TSTP Solution File: ITP021+2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ITP021+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:43:21 EDT 2023
% Result : Theorem 28.03s 13.95s
% Output : CNFRefutation 28.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 40
% Syntax : Number of formulae : 407 ( 175 unt; 26 typ; 0 def)
% Number of atoms : 798 ( 181 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 806 ( 389 ~; 393 |; 3 &)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 12 >; 8 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 14 con; 0-4 aty)
% Number of variables : 211 (; 211 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ mem > p > ne > k > arr > ap > #nlpp > i > c_2Emin_2E_3D > c_2Ebool_2E_21 > c_2Ebool_2ECOND > ty_2Eextreal_2Eextreal > ind > c_2Emin_2E_3D_3D_3E > c_2Eextreal_2Eextreal__max > c_2Eextreal_2Eextreal__le > c_2Ebool_2E_7E > c_2Ebool_2E_5C_2F > c_2Ebool_2E_2F_5C > c_2Ebool_2ET > c_2Ebool_2EF > bool > #skF_5 > #skF_3 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(arr,type,
arr: ( $i * $i ) > $i ).
tff(ne,type,
ne: $i > $o ).
tff(c_2Ebool_2EF,type,
c_2Ebool_2EF: $i ).
tff(c_2Ebool_2ECOND,type,
c_2Ebool_2ECOND: $i > $i ).
tff(i,type,
i: $i > $i ).
tff(c_2Ebool_2E_21,type,
c_2Ebool_2E_21: $i > $i ).
tff(ty_2Eextreal_2Eextreal,type,
ty_2Eextreal_2Eextreal: $i ).
tff(c_2Eextreal_2Eextreal__max,type,
c_2Eextreal_2Eextreal__max: $i ).
tff(bool,type,
bool: $i ).
tff(mem,type,
mem: ( $i * $i ) > $o ).
tff(ap,type,
ap: ( $i * $i ) > $i ).
tff(p,type,
p: $i > $o ).
tff(ind,type,
ind: $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(c_2Emin_2E_3D_3D_3E,type,
c_2Emin_2E_3D_3D_3E: $i ).
tff(c_2Eextreal_2Eextreal__le,type,
c_2Eextreal_2Eextreal__le: $i ).
tff(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(c_2Ebool_2E_7E,type,
c_2Ebool_2E_7E: $i ).
tff(c_2Ebool_2ET,type,
c_2Ebool_2ET: $i ).
tff(k,type,
k: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i * $i * $i ) > $i ).
tff(c_2Emin_2E_3D,type,
c_2Emin_2E_3D: $i > $i ).
tff(c_2Ebool_2E_2F_5C,type,
c_2Ebool_2E_2F_5C: $i ).
tff(f_112,axiom,
~ p(c_2Ebool_2EF),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_false_p) ).
tff(f_648,negated_conjecture,
~ ! [V0z] :
( mem(V0z,ty_2Eextreal_2Eextreal)
=> ! [V1x] :
( mem(V1x,ty_2Eextreal_2Eextreal)
=> ! [V2y] :
( mem(V2y,ty_2Eextreal_2Eextreal)
=> ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,V1x),V2y)),V0z))
<=> ( p(ap(ap(c_2Eextreal_2Eextreal__le,V1x),V0z))
& p(ap(ap(c_2Eextreal_2Eextreal__le,V2y),V0z)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eextreal_2Emax__le) ).
tff(f_102,axiom,
p(c_2Ebool_2ET),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_true_p) ).
tff(f_103,axiom,
ne(ty_2Eextreal_2Eextreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ne_ty_2Eextreal_2Eextreal) ).
tff(f_406,axiom,
! [V0x] :
( mem(V0x,ty_2Eextreal_2Eextreal)
=> ! [V1y] :
( mem(V1y,ty_2Eextreal_2Eextreal)
=> ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y))
| p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),V0x)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eextreal_2Ele__total) ).
tff(f_104,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) ).
tff(f_67,axiom,
! [A,B,F] :
( mem(F,arr(A,B))
=> ! [X] :
( mem(X,A)
=> mem(ap(F,X),B) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP001+2.ax',ap_tp) ).
tff(f_101,axiom,
mem(c_2Ebool_2ET,bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2ET) ).
tff(f_78,axiom,
! [Q] :
( mem(Q,bool)
=> ! [R] :
( mem(R,bool)
=> ( ( p(Q)
<=> p(R) )
=> ( Q = R ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP001+2.ax',boolext) ).
tff(f_109,axiom,
mem(c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eextreal_2Eextreal__max) ).
tff(f_413,axiom,
! [V0x] :
( mem(V0x,ty_2Eextreal_2Eextreal)
=> ! [V1y] :
( mem(V1y,ty_2Eextreal_2Eextreal)
=> ( ap(ap(c_2Eextreal_2Eextreal__max,V0x),V1y) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y)),V1y),V0x) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Eextreal_2Eextreal__max__def) ).
tff(f_323,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0t1] :
( mem(V0t1,A_27a)
=> ! [V1t2] :
( mem(V1t2,A_27a)
=> ( ( ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2ET),V0t1),V1t2) = V0t1 )
& ( ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2EF),V0t1),V1t2) = V1t2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ECOND__CLAUSES) ).
tff(f_110,axiom,
mem(c_2Ebool_2EF,bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2EF) ).
tff(f_397,axiom,
! [V0x] :
( mem(V0x,ty_2Eextreal_2Eextreal)
=> ! [V1y] :
( mem(V1y,ty_2Eextreal_2Eextreal)
=> ! [V2z] :
( mem(V2z,ty_2Eextreal_2Eextreal)
=> ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y))
& p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),V2z)) )
=> p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V2z)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eextreal_2Ele__trans) ).
tff(c_40,plain,
~ p(c_2Ebool_2EF),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_1626,plain,
mem('#skF_4',ty_2Eextreal_2Eextreal),
inference(cnfTransformation,[status(thm)],[f_648]) ).
tff(c_28,plain,
p(c_2Ebool_2ET),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_1636,plain,
( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5')),'#skF_3'))
| p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3')) ),
inference(cnfTransformation,[status(thm)],[f_648]) ).
tff(c_1641,plain,
p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3')),
inference(splitLeft,[status(thm)],[c_1636]) ).
tff(c_30,plain,
ne(ty_2Eextreal_2Eextreal),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_1624,plain,
mem('#skF_5',ty_2Eextreal_2Eextreal),
inference(cnfTransformation,[status(thm)],[f_648]) ).
tff(c_158,plain,
! [V1y_101,V0x_99] :
( p(ap(ap(c_2Eextreal_2Eextreal__le,V1y_101),V0x_99))
| p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_99),V1y_101))
| ~ mem(V1y_101,ty_2Eextreal_2Eextreal)
| ~ mem(V0x_99,ty_2Eextreal_2Eextreal) ),
inference(cnfTransformation,[status(thm)],[f_406]) ).
tff(c_32,plain,
mem(c_2Eextreal_2Eextreal__le,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_1718,plain,
! [F_169,X_170,B_171,A_172] :
( mem(ap(F_169,X_170),B_171)
| ~ mem(X_170,A_172)
| ~ mem(F_169,arr(A_172,B_171)) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_1759,plain,
! [F_169,B_171] :
( mem(ap(F_169,'#skF_5'),B_171)
| ~ mem(F_169,arr(ty_2Eextreal_2Eextreal,B_171)) ),
inference(resolution,[status(thm)],[c_1624,c_1718]) ).
tff(c_1852,plain,
! [F_181,B_182] :
( mem(ap(F_181,'#skF_4'),B_182)
| ~ mem(F_181,arr(ty_2Eextreal_2Eextreal,B_182)) ),
inference(resolution,[status(thm)],[c_1626,c_1718]) ).
tff(c_26,plain,
mem(c_2Ebool_2ET,bool),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_1696,plain,
! [R_165,Q_166] :
( ~ p(R_165)
| ~ p(Q_166)
| ( R_165 = Q_166 )
| ~ mem(R_165,bool)
| ~ mem(Q_166,bool) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_1700,plain,
! [Q_166] :
( ~ p(c_2Ebool_2ET)
| ~ p(Q_166)
| ( c_2Ebool_2ET = Q_166 )
| ~ mem(Q_166,bool) ),
inference(resolution,[status(thm)],[c_26,c_1696]) ).
tff(c_1704,plain,
! [Q_166] :
( ~ p(Q_166)
| ( c_2Ebool_2ET = Q_166 )
| ~ mem(Q_166,bool) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_1700]) ).
tff(c_2321,plain,
! [F_231] :
( ~ p(ap(F_231,'#skF_4'))
| ( ap(F_231,'#skF_4') = c_2Ebool_2ET )
| ~ mem(F_231,arr(ty_2Eextreal_2Eextreal,bool)) ),
inference(resolution,[status(thm)],[c_1852,c_1704]) ).
tff(c_26260,plain,
! [F_772] :
( ~ p(ap(ap(F_772,'#skF_5'),'#skF_4'))
| ( ap(ap(F_772,'#skF_5'),'#skF_4') = c_2Ebool_2ET )
| ~ mem(F_772,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))) ),
inference(resolution,[status(thm)],[c_1759,c_2321]) ).
tff(c_26353,plain,
( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4'))
| ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4') = c_2Ebool_2ET ) ),
inference(resolution,[status(thm)],[c_32,c_26260]) ).
tff(c_26354,plain,
~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4')),
inference(splitLeft,[status(thm)],[c_26353]) ).
tff(c_26360,plain,
( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5'))
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[c_158,c_26354]) ).
tff(c_26369,plain,
p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1624,c_26360]) ).
tff(c_36,plain,
mem(c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_1757,plain,
! [F_169,B_171] :
( mem(ap(F_169,'#skF_4'),B_171)
| ~ mem(F_169,arr(ty_2Eextreal_2Eextreal,B_171)) ),
inference(resolution,[status(thm)],[c_1626,c_1718]) ).
tff(c_1628,plain,
mem('#skF_3',ty_2Eextreal_2Eextreal),
inference(cnfTransformation,[status(thm)],[f_648]) ).
tff(c_1640,plain,
( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5')),'#skF_3'))
| p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3')) ),
inference(cnfTransformation,[status(thm)],[f_648]) ).
tff(c_1651,plain,
p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3')),
inference(splitLeft,[status(thm)],[c_1640]) ).
tff(c_1882,plain,
! [F_183,B_184] :
( mem(ap(F_183,'#skF_3'),B_184)
| ~ mem(F_183,arr(ty_2Eextreal_2Eextreal,B_184)) ),
inference(resolution,[status(thm)],[c_1628,c_1718]) ).
tff(c_2091,plain,
! [F_207] :
( ~ p(ap(F_207,'#skF_3'))
| ( ap(F_207,'#skF_3') = c_2Ebool_2ET )
| ~ mem(F_207,arr(ty_2Eextreal_2Eextreal,bool)) ),
inference(resolution,[status(thm)],[c_1882,c_1704]) ).
tff(c_13246,plain,
! [F_533] :
( ~ p(ap(ap(F_533,'#skF_4'),'#skF_3'))
| ( ap(ap(F_533,'#skF_4'),'#skF_3') = c_2Ebool_2ET )
| ~ mem(F_533,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))) ),
inference(resolution,[status(thm)],[c_1757,c_2091]) ).
tff(c_13317,plain,
( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3'))
| ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3') = c_2Ebool_2ET ) ),
inference(resolution,[status(thm)],[c_32,c_13246]) ).
tff(c_13341,plain,
ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3') = c_2Ebool_2ET,
inference(demodulation,[status(thm),theory(equality)],[c_1651,c_13317]) ).
tff(c_160,plain,
! [V0x_102,V1y_104] :
( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Eextreal_2Eextreal__le,V0x_102),V1y_104)),V1y_104),V0x_102) = ap(ap(c_2Eextreal_2Eextreal__max,V0x_102),V1y_104) )
| ~ mem(V1y_104,ty_2Eextreal_2Eextreal)
| ~ mem(V0x_102,ty_2Eextreal_2Eextreal) ),
inference(cnfTransformation,[status(thm)],[f_413]) ).
tff(c_13377,plain,
( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_3'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_3') )
| ~ mem('#skF_3',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_13341,c_160]) ).
tff(c_13418,plain,
ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_3'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1628,c_13377]) ).
tff(c_132,plain,
! [A_27a_72,V0t1_76,V1t2_78] :
( ( ap(ap(ap(c_2Ebool_2ECOND(A_27a_72),c_2Ebool_2ET),V0t1_76),V1t2_78) = V0t1_76 )
| ~ mem(V1t2_78,A_27a_72)
| ~ mem(V0t1_76,A_27a_72)
| ~ ne(A_27a_72) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_13468,plain,
( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_3') = '#skF_3' )
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_3',ty_2Eextreal_2Eextreal)
| ~ ne(ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_13418,c_132]) ).
tff(c_13484,plain,
ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_3') = '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_30,c_1628,c_1626,c_13468]) ).
tff(c_8,plain,
! [F_6,X_8,B_5,A_4] :
( mem(ap(F_6,X_8),B_5)
| ~ mem(X_8,A_4)
| ~ mem(F_6,arr(A_4,B_5)) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_4158,plain,
! [F_319,F_320,B_321,B_322] :
( mem(ap(F_319,ap(F_320,'#skF_3')),B_321)
| ~ mem(F_319,arr(B_322,B_321))
| ~ mem(F_320,arr(ty_2Eextreal_2Eextreal,B_322)) ),
inference(resolution,[status(thm)],[c_1882,c_8]) ).
tff(c_4239,plain,
! [F_320] :
( mem(ap(c_2Eextreal_2Eextreal__le,ap(F_320,'#skF_3')),arr(ty_2Eextreal_2Eextreal,bool))
| ~ mem(F_320,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
inference(resolution,[status(thm)],[c_32,c_4158]) ).
tff(c_13516,plain,
( mem(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),arr(ty_2Eextreal_2Eextreal,bool))
| ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
inference(superposition,[status(thm),theory(equality)],[c_13484,c_4239]) ).
tff(c_14402,plain,
~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)),
inference(splitLeft,[status(thm)],[c_13516]) ).
tff(c_14405,plain,
~ mem(c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))),
inference(resolution,[status(thm)],[c_1757,c_14402]) ).
tff(c_14409,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_36,c_14405]) ).
tff(c_14411,plain,
mem(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)),
inference(splitRight,[status(thm)],[c_13516]) ).
tff(c_4240,plain,
! [F_320] :
( mem(ap(c_2Eextreal_2Eextreal__max,ap(F_320,'#skF_3')),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))
| ~ mem(F_320,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
inference(resolution,[status(thm)],[c_36,c_4158]) ).
tff(c_13513,plain,
( mem(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))
| ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
inference(superposition,[status(thm),theory(equality)],[c_13484,c_4240]) ).
tff(c_33170,plain,
mem(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)),
inference(demodulation,[status(thm),theory(equality)],[c_14411,c_13513]) ).
tff(c_14410,plain,
mem(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),arr(ty_2Eextreal_2Eextreal,bool)),
inference(splitRight,[status(thm)],[c_13516]) ).
tff(c_1878,plain,
! [F_181] :
( ~ p(ap(F_181,'#skF_4'))
| ( ap(F_181,'#skF_4') = c_2Ebool_2ET )
| ~ mem(F_181,arr(ty_2Eextreal_2Eextreal,bool)) ),
inference(resolution,[status(thm)],[c_1852,c_1704]) ).
tff(c_14494,plain,
( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),'#skF_4'))
| ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),'#skF_4') = c_2Ebool_2ET ) ),
inference(resolution,[status(thm)],[c_14410,c_1878]) ).
tff(c_14501,plain,
~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),'#skF_4')),
inference(splitLeft,[status(thm)],[c_14494]) ).
tff(c_38,plain,
mem(c_2Ebool_2EF,bool),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_1670,plain,
! [Q_160,R_161] :
( p(Q_160)
| p(R_161)
| ( R_161 = Q_160 )
| ~ mem(R_161,bool)
| ~ mem(Q_160,bool) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_1672,plain,
! [Q_160] :
( p(Q_160)
| p(c_2Ebool_2EF)
| ( c_2Ebool_2EF = Q_160 )
| ~ mem(Q_160,bool) ),
inference(resolution,[status(thm)],[c_38,c_1670]) ).
tff(c_1677,plain,
! [Q_160] :
( p(Q_160)
| ( c_2Ebool_2EF = Q_160 )
| ~ mem(Q_160,bool) ),
inference(negUnitSimplification,[status(thm)],[c_40,c_1672]) ).
tff(c_1880,plain,
! [F_181] :
( p(ap(F_181,'#skF_4'))
| ( ap(F_181,'#skF_4') = c_2Ebool_2EF )
| ~ mem(F_181,arr(ty_2Eextreal_2Eextreal,bool)) ),
inference(resolution,[status(thm)],[c_1852,c_1677]) ).
tff(c_14495,plain,
( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),'#skF_4'))
| ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),'#skF_4') = c_2Ebool_2EF ) ),
inference(resolution,[status(thm)],[c_14410,c_1880]) ).
tff(c_20249,plain,
ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),'#skF_4') = c_2Ebool_2EF,
inference(negUnitSimplification,[status(thm)],[c_14501,c_14495]) ).
tff(c_1762,plain,
! [F_175,B_176] :
( mem(ap(F_175,'#skF_5'),B_176)
| ~ mem(F_175,arr(ty_2Eextreal_2Eextreal,B_176)) ),
inference(resolution,[status(thm)],[c_1624,c_1718]) ).
tff(c_2038,plain,
! [F_202] :
( ~ p(ap(F_202,'#skF_5'))
| ( ap(F_202,'#skF_5') = c_2Ebool_2ET )
| ~ mem(F_202,arr(ty_2Eextreal_2Eextreal,bool)) ),
inference(resolution,[status(thm)],[c_1762,c_1704]) ).
tff(c_23928,plain,
! [F_721] :
( ~ p(ap(ap(F_721,'#skF_4'),'#skF_5'))
| ( ap(ap(F_721,'#skF_4'),'#skF_5') = c_2Ebool_2ET )
| ~ mem(F_721,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))) ),
inference(resolution,[status(thm)],[c_1757,c_2038]) ).
tff(c_24043,plain,
( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5'))
| ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2ET ) ),
inference(resolution,[status(thm)],[c_32,c_23928]) ).
tff(c_24044,plain,
~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5')),
inference(splitLeft,[status(thm)],[c_24043]) ).
tff(c_24450,plain,
! [F_735] :
( ~ p(ap(ap(F_735,'#skF_5'),'#skF_4'))
| ( ap(ap(F_735,'#skF_5'),'#skF_4') = c_2Ebool_2ET )
| ~ mem(F_735,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))) ),
inference(resolution,[status(thm)],[c_1759,c_2321]) ).
tff(c_24565,plain,
( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4'))
| ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4') = c_2Ebool_2ET ) ),
inference(resolution,[status(thm)],[c_32,c_24450]) ).
tff(c_24566,plain,
~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4')),
inference(splitLeft,[status(thm)],[c_24565]) ).
tff(c_24572,plain,
( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5'))
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[c_158,c_24566]) ).
tff(c_24581,plain,
p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1624,c_24572]) ).
tff(c_24583,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_24044,c_24581]) ).
tff(c_24584,plain,
ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4') = c_2Ebool_2ET,
inference(splitRight,[status(thm)],[c_24565]) ).
tff(c_24623,plain,
( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_4'),'#skF_5') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_4') )
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_24584,c_160]) ).
tff(c_24666,plain,
ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_4'),'#skF_5') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_1624,c_1626,c_24623]) ).
tff(c_24767,plain,
( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_4') = '#skF_4' )
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
| ~ ne(ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_24666,c_132]) ).
tff(c_24777,plain,
ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_4') = '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_30,c_1626,c_1624,c_24767]) ).
tff(c_3496,plain,
! [F_294,F_295,B_296,B_297] :
( mem(ap(F_294,ap(F_295,'#skF_4')),B_296)
| ~ mem(F_294,arr(B_297,B_296))
| ~ mem(F_295,arr(ty_2Eextreal_2Eextreal,B_297)) ),
inference(resolution,[status(thm)],[c_1852,c_8]) ).
tff(c_3547,plain,
! [F_295] :
( mem(ap(c_2Eextreal_2Eextreal__le,ap(F_295,'#skF_4')),arr(ty_2Eextreal_2Eextreal,bool))
| ~ mem(F_295,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
inference(resolution,[status(thm)],[c_32,c_3496]) ).
tff(c_24821,plain,
( mem(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),arr(ty_2Eextreal_2Eextreal,bool))
| ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
inference(superposition,[status(thm),theory(equality)],[c_24777,c_3547]) ).
tff(c_24976,plain,
~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)),
inference(splitLeft,[status(thm)],[c_24821]) ).
tff(c_24979,plain,
~ mem(c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))),
inference(resolution,[status(thm)],[c_1759,c_24976]) ).
tff(c_24983,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_36,c_24979]) ).
tff(c_24984,plain,
mem(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),arr(ty_2Eextreal_2Eextreal,bool)),
inference(splitRight,[status(thm)],[c_24821]) ).
tff(c_1790,plain,
! [F_175] :
( p(ap(F_175,'#skF_5'))
| ( ap(F_175,'#skF_5') = c_2Ebool_2EF )
| ~ mem(F_175,arr(ty_2Eextreal_2Eextreal,bool)) ),
inference(resolution,[status(thm)],[c_1762,c_1677]) ).
tff(c_25159,plain,
( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5'))
| ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2EF ) ),
inference(resolution,[status(thm)],[c_24984,c_1790]) ).
tff(c_25183,plain,
ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2EF,
inference(negUnitSimplification,[status(thm)],[c_24044,c_25159]) ).
tff(c_25225,plain,
( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2EF),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') )
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_25183,c_160]) ).
tff(c_25270,plain,
ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2EF),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1624,c_25225]) ).
tff(c_130,plain,
! [A_27a_72,V0t1_76,V1t2_78] :
( ( ap(ap(ap(c_2Ebool_2ECOND(A_27a_72),c_2Ebool_2EF),V0t1_76),V1t2_78) = V1t2_78 )
| ~ mem(V1t2_78,A_27a_72)
| ~ mem(V0t1_76,A_27a_72)
| ~ ne(A_27a_72) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_25888,plain,
( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_4' )
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ ne(ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_25270,c_130]) ).
tff(c_25898,plain,
ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_30,c_1624,c_1626,c_25888]) ).
tff(c_5409,plain,
! [V0x_381,V2z_382,V1y_383] :
( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_381),V2z_382))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V1y_383),V2z_382))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_381),V1y_383))
| ~ mem(V2z_382,ty_2Eextreal_2Eextreal)
| ~ mem(V1y_383,ty_2Eextreal_2Eextreal)
| ~ mem(V0x_381,ty_2Eextreal_2Eextreal) ),
inference(cnfTransformation,[status(thm)],[f_397]) ).
tff(c_5417,plain,
! [V0x_381] :
( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_381),'#skF_3'))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_381),'#skF_4'))
| ~ mem('#skF_3',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
| ~ mem(V0x_381,ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[c_1651,c_5409]) ).
tff(c_5429,plain,
! [V0x_384] :
( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_384),'#skF_3'))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_384),'#skF_4'))
| ~ mem(V0x_384,ty_2Eextreal_2Eextreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1628,c_5417]) ).
tff(c_1630,plain,
( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3'))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3'))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5')),'#skF_3')) ),
inference(cnfTransformation,[status(thm)],[f_648]) ).
tff(c_1694,plain,
~ p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5')),'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_1651,c_1641,c_1630]) ).
tff(c_5438,plain,
( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5')),'#skF_4'))
| ~ mem(ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[c_5429,c_1694]) ).
tff(c_5490,plain,
~ mem(ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),ty_2Eextreal_2Eextreal),
inference(splitLeft,[status(thm)],[c_5438]) ).
tff(c_5494,plain,
~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)),
inference(resolution,[status(thm)],[c_1759,c_5490]) ).
tff(c_5497,plain,
~ mem(c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))),
inference(resolution,[status(thm)],[c_1757,c_5494]) ).
tff(c_5501,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_36,c_5497]) ).
tff(c_5503,plain,
mem(ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),ty_2Eextreal_2Eextreal),
inference(splitRight,[status(thm)],[c_5438]) ).
tff(c_4435,plain,
! [V1y_328,V0x_329] :
( p(ap(ap(c_2Eextreal_2Eextreal__le,V1y_328),V0x_329))
| p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_329),V1y_328))
| ~ mem(V1y_328,ty_2Eextreal_2Eextreal)
| ~ mem(V0x_329,ty_2Eextreal_2Eextreal) ),
inference(cnfTransformation,[status(thm)],[f_406]) ).
tff(c_4443,plain,
( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5')))
| ~ mem('#skF_3',ty_2Eextreal_2Eextreal)
| ~ mem(ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[c_4435,c_1694]) ).
tff(c_4449,plain,
( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5')))
| ~ mem(ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),ty_2Eextreal_2Eextreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_1628,c_4443]) ).
tff(c_5530,plain,
p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'))),
inference(demodulation,[status(thm),theory(equality)],[c_5503,c_4449]) ).
tff(c_25906,plain,
p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),'#skF_4')),
inference(demodulation,[status(thm),theory(equality)],[c_25898,c_5530]) ).
tff(c_25912,plain,
p(c_2Ebool_2EF),
inference(demodulation,[status(thm),theory(equality)],[c_20249,c_25906]) ).
tff(c_25914,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_40,c_25912]) ).
tff(c_25915,plain,
ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2ET,
inference(splitRight,[status(thm)],[c_24043]) ).
tff(c_25955,plain,
( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') )
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_25915,c_160]) ).
tff(c_25994,plain,
ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1624,c_25955]) ).
tff(c_26043,plain,
( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_5' )
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ ne(ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_25994,c_132]) ).
tff(c_26059,plain,
ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_5',
inference(demodulation,[status(thm),theory(equality)],[c_30,c_1624,c_1626,c_26043]) ).
tff(c_26070,plain,
~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_26059,c_1694]) ).
tff(c_26076,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1641,c_26070]) ).
tff(c_26077,plain,
ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),'#skF_4') = c_2Ebool_2ET,
inference(splitRight,[status(thm)],[c_14494]) ).
tff(c_26188,plain,
( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_4'),'#skF_3') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),'#skF_4') )
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_3',ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_26077,c_160]) ).
tff(c_26235,plain,
ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_4'),'#skF_3') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),'#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_1628,c_1626,c_26188]) ).
tff(c_32233,plain,
( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),'#skF_4') = '#skF_4' )
| ~ mem('#skF_3',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
| ~ ne(ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_26235,c_132]) ).
tff(c_32243,plain,
ap(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),'#skF_4') = '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_30,c_1626,c_1628,c_32233]) ).
tff(c_32610,plain,
( mem(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),arr(ty_2Eextreal_2Eextreal,bool))
| ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
inference(superposition,[status(thm),theory(equality)],[c_32243,c_3547]) ).
tff(c_36288,plain,
mem(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),arr(ty_2Eextreal_2Eextreal,bool)),
inference(demodulation,[status(thm),theory(equality)],[c_33170,c_32610]) ).
tff(c_1788,plain,
! [F_175] :
( ~ p(ap(F_175,'#skF_5'))
| ( ap(F_175,'#skF_5') = c_2Ebool_2ET )
| ~ mem(F_175,arr(ty_2Eextreal_2Eextreal,bool)) ),
inference(resolution,[status(thm)],[c_1762,c_1704]) ).
tff(c_36321,plain,
( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5'))
| ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2ET ) ),
inference(resolution,[status(thm)],[c_36288,c_1788]) ).
tff(c_36344,plain,
ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2ET,
inference(demodulation,[status(thm),theory(equality)],[c_26369,c_36321]) ).
tff(c_36421,plain,
( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') )
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_36344,c_160]) ).
tff(c_36466,plain,
ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1624,c_36421]) ).
tff(c_37051,plain,
( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_5' )
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ ne(ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_36466,c_132]) ).
tff(c_37067,plain,
ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_5',
inference(demodulation,[status(thm),theory(equality)],[c_30,c_1624,c_1626,c_37051]) ).
tff(c_37078,plain,
~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_37067,c_1694]) ).
tff(c_37085,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1641,c_37078]) ).
tff(c_37086,plain,
ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4') = c_2Ebool_2ET,
inference(splitRight,[status(thm)],[c_26353]) ).
tff(c_4433,plain,
! [V1y_101] :
( ~ mem(V1y_101,ty_2Eextreal_2Eextreal)
| p(ap(ap(c_2Eextreal_2Eextreal__le,V1y_101),V1y_101)) ),
inference(factorization,[status(thm),theory(equality)],[c_158]) ).
tff(c_37116,plain,
( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_4'),'#skF_5') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_4') )
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_37086,c_160]) ).
tff(c_37159,plain,
ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_4'),'#skF_5') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_1624,c_1626,c_37116]) ).
tff(c_40311,plain,
( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_4') = '#skF_4' )
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
| ~ ne(ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_37159,c_132]) ).
tff(c_40321,plain,
ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_4') = '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_30,c_1626,c_1624,c_40311]) ).
tff(c_40356,plain,
( mem(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),arr(ty_2Eextreal_2Eextreal,bool))
| ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
inference(superposition,[status(thm),theory(equality)],[c_40321,c_3547]) ).
tff(c_41558,plain,
~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)),
inference(splitLeft,[status(thm)],[c_40356]) ).
tff(c_41561,plain,
~ mem(c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))),
inference(resolution,[status(thm)],[c_1759,c_41558]) ).
tff(c_41565,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_36,c_41561]) ).
tff(c_41566,plain,
mem(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),arr(ty_2Eextreal_2Eextreal,bool)),
inference(splitRight,[status(thm)],[c_40356]) ).
tff(c_41637,plain,
( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4'))
| ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4') = c_2Ebool_2ET ) ),
inference(resolution,[status(thm)],[c_41566,c_1878]) ).
tff(c_41648,plain,
~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4')),
inference(splitLeft,[status(thm)],[c_41637]) ).
tff(c_41667,plain,
~ mem('#skF_4',ty_2Eextreal_2Eextreal),
inference(resolution,[status(thm)],[c_4433,c_41648]) ).
tff(c_41673,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1626,c_41667]) ).
tff(c_41674,plain,
ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4') = c_2Ebool_2ET,
inference(splitRight,[status(thm)],[c_41637]) ).
tff(c_41646,plain,
( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5'))
| ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2ET ) ),
inference(resolution,[status(thm)],[c_41566,c_1788]) ).
tff(c_41884,plain,
~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5')),
inference(splitLeft,[status(thm)],[c_41646]) ).
tff(c_41645,plain,
( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5'))
| ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2EF ) ),
inference(resolution,[status(thm)],[c_41566,c_1790]) ).
tff(c_41888,plain,
ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2EF,
inference(negUnitSimplification,[status(thm)],[c_41884,c_41645]) ).
tff(c_41919,plain,
( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2EF),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') )
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_41888,c_160]) ).
tff(c_41964,plain,
ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2EF),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1624,c_41919]) ).
tff(c_42213,plain,
( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_4' )
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ ne(ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_41964,c_130]) ).
tff(c_42223,plain,
ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_30,c_1624,c_1626,c_42213]) ).
tff(c_5502,plain,
~ p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5')),'#skF_4')),
inference(splitRight,[status(thm)],[c_5438]) ).
tff(c_42232,plain,
~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4')),
inference(demodulation,[status(thm),theory(equality)],[c_42223,c_5502]) ).
tff(c_42240,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_41674,c_42232]) ).
tff(c_42241,plain,
ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2ET,
inference(splitRight,[status(thm)],[c_41646]) ).
tff(c_42272,plain,
( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') )
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_42241,c_160]) ).
tff(c_42317,plain,
ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1624,c_42272]) ).
tff(c_42378,plain,
( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_5' )
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ ne(ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_42317,c_132]) ).
tff(c_42394,plain,
ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_5',
inference(demodulation,[status(thm),theory(equality)],[c_30,c_1624,c_1626,c_42378]) ).
tff(c_42409,plain,
~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4')),
inference(demodulation,[status(thm),theory(equality)],[c_42394,c_5502]) ).
tff(c_42416,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_37086,c_42409]) ).
tff(c_42418,plain,
~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3')),
inference(splitRight,[status(thm)],[c_1640]) ).
tff(c_42485,plain,
! [F_1083,X_1084,B_1085,A_1086] :
( mem(ap(F_1083,X_1084),B_1085)
| ~ mem(X_1084,A_1086)
| ~ mem(F_1083,arr(A_1086,B_1085)) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_42526,plain,
! [F_1083,B_1085] :
( mem(ap(F_1083,'#skF_5'),B_1085)
| ~ mem(F_1083,arr(ty_2Eextreal_2Eextreal,B_1085)) ),
inference(resolution,[status(thm)],[c_1624,c_42485]) ).
tff(c_42648,plain,
! [F_1095,B_1096] :
( mem(ap(F_1095,'#skF_3'),B_1096)
| ~ mem(F_1095,arr(ty_2Eextreal_2Eextreal,B_1096)) ),
inference(resolution,[status(thm)],[c_1628,c_42485]) ).
tff(c_42462,plain,
! [R_1077,Q_1078] :
( ~ p(R_1077)
| ~ p(Q_1078)
| ( R_1077 = Q_1078 )
| ~ mem(R_1077,bool)
| ~ mem(Q_1078,bool) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_42466,plain,
! [Q_1078] :
( ~ p(c_2Ebool_2ET)
| ~ p(Q_1078)
| ( c_2Ebool_2ET = Q_1078 )
| ~ mem(Q_1078,bool) ),
inference(resolution,[status(thm)],[c_26,c_42462]) ).
tff(c_42470,plain,
! [Q_1078] :
( ~ p(Q_1078)
| ( c_2Ebool_2ET = Q_1078 )
| ~ mem(Q_1078,bool) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_42466]) ).
tff(c_42831,plain,
! [F_1119] :
( ~ p(ap(F_1119,'#skF_3'))
| ( ap(F_1119,'#skF_3') = c_2Ebool_2ET )
| ~ mem(F_1119,arr(ty_2Eextreal_2Eextreal,bool)) ),
inference(resolution,[status(thm)],[c_42648,c_42470]) ).
tff(c_53809,plain,
! [F_1456] :
( ~ p(ap(ap(F_1456,'#skF_5'),'#skF_3'))
| ( ap(ap(F_1456,'#skF_5'),'#skF_3') = c_2Ebool_2ET )
| ~ mem(F_1456,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))) ),
inference(resolution,[status(thm)],[c_42526,c_42831]) ).
tff(c_53880,plain,
( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3'))
| ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3') = c_2Ebool_2ET ) ),
inference(resolution,[status(thm)],[c_32,c_53809]) ).
tff(c_53902,plain,
ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3') = c_2Ebool_2ET,
inference(demodulation,[status(thm),theory(equality)],[c_1641,c_53880]) ).
tff(c_53934,plain,
( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_3'),'#skF_5') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_3') )
| ~ mem('#skF_3',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_53902,c_160]) ).
tff(c_53977,plain,
ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_3'),'#skF_5') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_1624,c_1628,c_53934]) ).
tff(c_54019,plain,
( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_3') = '#skF_3' )
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_3',ty_2Eextreal_2Eextreal)
| ~ ne(ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_53977,c_132]) ).
tff(c_54047,plain,
ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_3') = '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_30,c_1628,c_1624,c_54019]) ).
tff(c_44847,plain,
! [F_1237,F_1238,B_1239,B_1240] :
( mem(ap(F_1237,ap(F_1238,'#skF_3')),B_1239)
| ~ mem(F_1237,arr(B_1240,B_1239))
| ~ mem(F_1238,arr(ty_2Eextreal_2Eextreal,B_1240)) ),
inference(resolution,[status(thm)],[c_42648,c_8]) ).
tff(c_44922,plain,
! [F_1238] :
( mem(ap(c_2Eextreal_2Eextreal__le,ap(F_1238,'#skF_3')),arr(ty_2Eextreal_2Eextreal,bool))
| ~ mem(F_1238,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
inference(resolution,[status(thm)],[c_32,c_44847]) ).
tff(c_54073,plain,
( mem(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),arr(ty_2Eextreal_2Eextreal,bool))
| ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
inference(superposition,[status(thm),theory(equality)],[c_54047,c_44922]) ).
tff(c_54258,plain,
~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)),
inference(splitLeft,[status(thm)],[c_54073]) ).
tff(c_54355,plain,
~ mem(c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))),
inference(resolution,[status(thm)],[c_42526,c_54258]) ).
tff(c_54359,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_36,c_54355]) ).
tff(c_54361,plain,
mem(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)),
inference(splitRight,[status(thm)],[c_54073]) ).
tff(c_46916,plain,
! [V0x_1324,V2z_1325,V1y_1326] :
( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1324),V2z_1325))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V1y_1326),V2z_1325))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1324),V1y_1326))
| ~ mem(V2z_1325,ty_2Eextreal_2Eextreal)
| ~ mem(V1y_1326,ty_2Eextreal_2Eextreal)
| ~ mem(V0x_1324,ty_2Eextreal_2Eextreal) ),
inference(cnfTransformation,[status(thm)],[f_397]) ).
tff(c_50968,plain,
! [V0x_1409,V0x_1410,V1y_1411] :
( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1409),V0x_1410))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1409),V1y_1411))
| ~ mem(V0x_1409,ty_2Eextreal_2Eextreal)
| p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1410),V1y_1411))
| ~ mem(V1y_1411,ty_2Eextreal_2Eextreal)
| ~ mem(V0x_1410,ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[c_158,c_46916]) ).
tff(c_50978,plain,
! [V0x_1410] :
( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),V0x_1410))
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1410),'#skF_3'))
| ~ mem('#skF_3',ty_2Eextreal_2Eextreal)
| ~ mem(V0x_1410,ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[c_1641,c_50968]) ).
tff(c_50987,plain,
! [V0x_1410] :
( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),V0x_1410))
| p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1410),'#skF_3'))
| ~ mem(V0x_1410,ty_2Eextreal_2Eextreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_1628,c_1624,c_50978]) ).
tff(c_42618,plain,
! [F_1093,B_1094] :
( mem(ap(F_1093,'#skF_4'),B_1094)
| ~ mem(F_1093,arr(ty_2Eextreal_2Eextreal,B_1094)) ),
inference(resolution,[status(thm)],[c_1626,c_42485]) ).
tff(c_42804,plain,
! [F_1115] :
( ~ p(ap(F_1115,'#skF_4'))
| ( ap(F_1115,'#skF_4') = c_2Ebool_2ET )
| ~ mem(F_1115,arr(ty_2Eextreal_2Eextreal,bool)) ),
inference(resolution,[status(thm)],[c_42618,c_42470]) ).
tff(c_54743,plain,
! [F_1470] :
( ~ p(ap(ap(F_1470,'#skF_5'),'#skF_4'))
| ( ap(ap(F_1470,'#skF_5'),'#skF_4') = c_2Ebool_2ET )
| ~ mem(F_1470,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))) ),
inference(resolution,[status(thm)],[c_42526,c_42804]) ).
tff(c_54836,plain,
( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4'))
| ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4') = c_2Ebool_2ET ) ),
inference(resolution,[status(thm)],[c_32,c_54743]) ).
tff(c_54847,plain,
~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4')),
inference(splitLeft,[status(thm)],[c_54836]) ).
tff(c_54850,plain,
( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3'))
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[c_50987,c_54847]) ).
tff(c_54859,plain,
p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_1626,c_54850]) ).
tff(c_54861,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_42418,c_54859]) ).
tff(c_54862,plain,
ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4') = c_2Ebool_2ET,
inference(splitRight,[status(thm)],[c_54836]) ).
tff(c_54892,plain,
( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_4'),'#skF_5') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_4') )
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_54862,c_160]) ).
tff(c_54936,plain,
ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_4'),'#skF_5') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_1624,c_1626,c_54892]) ).
tff(c_55290,plain,
( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_4') = '#skF_4' )
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
| ~ ne(ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_54936,c_132]) ).
tff(c_55318,plain,
ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_4') = '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_30,c_1626,c_1624,c_55290]) ).
tff(c_43411,plain,
! [F_1174,F_1175,B_1176,B_1177] :
( mem(ap(F_1174,ap(F_1175,'#skF_4')),B_1176)
| ~ mem(F_1174,arr(B_1177,B_1176))
| ~ mem(F_1175,arr(ty_2Eextreal_2Eextreal,B_1177)) ),
inference(resolution,[status(thm)],[c_42618,c_8]) ).
tff(c_43455,plain,
! [F_1175] :
( mem(ap(c_2Eextreal_2Eextreal__le,ap(F_1175,'#skF_4')),arr(ty_2Eextreal_2Eextreal,bool))
| ~ mem(F_1175,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
inference(resolution,[status(thm)],[c_32,c_43411]) ).
tff(c_55347,plain,
( mem(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),arr(ty_2Eextreal_2Eextreal,bool))
| ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
inference(superposition,[status(thm),theory(equality)],[c_55318,c_43455]) ).
tff(c_55366,plain,
mem(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),arr(ty_2Eextreal_2Eextreal,bool)),
inference(demodulation,[status(thm),theory(equality)],[c_54361,c_55347]) ).
tff(c_42439,plain,
! [Q_1074,R_1075] :
( p(Q_1074)
| p(R_1075)
| ( R_1075 = Q_1074 )
| ~ mem(R_1075,bool)
| ~ mem(Q_1074,bool) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_42441,plain,
! [Q_1074] :
( p(Q_1074)
| p(c_2Ebool_2EF)
| ( c_2Ebool_2EF = Q_1074 )
| ~ mem(Q_1074,bool) ),
inference(resolution,[status(thm)],[c_38,c_42439]) ).
tff(c_42446,plain,
! [Q_1074] :
( p(Q_1074)
| ( c_2Ebool_2EF = Q_1074 )
| ~ mem(Q_1074,bool) ),
inference(negUnitSimplification,[status(thm)],[c_40,c_42441]) ).
tff(c_42676,plain,
! [F_1095] :
( p(ap(F_1095,'#skF_3'))
| ( ap(F_1095,'#skF_3') = c_2Ebool_2EF )
| ~ mem(F_1095,arr(ty_2Eextreal_2Eextreal,bool)) ),
inference(resolution,[status(thm)],[c_42648,c_42446]) ).
tff(c_55559,plain,
( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3'))
| ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3') = c_2Ebool_2EF ) ),
inference(resolution,[status(thm)],[c_55366,c_42676]) ).
tff(c_55578,plain,
ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3') = c_2Ebool_2EF,
inference(negUnitSimplification,[status(thm)],[c_42418,c_55559]) ).
tff(c_42588,plain,
! [F_1091,B_1092] :
( mem(ap(F_1091,'#skF_5'),B_1092)
| ~ mem(F_1091,arr(ty_2Eextreal_2Eextreal,B_1092)) ),
inference(resolution,[status(thm)],[c_1624,c_42485]) ).
tff(c_42616,plain,
! [F_1091] :
( p(ap(F_1091,'#skF_5'))
| ( ap(F_1091,'#skF_5') = c_2Ebool_2EF )
| ~ mem(F_1091,arr(ty_2Eextreal_2Eextreal,bool)) ),
inference(resolution,[status(thm)],[c_42588,c_42446]) ).
tff(c_55573,plain,
( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5'))
| ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2EF ) ),
inference(resolution,[status(thm)],[c_55366,c_42616]) ).
tff(c_55896,plain,
ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2EF,
inference(splitLeft,[status(thm)],[c_55573]) ).
tff(c_55925,plain,
( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2EF),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') )
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_55896,c_160]) ).
tff(c_55971,plain,
ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2EF),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1624,c_55925]) ).
tff(c_57292,plain,
( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_4' )
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ ne(ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_55971,c_130]) ).
tff(c_57320,plain,
ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_30,c_1624,c_1626,c_57292]) ).
tff(c_42417,plain,
p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5')),'#skF_3')),
inference(splitRight,[status(thm)],[c_1640]) ).
tff(c_57328,plain,
p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_57320,c_42417]) ).
tff(c_57330,plain,
p(c_2Ebool_2EF),
inference(demodulation,[status(thm),theory(equality)],[c_55578,c_57328]) ).
tff(c_57332,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_40,c_57330]) ).
tff(c_57333,plain,
p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5')),
inference(splitRight,[status(thm)],[c_55573]) ).
tff(c_46926,plain,
! [V0x_1324] :
( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1324),'#skF_3'))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1324),'#skF_5'))
| ~ mem('#skF_3',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ mem(V0x_1324,ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[c_1641,c_46916]) ).
tff(c_46935,plain,
! [V0x_1324] :
( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1324),'#skF_3'))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1324),'#skF_5'))
| ~ mem(V0x_1324,ty_2Eextreal_2Eextreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_1624,c_1628,c_46926]) ).
tff(c_57339,plain,
( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3'))
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[c_57333,c_46935]) ).
tff(c_57347,plain,
p(c_2Ebool_2EF),
inference(demodulation,[status(thm),theory(equality)],[c_1626,c_55578,c_57339]) ).
tff(c_57349,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_40,c_57347]) ).
tff(c_57351,plain,
~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3')),
inference(splitRight,[status(thm)],[c_1636]) ).
tff(c_57428,plain,
! [F_1523,X_1524,B_1525,A_1526] :
( mem(ap(F_1523,X_1524),B_1525)
| ~ mem(X_1524,A_1526)
| ~ mem(F_1523,arr(A_1526,B_1525)) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_57470,plain,
! [F_1523,B_1525] :
( mem(ap(F_1523,'#skF_3'),B_1525)
| ~ mem(F_1523,arr(ty_2Eextreal_2Eextreal,B_1525)) ),
inference(resolution,[status(thm)],[c_1628,c_57428]) ).
tff(c_60262,plain,
! [V1y_1683,V0x_1684] :
( p(ap(ap(c_2Eextreal_2Eextreal__le,V1y_1683),V0x_1684))
| p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1684),V1y_1683))
| ~ mem(V1y_1683,ty_2Eextreal_2Eextreal)
| ~ mem(V0x_1684,ty_2Eextreal_2Eextreal) ),
inference(cnfTransformation,[status(thm)],[f_406]) ).
tff(c_60266,plain,
( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),'#skF_5'))
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_3',ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[c_60262,c_57351]) ).
tff(c_60273,plain,
p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),'#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_1628,c_1624,c_60266]) ).
tff(c_57471,plain,
! [F_1527,B_1528] :
( mem(ap(F_1527,'#skF_5'),B_1528)
| ~ mem(F_1527,arr(ty_2Eextreal_2Eextreal,B_1528)) ),
inference(resolution,[status(thm)],[c_1624,c_57428]) ).
tff(c_57382,plain,
! [R_1514,Q_1515] :
( ~ p(R_1514)
| ~ p(Q_1515)
| ( R_1514 = Q_1515 )
| ~ mem(R_1514,bool)
| ~ mem(Q_1515,bool) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_57386,plain,
! [Q_1515] :
( ~ p(c_2Ebool_2ET)
| ~ p(Q_1515)
| ( c_2Ebool_2ET = Q_1515 )
| ~ mem(Q_1515,bool) ),
inference(resolution,[status(thm)],[c_26,c_57382]) ).
tff(c_57390,plain,
! [Q_1515] :
( ~ p(Q_1515)
| ( c_2Ebool_2ET = Q_1515 )
| ~ mem(Q_1515,bool) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_57386]) ).
tff(c_57744,plain,
! [F_1558] :
( ~ p(ap(F_1558,'#skF_5'))
| ( ap(F_1558,'#skF_5') = c_2Ebool_2ET )
| ~ mem(F_1558,arr(ty_2Eextreal_2Eextreal,bool)) ),
inference(resolution,[status(thm)],[c_57471,c_57390]) ).
tff(c_68861,plain,
! [F_1879] :
( ~ p(ap(ap(F_1879,'#skF_3'),'#skF_5'))
| ( ap(ap(F_1879,'#skF_3'),'#skF_5') = c_2Ebool_2ET )
| ~ mem(F_1879,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))) ),
inference(resolution,[status(thm)],[c_57470,c_57744]) ).
tff(c_68932,plain,
( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),'#skF_5'))
| ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),'#skF_5') = c_2Ebool_2ET ) ),
inference(resolution,[status(thm)],[c_32,c_68861]) ).
tff(c_68956,plain,
ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),'#skF_5') = c_2Ebool_2ET,
inference(demodulation,[status(thm),theory(equality)],[c_60273,c_68932]) ).
tff(c_68998,plain,
( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_5'),'#skF_3') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),'#skF_5') )
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_3',ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_68956,c_160]) ).
tff(c_69043,plain,
ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_5'),'#skF_3') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),'#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_1628,c_1624,c_68998]) ).
tff(c_69099,plain,
( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),'#skF_5') = '#skF_5' )
| ~ mem('#skF_3',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ ne(ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_69043,c_132]) ).
tff(c_69109,plain,
ap(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),'#skF_5') = '#skF_5',
inference(demodulation,[status(thm),theory(equality)],[c_30,c_1624,c_1628,c_69099]) ).
tff(c_59432,plain,
! [F_1653,F_1654,B_1655,B_1656] :
( mem(ap(F_1653,ap(F_1654,'#skF_5')),B_1655)
| ~ mem(F_1653,arr(B_1656,B_1655))
| ~ mem(F_1654,arr(ty_2Eextreal_2Eextreal,B_1656)) ),
inference(resolution,[status(thm)],[c_57471,c_8]) ).
tff(c_59493,plain,
! [F_1654] :
( mem(ap(c_2Eextreal_2Eextreal__max,ap(F_1654,'#skF_5')),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))
| ~ mem(F_1654,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
inference(resolution,[status(thm)],[c_36,c_59432]) ).
tff(c_69144,plain,
( mem(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))
| ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
inference(superposition,[status(thm),theory(equality)],[c_69109,c_59493]) ).
tff(c_69320,plain,
~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)),
inference(splitLeft,[status(thm)],[c_69144]) ).
tff(c_69404,plain,
~ mem(c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))),
inference(resolution,[status(thm)],[c_57470,c_69320]) ).
tff(c_69408,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_36,c_69404]) ).
tff(c_69410,plain,
mem(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)),
inference(splitRight,[status(thm)],[c_69144]) ).
tff(c_59495,plain,
! [F_1654] :
( mem(ap(c_2Eextreal_2Eextreal__le,ap(F_1654,'#skF_5')),arr(ty_2Eextreal_2Eextreal,bool))
| ~ mem(F_1654,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
inference(resolution,[status(thm)],[c_32,c_59432]) ).
tff(c_69135,plain,
( mem(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),arr(ty_2Eextreal_2Eextreal,bool))
| ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
inference(superposition,[status(thm),theory(equality)],[c_69109,c_59495]) ).
tff(c_69453,plain,
mem(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),arr(ty_2Eextreal_2Eextreal,bool)),
inference(demodulation,[status(thm),theory(equality)],[c_69410,c_69135]) ).
tff(c_57591,plain,
! [F_1535,B_1536] :
( mem(ap(F_1535,'#skF_3'),B_1536)
| ~ mem(F_1535,arr(ty_2Eextreal_2Eextreal,B_1536)) ),
inference(resolution,[status(thm)],[c_1628,c_57428]) ).
tff(c_57405,plain,
! [Q_1520,R_1521] :
( p(Q_1520)
| p(R_1521)
| ( R_1521 = Q_1520 )
| ~ mem(R_1521,bool)
| ~ mem(Q_1520,bool) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_57407,plain,
! [Q_1520] :
( p(Q_1520)
| p(c_2Ebool_2EF)
| ( c_2Ebool_2EF = Q_1520 )
| ~ mem(Q_1520,bool) ),
inference(resolution,[status(thm)],[c_38,c_57405]) ).
tff(c_57412,plain,
! [Q_1520] :
( p(Q_1520)
| ( c_2Ebool_2EF = Q_1520 )
| ~ mem(Q_1520,bool) ),
inference(negUnitSimplification,[status(thm)],[c_40,c_57407]) ).
tff(c_57617,plain,
! [F_1535] :
( p(ap(F_1535,'#skF_3'))
| ( ap(F_1535,'#skF_3') = c_2Ebool_2EF )
| ~ mem(F_1535,arr(ty_2Eextreal_2Eextreal,bool)) ),
inference(resolution,[status(thm)],[c_57591,c_57412]) ).
tff(c_69469,plain,
( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3'))
| ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3') = c_2Ebool_2EF ) ),
inference(resolution,[status(thm)],[c_69453,c_57617]) ).
tff(c_69492,plain,
ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3') = c_2Ebool_2EF,
inference(negUnitSimplification,[status(thm)],[c_57351,c_69469]) ).
tff(c_57352,plain,
p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3')),
inference(splitLeft,[status(thm)],[c_1640]) ).
tff(c_61310,plain,
! [V0x_1739,V2z_1740,V1y_1741] :
( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1739),V2z_1740))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V1y_1741),V2z_1740))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1739),V1y_1741))
| ~ mem(V2z_1740,ty_2Eextreal_2Eextreal)
| ~ mem(V1y_1741,ty_2Eextreal_2Eextreal)
| ~ mem(V0x_1739,ty_2Eextreal_2Eextreal) ),
inference(cnfTransformation,[status(thm)],[f_397]) ).
tff(c_61322,plain,
! [V0x_1739] :
( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1739),'#skF_3'))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1739),'#skF_4'))
| ~ mem('#skF_3',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
| ~ mem(V0x_1739,ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[c_57352,c_61310]) ).
tff(c_61550,plain,
! [V0x_1746] :
( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1746),'#skF_3'))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1746),'#skF_4'))
| ~ mem(V0x_1746,ty_2Eextreal_2Eextreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1628,c_61322]) ).
tff(c_61555,plain,
( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4'))
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[c_61550,c_57351]) ).
tff(c_61561,plain,
~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4')),
inference(demodulation,[status(thm),theory(equality)],[c_1624,c_61555]) ).
tff(c_61564,plain,
( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5'))
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[c_158,c_61561]) ).
tff(c_61570,plain,
p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1624,c_61564]) ).
tff(c_57467,plain,
! [F_1523,B_1525] :
( mem(ap(F_1523,'#skF_4'),B_1525)
| ~ mem(F_1523,arr(ty_2Eextreal_2Eextreal,B_1525)) ),
inference(resolution,[status(thm)],[c_1626,c_57428]) ).
tff(c_57561,plain,
! [F_1533,B_1534] :
( mem(ap(F_1533,'#skF_4'),B_1534)
| ~ mem(F_1533,arr(ty_2Eextreal_2Eextreal,B_1534)) ),
inference(resolution,[status(thm)],[c_1626,c_57428]) ).
tff(c_57863,plain,
! [F_1563] :
( p(ap(F_1563,'#skF_4'))
| ( ap(F_1563,'#skF_4') = c_2Ebool_2EF )
| ~ mem(F_1563,arr(ty_2Eextreal_2Eextreal,bool)) ),
inference(resolution,[status(thm)],[c_57561,c_57412]) ).
tff(c_74887,plain,
! [F_1980] :
( p(ap(ap(F_1980,'#skF_4'),'#skF_4'))
| ( ap(ap(F_1980,'#skF_4'),'#skF_4') = c_2Ebool_2EF )
| ~ mem(F_1980,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))) ),
inference(resolution,[status(thm)],[c_57467,c_57863]) ).
tff(c_75007,plain,
( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4'))
| ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4') = c_2Ebool_2EF ) ),
inference(resolution,[status(thm)],[c_32,c_74887]) ).
tff(c_75008,plain,
ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4') = c_2Ebool_2EF,
inference(splitLeft,[status(thm)],[c_75007]) ).
tff(c_60260,plain,
! [V1y_101] :
( ~ mem(V1y_101,ty_2Eextreal_2Eextreal)
| p(ap(ap(c_2Eextreal_2Eextreal__le,V1y_101),V1y_101)) ),
inference(factorization,[status(thm),theory(equality)],[c_158]) ).
tff(c_75051,plain,
( ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
| p(c_2Ebool_2EF) ),
inference(superposition,[status(thm),theory(equality)],[c_75008,c_60260]) ).
tff(c_75094,plain,
p(c_2Ebool_2EF),
inference(demodulation,[status(thm),theory(equality)],[c_1626,c_75051]) ).
tff(c_75096,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_40,c_75094]) ).
tff(c_75097,plain,
p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4')),
inference(splitRight,[status(thm)],[c_75007]) ).
tff(c_57977,plain,
! [F_1575] :
( ~ p(ap(F_1575,'#skF_4'))
| ( ap(F_1575,'#skF_4') = c_2Ebool_2ET )
| ~ mem(F_1575,arr(ty_2Eextreal_2Eextreal,bool)) ),
inference(resolution,[status(thm)],[c_57561,c_57390]) ).
tff(c_75472,plain,
! [F_1990] :
( ~ p(ap(ap(F_1990,'#skF_4'),'#skF_4'))
| ( ap(ap(F_1990,'#skF_4'),'#skF_4') = c_2Ebool_2ET )
| ~ mem(F_1990,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))) ),
inference(resolution,[status(thm)],[c_57467,c_57977]) ).
tff(c_75563,plain,
( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4'))
| ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4') = c_2Ebool_2ET ) ),
inference(resolution,[status(thm)],[c_32,c_75472]) ).
tff(c_75594,plain,
ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4') = c_2Ebool_2ET,
inference(demodulation,[status(thm),theory(equality)],[c_75097,c_75563]) ).
tff(c_75637,plain,
( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_4'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_4') )
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_75594,c_160]) ).
tff(c_75681,plain,
ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_4'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1626,c_75637]) ).
tff(c_75833,plain,
( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_4') = '#skF_4' )
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
| ~ ne(ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_75681,c_132]) ).
tff(c_75843,plain,
ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_4') = '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_30,c_1626,c_1626,c_75833]) ).
tff(c_58459,plain,
! [F_1620,F_1621,B_1622,B_1623] :
( mem(ap(F_1620,ap(F_1621,'#skF_4')),B_1622)
| ~ mem(F_1620,arr(B_1623,B_1622))
| ~ mem(F_1621,arr(ty_2Eextreal_2Eextreal,B_1623)) ),
inference(resolution,[status(thm)],[c_57561,c_8]) ).
tff(c_58506,plain,
! [F_1621] :
( mem(ap(c_2Eextreal_2Eextreal__le,ap(F_1621,'#skF_4')),arr(ty_2Eextreal_2Eextreal,bool))
| ~ mem(F_1621,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
inference(resolution,[status(thm)],[c_32,c_58459]) ).
tff(c_75922,plain,
( mem(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),arr(ty_2Eextreal_2Eextreal,bool))
| ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
inference(superposition,[status(thm),theory(equality)],[c_75843,c_58506]) ).
tff(c_76069,plain,
~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)),
inference(splitLeft,[status(thm)],[c_75922]) ).
tff(c_76072,plain,
~ mem(c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))),
inference(resolution,[status(thm)],[c_57467,c_76069]) ).
tff(c_76076,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_36,c_76072]) ).
tff(c_76077,plain,
mem(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),arr(ty_2Eextreal_2Eextreal,bool)),
inference(splitRight,[status(thm)],[c_75922]) ).
tff(c_57499,plain,
! [F_1527] :
( ~ p(ap(F_1527,'#skF_5'))
| ( ap(F_1527,'#skF_5') = c_2Ebool_2ET )
| ~ mem(F_1527,arr(ty_2Eextreal_2Eextreal,bool)) ),
inference(resolution,[status(thm)],[c_57471,c_57390]) ).
tff(c_76103,plain,
( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5'))
| ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2ET ) ),
inference(resolution,[status(thm)],[c_76077,c_57499]) ).
tff(c_76129,plain,
ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2ET,
inference(demodulation,[status(thm),theory(equality)],[c_61570,c_76103]) ).
tff(c_76203,plain,
( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') )
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_76129,c_160]) ).
tff(c_76252,plain,
ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1624,c_76203]) ).
tff(c_76546,plain,
( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_5' )
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ ne(ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_76252,c_132]) ).
tff(c_76556,plain,
ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_5',
inference(demodulation,[status(thm),theory(equality)],[c_30,c_1624,c_1626,c_76546]) ).
tff(c_57350,plain,
p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5')),'#skF_3')),
inference(splitRight,[status(thm)],[c_1636]) ).
tff(c_76564,plain,
p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_76556,c_57350]) ).
tff(c_76566,plain,
p(c_2Ebool_2EF),
inference(demodulation,[status(thm),theory(equality)],[c_69492,c_76564]) ).
tff(c_76568,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_40,c_76566]) ).
tff(c_76570,plain,
~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3')),
inference(splitRight,[status(thm)],[c_1640]) ).
tff(c_76645,plain,
! [F_2032,X_2033,B_2034,A_2035] :
( mem(ap(F_2032,X_2033),B_2034)
| ~ mem(X_2033,A_2035)
| ~ mem(F_2032,arr(A_2035,B_2034)) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_76684,plain,
! [F_2032,B_2034] :
( mem(ap(F_2032,'#skF_4'),B_2034)
| ~ mem(F_2032,arr(ty_2Eextreal_2Eextreal,B_2034)) ),
inference(resolution,[status(thm)],[c_1626,c_76645]) ).
tff(c_79994,plain,
! [V1y_101] :
( ~ mem(V1y_101,ty_2Eextreal_2Eextreal)
| p(ap(ap(c_2Eextreal_2Eextreal__le,V1y_101),V1y_101)) ),
inference(factorization,[status(thm),theory(equality)],[c_158]) ).
tff(c_76809,plain,
! [F_2046,B_2047] :
( mem(ap(F_2046,'#skF_4'),B_2047)
| ~ mem(F_2046,arr(ty_2Eextreal_2Eextreal,B_2047)) ),
inference(resolution,[status(thm)],[c_1626,c_76645]) ).
tff(c_76599,plain,
! [R_2023,Q_2024] :
( ~ p(R_2023)
| ~ p(Q_2024)
| ( R_2023 = Q_2024 )
| ~ mem(R_2023,bool)
| ~ mem(Q_2024,bool) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_76603,plain,
! [Q_2024] :
( ~ p(c_2Ebool_2ET)
| ~ p(Q_2024)
| ( c_2Ebool_2ET = Q_2024 )
| ~ mem(Q_2024,bool) ),
inference(resolution,[status(thm)],[c_26,c_76599]) ).
tff(c_76607,plain,
! [Q_2024] :
( ~ p(Q_2024)
| ( c_2Ebool_2ET = Q_2024 )
| ~ mem(Q_2024,bool) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_76603]) ).
tff(c_77046,plain,
! [F_2074] :
( ~ p(ap(F_2074,'#skF_4'))
| ( ap(F_2074,'#skF_4') = c_2Ebool_2ET )
| ~ mem(F_2074,arr(ty_2Eextreal_2Eextreal,bool)) ),
inference(resolution,[status(thm)],[c_76809,c_76607]) ).
tff(c_87882,plain,
! [F_2400] :
( ~ p(ap(ap(F_2400,'#skF_4'),'#skF_4'))
| ( ap(ap(F_2400,'#skF_4'),'#skF_4') = c_2Ebool_2ET )
| ~ mem(F_2400,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))) ),
inference(resolution,[status(thm)],[c_76684,c_77046]) ).
tff(c_87975,plain,
( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4'))
| ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4') = c_2Ebool_2ET ) ),
inference(resolution,[status(thm)],[c_32,c_87882]) ).
tff(c_87976,plain,
~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4')),
inference(splitLeft,[status(thm)],[c_87975]) ).
tff(c_87979,plain,
~ mem('#skF_4',ty_2Eextreal_2Eextreal),
inference(resolution,[status(thm)],[c_79994,c_87976]) ).
tff(c_87985,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1626,c_87979]) ).
tff(c_87986,plain,
ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4') = c_2Ebool_2ET,
inference(splitRight,[status(thm)],[c_87975]) ).
tff(c_88013,plain,
( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_4'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_4') )
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_87986,c_160]) ).
tff(c_88057,plain,
ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_4'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1626,c_88013]) ).
tff(c_88131,plain,
( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_4') = '#skF_4' )
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
| ~ ne(ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_88057,c_132]) ).
tff(c_88141,plain,
ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_4') = '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_30,c_1626,c_1626,c_88131]) ).
tff(c_79430,plain,
! [F_2199,F_2200,B_2201,B_2202] :
( mem(ap(F_2199,ap(F_2200,'#skF_4')),B_2201)
| ~ mem(F_2199,arr(B_2202,B_2201))
| ~ mem(F_2200,arr(ty_2Eextreal_2Eextreal,B_2202)) ),
inference(resolution,[status(thm)],[c_76809,c_8]) ).
tff(c_79508,plain,
! [F_2200] :
( mem(ap(c_2Eextreal_2Eextreal__le,ap(F_2200,'#skF_4')),arr(ty_2Eextreal_2Eextreal,bool))
| ~ mem(F_2200,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
inference(resolution,[status(thm)],[c_32,c_79430]) ).
tff(c_88173,plain,
( mem(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),arr(ty_2Eextreal_2Eextreal,bool))
| ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
inference(superposition,[status(thm),theory(equality)],[c_88141,c_79508]) ).
tff(c_89048,plain,
~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)),
inference(splitLeft,[status(thm)],[c_88173]) ).
tff(c_89125,plain,
~ mem(c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))),
inference(resolution,[status(thm)],[c_76684,c_89048]) ).
tff(c_89129,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_36,c_89125]) ).
tff(c_89130,plain,
mem(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),arr(ty_2Eextreal_2Eextreal,bool)),
inference(splitRight,[status(thm)],[c_88173]) ).
tff(c_76779,plain,
! [F_2044,B_2045] :
( mem(ap(F_2044,'#skF_3'),B_2045)
| ~ mem(F_2044,arr(ty_2Eextreal_2Eextreal,B_2045)) ),
inference(resolution,[status(thm)],[c_1628,c_76645]) ).
tff(c_76621,plain,
! [Q_2028,R_2029] :
( p(Q_2028)
| p(R_2029)
| ( R_2029 = Q_2028 )
| ~ mem(R_2029,bool)
| ~ mem(Q_2028,bool) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_76623,plain,
! [Q_2028] :
( p(Q_2028)
| p(c_2Ebool_2EF)
| ( c_2Ebool_2EF = Q_2028 )
| ~ mem(Q_2028,bool) ),
inference(resolution,[status(thm)],[c_38,c_76621]) ).
tff(c_76628,plain,
! [Q_2028] :
( p(Q_2028)
| ( c_2Ebool_2EF = Q_2028 )
| ~ mem(Q_2028,bool) ),
inference(negUnitSimplification,[status(thm)],[c_40,c_76623]) ).
tff(c_76805,plain,
! [F_2044] :
( p(ap(F_2044,'#skF_3'))
| ( ap(F_2044,'#skF_3') = c_2Ebool_2EF )
| ~ mem(F_2044,arr(ty_2Eextreal_2Eextreal,bool)) ),
inference(resolution,[status(thm)],[c_76779,c_76628]) ).
tff(c_89159,plain,
( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3'))
| ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3') = c_2Ebool_2EF ) ),
inference(resolution,[status(thm)],[c_89130,c_76805]) ).
tff(c_89180,plain,
ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3') = c_2Ebool_2EF,
inference(negUnitSimplification,[status(thm)],[c_76570,c_89159]) ).
tff(c_76748,plain,
! [F_2040,B_2041] :
( mem(ap(F_2040,'#skF_5'),B_2041)
| ~ mem(F_2040,arr(ty_2Eextreal_2Eextreal,B_2041)) ),
inference(resolution,[status(thm)],[c_1624,c_76645]) ).
tff(c_76774,plain,
! [F_2040] :
( p(ap(F_2040,'#skF_5'))
| ( ap(F_2040,'#skF_5') = c_2Ebool_2EF )
| ~ mem(F_2040,arr(ty_2Eextreal_2Eextreal,bool)) ),
inference(resolution,[status(thm)],[c_76748,c_76628]) ).
tff(c_89177,plain,
( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5'))
| ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2EF ) ),
inference(resolution,[status(thm)],[c_89130,c_76774]) ).
tff(c_89303,plain,
ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2EF,
inference(splitLeft,[status(thm)],[c_89177]) ).
tff(c_89329,plain,
( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2EF),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') )
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_89303,c_160]) ).
tff(c_89372,plain,
ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2EF),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1624,c_89329]) ).
tff(c_89662,plain,
( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_4' )
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ ne(ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_89372,c_130]) ).
tff(c_89672,plain,
ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_30,c_1624,c_1626,c_89662]) ).
tff(c_89680,plain,
p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_89672,c_57350]) ).
tff(c_89682,plain,
p(c_2Ebool_2EF),
inference(demodulation,[status(thm),theory(equality)],[c_89180,c_89680]) ).
tff(c_89684,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_40,c_89682]) ).
tff(c_89685,plain,
p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5')),
inference(splitRight,[status(thm)],[c_89177]) ).
tff(c_76776,plain,
! [F_2040] :
( ~ p(ap(F_2040,'#skF_5'))
| ( ap(F_2040,'#skF_5') = c_2Ebool_2ET )
| ~ mem(F_2040,arr(ty_2Eextreal_2Eextreal,bool)) ),
inference(resolution,[status(thm)],[c_76748,c_76607]) ).
tff(c_89172,plain,
( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5'))
| ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2ET ) ),
inference(resolution,[status(thm)],[c_89130,c_76776]) ).
tff(c_89772,plain,
ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2ET,
inference(demodulation,[status(thm),theory(equality)],[c_89685,c_89172]) ).
tff(c_89801,plain,
( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') )
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_89772,c_160]) ).
tff(c_89844,plain,
ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1624,c_89801]) ).
tff(c_90058,plain,
( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_5' )
| ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
| ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
| ~ ne(ty_2Eextreal_2Eextreal) ),
inference(superposition,[status(thm),theory(equality)],[c_89844,c_132]) ).
tff(c_90068,plain,
ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_5',
inference(demodulation,[status(thm),theory(equality)],[c_30,c_1624,c_1626,c_90058]) ).
tff(c_90076,plain,
p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_90068,c_57350]) ).
tff(c_90079,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_57351,c_90076]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ITP021+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.17/0.35 % Computer : n013.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Thu Aug 3 18:56:17 EDT 2023
% 0.17/0.35 % CPUTime :
% 28.03/13.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.03/13.98
% 28.03/13.98 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 28.20/14.04
% 28.20/14.04 Inference rules
% 28.20/14.04 ----------------------
% 28.20/14.04 #Ref : 4
% 28.20/14.04 #Sup : 20604
% 28.20/14.04 #Fact : 12
% 28.20/14.04 #Define : 0
% 28.20/14.04 #Split : 248
% 28.20/14.04 #Chain : 0
% 28.20/14.04 #Close : 0
% 28.20/14.04
% 28.20/14.04 Ordering : KBO
% 28.20/14.04
% 28.20/14.04 Simplification rules
% 28.20/14.04 ----------------------
% 28.20/14.04 #Subsume : 1616
% 28.20/14.04 #Demod : 9481
% 28.20/14.04 #Tautology : 4060
% 28.20/14.04 #SimpNegUnit : 350
% 28.20/14.04 #BackRed : 291
% 28.20/14.04
% 28.20/14.04 #Partial instantiations: 0
% 28.20/14.04 #Strategies tried : 1
% 28.20/14.04
% 28.20/14.04 Timing (in seconds)
% 28.20/14.04 ----------------------
% 28.20/14.04 Preprocessing : 0.90
% 28.20/14.04 Parsing : 0.26
% 28.20/14.04 CNF conversion : 0.09
% 28.20/14.04 Main loop : 12.01
% 28.20/14.04 Inferencing : 3.24
% 28.20/14.04 Reduction : 4.50
% 28.20/14.04 Demodulation : 3.39
% 28.20/14.04 BG Simplification : 0.29
% 28.20/14.04 Subsumption : 3.09
% 28.20/14.04 Abstraction : 0.23
% 28.20/14.04 MUC search : 0.00
% 28.20/14.04 Cooper : 0.00
% 28.20/14.05 Total : 13.02
% 28.20/14.05 Index Insertion : 0.00
% 28.20/14.05 Index Deletion : 0.00
% 28.20/14.05 Index Matching : 0.00
% 28.20/14.05 BG Taut test : 0.00
%------------------------------------------------------------------------------