,s728,s343])).
cnf(s735, plain, ~spl20_9, inference(rat,[],[s33,s734])).
cnf(s736, plain, spl20_8, inference(rat,[],[s14,s735])).
cnf(s739, plain, spl20_24, inference(rat,[],[s731,s736])).
cnf(s741, plain, spl20_6, inference(rat,[],[s607,s402,s612,s315,s614,s501,s22,s725,s30,s17,s25,s82,s365,s728,s739])).
cnf(s742, plain, ~spl20_12, inference(rat,[],[s37,s741])).
cnf(s743, plain, ~spl20_7, inference(rat,[],[s4,s734,s741])).
cnf(s744, plain, spl20_11, inference(rat,[],[s16,s742])).
cnf(s746, plain, spl20_16, inference(rat,[],[s23,s743])).
cnf(s751, plain, ~spl20_15, inference(rat,[],[s38,s746])).
cnf(s753, plain, ~spl20_21, inference(rat,[],[s131,s751])).
cnf(s754, plain, ~spl20_302, inference(rat,[],[s624,s744,s751])).
cnf(s755, plain, ~spl20_52, inference(rat,[],[s460,s739,s82,s753])).
cnf(s756, plain, ~spl20_271, inference(rat,[],[s607,s82,s754])).
cnf(s757, plain, ~spl20_50, inference(rat,[],[s491,s365,s755])).
cnf(s758, plain, $false, inference(rat,[],[s401,s365,s756,s757])).
thf(f8858,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s758])).
% SZS output end Proof for theBenchmark