TSTP Solution File: ANA002-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ANA002-1 : TPTP v8.1.2. Bugfixed v1.0.1.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n027.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 10:32:44 EDT 2023
% Result : Unsatisfiable 166.52s 150.99s
% Output : CNFRefutation 166.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 29
% Syntax : Number of formulae : 117 ( 39 unt; 11 typ; 0 def)
% Number of atoms : 245 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 245 ( 106 ~; 139 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 7 >; 4 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 88 (; 88 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in_interval > less_than_or_equal > q > #nlpp > k > h > g > f > upper_bound > n0 > lower_bound > l
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(in_interval,type,
in_interval: ( $i * $i * $i ) > $o ).
tff(lower_bound,type,
lower_bound: $i ).
tff(l,type,
l: $i ).
tff(less_than_or_equal,type,
less_than_or_equal: ( $i * $i ) > $o ).
tff(f,type,
f: $i > $i ).
tff(g,type,
g: $i > $i ).
tff(q,type,
q: ( $i * $i ) > $i ).
tff(n0,type,
n0: $i ).
tff(h,type,
h: $i > $i ).
tff(k,type,
k: $i > $i ).
tff(upper_bound,type,
upper_bound: $i ).
tff(f_130,axiom,
less_than_or_equal(n0,f(upper_bound)),
file(unknown,unknown) ).
tff(f_128,axiom,
less_than_or_equal(lower_bound,upper_bound),
file(unknown,unknown) ).
tff(f_129,axiom,
less_than_or_equal(f(lower_bound),n0),
file(unknown,unknown) ).
tff(f_113,axiom,
! [X] :
( less_than_or_equal(X,l)
| ~ less_than_or_equal(X,upper_bound)
| ~ less_than_or_equal(f(X),n0) ),
file(unknown,unknown) ).
tff(f_117,axiom,
! [X] :
( less_than_or_equal(g(X),upper_bound)
| less_than_or_equal(l,X) ),
file(unknown,unknown) ).
tff(f_126,axiom,
! [X] :
( ~ less_than_or_equal(g(X),X)
| less_than_or_equal(l,X) ),
file(unknown,unknown) ).
tff(f_35,axiom,
! [Lower,X,Upper] :
( in_interval(Lower,X,Upper)
| ~ less_than_or_equal(Lower,X)
| ~ less_than_or_equal(X,Upper) ),
file(unknown,unknown) ).
tff(f_121,axiom,
! [X] :
( less_than_or_equal(f(g(X)),n0)
| less_than_or_equal(l,X) ),
file(unknown,unknown) ).
tff(f_83,axiom,
! [X,Y] :
( less_than_or_equal(f(X),n0)
| ~ less_than_or_equal(Y,X)
| ~ less_than_or_equal(f(Y),n0)
| less_than_or_equal(Y,h(X))
| ~ in_interval(lower_bound,X,upper_bound) ),
file(unknown,unknown) ).
tff(f_133,axiom,
! [X] : ~ in_interval(f(X),n0,f(X)),
file(unknown,unknown) ).
tff(f_38,axiom,
! [X] : less_than_or_equal(X,X),
file(unknown,unknown) ).
tff(f_50,axiom,
! [X,Z,Y] :
( less_than_or_equal(X,Z)
| ~ less_than_or_equal(X,Y)
| ~ less_than_or_equal(Y,Z) ),
file(unknown,unknown) ).
tff(f_70,axiom,
! [X] :
( less_than_or_equal(f(X),n0)
| ~ less_than_or_equal(X,h(X))
| ~ in_interval(lower_bound,X,upper_bound) ),
file(unknown,unknown) ).
tff(f_42,axiom,
! [X,Y] :
( less_than_or_equal(X,Y)
| less_than_or_equal(Y,X) ),
file(unknown,unknown) ).
tff(f_104,axiom,
! [X,Y] :
( less_than_or_equal(n0,f(X))
| ~ less_than_or_equal(X,Y)
| ~ less_than_or_equal(n0,f(Y))
| less_than_or_equal(k(X),Y)
| ~ in_interval(lower_bound,X,upper_bound) ),
file(unknown,unknown) ).
tff(f_56,axiom,
! [X,Y] :
( ~ less_than_or_equal(X,q(Y,X))
| less_than_or_equal(X,Y) ),
file(unknown,unknown) ).
tff(f_61,axiom,
! [X,Y] :
( ~ less_than_or_equal(q(X,Y),X)
| less_than_or_equal(Y,X) ),
file(unknown,unknown) ).
tff(f_91,axiom,
! [X] :
( less_than_or_equal(n0,f(X))
| ~ less_than_or_equal(k(X),X)
| ~ in_interval(lower_bound,X,upper_bound) ),
file(unknown,unknown) ).
tff(c_34,plain,
less_than_or_equal(n0,f(upper_bound)),
inference(cnfTransformation,[status(thm)],[f_130]) ).
tff(c_30,plain,
less_than_or_equal(lower_bound,upper_bound),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_32,plain,
less_than_or_equal(f(lower_bound),n0),
inference(cnfTransformation,[status(thm)],[f_129]) ).
tff(c_176,plain,
! [X_45] :
( ~ less_than_or_equal(f(X_45),n0)
| ~ less_than_or_equal(X_45,upper_bound)
| less_than_or_equal(X_45,l) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_188,plain,
( ~ less_than_or_equal(lower_bound,upper_bound)
| less_than_or_equal(lower_bound,l) ),
inference(resolution,[status(thm)],[c_32,c_176]) ).
tff(c_194,plain,
less_than_or_equal(lower_bound,l),
inference(demodulation,[status(thm),theory(equality)],[c_30,c_188]) ).
tff(c_24,plain,
! [X_21] :
( less_than_or_equal(l,X_21)
| less_than_or_equal(g(X_21),upper_bound) ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_57,plain,
! [X_30] :
( less_than_or_equal(l,X_30)
| ~ less_than_or_equal(g(X_30),X_30) ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_70,plain,
less_than_or_equal(l,upper_bound),
inference(resolution,[status(thm)],[c_24,c_57]) ).
tff(c_2,plain,
! [X_2,Upper_3,Lower_1] :
( ~ less_than_or_equal(X_2,Upper_3)
| ~ less_than_or_equal(Lower_1,X_2)
| in_interval(Lower_1,X_2,Upper_3) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_26,plain,
! [X_22] :
( less_than_or_equal(l,X_22)
| less_than_or_equal(f(g(X_22)),n0) ),
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_3199,plain,
! [X_118] :
( ~ less_than_or_equal(g(X_118),upper_bound)
| less_than_or_equal(g(X_118),l)
| less_than_or_equal(l,X_118) ),
inference(resolution,[status(thm)],[c_26,c_176]) ).
tff(c_3259,plain,
! [X_21] :
( less_than_or_equal(g(X_21),l)
| less_than_or_equal(l,X_21) ),
inference(resolution,[status(thm)],[c_24,c_3199]) ).
tff(c_476,plain,
! [X_63,Y_64] :
( ~ in_interval(lower_bound,X_63,upper_bound)
| less_than_or_equal(Y_64,h(X_63))
| ~ less_than_or_equal(f(Y_64),n0)
| ~ less_than_or_equal(Y_64,X_63)
| less_than_or_equal(f(X_63),n0) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_6582,plain,
! [X_154,X_155] :
( ~ in_interval(lower_bound,X_154,upper_bound)
| less_than_or_equal(g(X_155),h(X_154))
| ~ less_than_or_equal(g(X_155),X_154)
| less_than_or_equal(f(X_154),n0)
| less_than_or_equal(l,X_155) ),
inference(resolution,[status(thm)],[c_26,c_476]) ).
tff(c_28,plain,
! [X_23] :
( less_than_or_equal(l,X_23)
| ~ less_than_or_equal(g(X_23),X_23) ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_20812,plain,
! [X_284] :
( ~ in_interval(lower_bound,X_284,upper_bound)
| ~ less_than_or_equal(g(h(X_284)),X_284)
| less_than_or_equal(f(X_284),n0)
| less_than_or_equal(l,h(X_284)) ),
inference(resolution,[status(thm)],[c_6582,c_28]) ).
tff(c_21196,plain,
( ~ in_interval(lower_bound,l,upper_bound)
| less_than_or_equal(f(l),n0)
| less_than_or_equal(l,h(l)) ),
inference(resolution,[status(thm)],[c_3259,c_20812]) ).
tff(c_91133,plain,
~ in_interval(lower_bound,l,upper_bound),
inference(splitLeft,[status(thm)],[c_21196]) ).
tff(c_91136,plain,
( ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(lower_bound,l) ),
inference(resolution,[status(thm)],[c_2,c_91133]) ).
tff(c_91140,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_194,c_70,c_91136]) ).
tff(c_91141,plain,
( less_than_or_equal(l,h(l))
| less_than_or_equal(f(l),n0) ),
inference(splitRight,[status(thm)],[c_21196]) ).
tff(c_91143,plain,
less_than_or_equal(f(l),n0),
inference(splitLeft,[status(thm)],[c_91141]) ).
tff(c_260,plain,
! [X_49,Upper_50,Lower_51] :
( ~ less_than_or_equal(X_49,Upper_50)
| ~ less_than_or_equal(Lower_51,X_49)
| in_interval(Lower_51,X_49,Upper_50) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_36,plain,
! [X_24] : ~ in_interval(f(X_24),n0,f(X_24)),
inference(cnfTransformation,[status(thm)],[f_133]) ).
tff(c_264,plain,
! [X_24] :
( ~ less_than_or_equal(n0,f(X_24))
| ~ less_than_or_equal(f(X_24),n0) ),
inference(resolution,[status(thm)],[c_260,c_36]) ).
tff(c_91657,plain,
~ less_than_or_equal(n0,f(l)),
inference(resolution,[status(thm)],[c_91143,c_264]) ).
tff(c_91142,plain,
in_interval(lower_bound,l,upper_bound),
inference(splitRight,[status(thm)],[c_21196]) ).
tff(c_4,plain,
! [X_4] : less_than_or_equal(X_4,X_4),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_98,plain,
! [Y_39,Z_40,X_41] :
( ~ less_than_or_equal(Y_39,Z_40)
| ~ less_than_or_equal(X_41,Y_39)
| less_than_or_equal(X_41,Z_40) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_129,plain,
! [X_41] :
( ~ less_than_or_equal(X_41,n0)
| less_than_or_equal(X_41,f(upper_bound)) ),
inference(resolution,[status(thm)],[c_34,c_98]) ).
tff(c_4505,plain,
! [X_133] :
( ~ in_interval(lower_bound,X_133,upper_bound)
| less_than_or_equal(lower_bound,h(X_133))
| ~ less_than_or_equal(lower_bound,X_133)
| less_than_or_equal(f(X_133),n0) ),
inference(resolution,[status(thm)],[c_32,c_476]) ).
tff(c_18969,plain,
! [X_274] :
( ~ less_than_or_equal(n0,f(X_274))
| ~ in_interval(lower_bound,X_274,upper_bound)
| less_than_or_equal(lower_bound,h(X_274))
| ~ less_than_or_equal(lower_bound,X_274) ),
inference(resolution,[status(thm)],[c_4505,c_264]) ).
tff(c_19052,plain,
( ~ in_interval(lower_bound,upper_bound,upper_bound)
| less_than_or_equal(lower_bound,h(upper_bound))
| ~ less_than_or_equal(lower_bound,upper_bound)
| ~ less_than_or_equal(n0,n0) ),
inference(resolution,[status(thm)],[c_129,c_18969]) ).
tff(c_19099,plain,
( ~ in_interval(lower_bound,upper_bound,upper_bound)
| less_than_or_equal(lower_bound,h(upper_bound)) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_30,c_19052]) ).
tff(c_19103,plain,
~ in_interval(lower_bound,upper_bound,upper_bound),
inference(splitLeft,[status(thm)],[c_19099]) ).
tff(c_19106,plain,
( ~ less_than_or_equal(upper_bound,upper_bound)
| ~ less_than_or_equal(lower_bound,upper_bound) ),
inference(resolution,[status(thm)],[c_2,c_19103]) ).
tff(c_19110,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_30,c_4,c_19106]) ).
tff(c_19112,plain,
in_interval(lower_bound,upper_bound,upper_bound),
inference(splitRight,[status(thm)],[c_19099]) ).
tff(c_21136,plain,
( ~ in_interval(lower_bound,upper_bound,upper_bound)
| less_than_or_equal(f(upper_bound),n0)
| less_than_or_equal(l,h(upper_bound)) ),
inference(resolution,[status(thm)],[c_24,c_20812]) ).
tff(c_21239,plain,
( less_than_or_equal(f(upper_bound),n0)
| less_than_or_equal(l,h(upper_bound)) ),
inference(demodulation,[status(thm),theory(equality)],[c_19112,c_21136]) ).
tff(c_21328,plain,
less_than_or_equal(l,h(upper_bound)),
inference(splitLeft,[status(thm)],[c_21239]) ).
tff(c_8,plain,
! [Y_9,Z_8,X_7] :
( ~ less_than_or_equal(Y_9,Z_8)
| ~ less_than_or_equal(X_7,Y_9)
| less_than_or_equal(X_7,Z_8) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_21398,plain,
! [X_285] :
( ~ less_than_or_equal(X_285,l)
| less_than_or_equal(X_285,h(upper_bound)) ),
inference(resolution,[status(thm)],[c_21328,c_8]) ).
tff(c_14,plain,
! [X_14] :
( ~ in_interval(lower_bound,X_14,upper_bound)
| ~ less_than_or_equal(X_14,h(X_14))
| less_than_or_equal(f(X_14),n0) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_21439,plain,
( ~ in_interval(lower_bound,upper_bound,upper_bound)
| less_than_or_equal(f(upper_bound),n0)
| ~ less_than_or_equal(upper_bound,l) ),
inference(resolution,[status(thm)],[c_21398,c_14]) ).
tff(c_21482,plain,
( less_than_or_equal(f(upper_bound),n0)
| ~ less_than_or_equal(upper_bound,l) ),
inference(demodulation,[status(thm),theory(equality)],[c_19112,c_21439]) ).
tff(c_21578,plain,
~ less_than_or_equal(upper_bound,l),
inference(splitLeft,[status(thm)],[c_21482]) ).
tff(c_6,plain,
! [Y_6,X_5] :
( less_than_or_equal(Y_6,X_5)
| less_than_or_equal(X_5,Y_6) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_191,plain,
! [X_45] :
( ~ less_than_or_equal(X_45,upper_bound)
| less_than_or_equal(X_45,l)
| less_than_or_equal(n0,f(X_45)) ),
inference(resolution,[status(thm)],[c_6,c_176]) ).
tff(c_392,plain,
! [X_57,Y_58] :
( ~ in_interval(lower_bound,X_57,upper_bound)
| less_than_or_equal(k(X_57),Y_58)
| ~ less_than_or_equal(n0,f(Y_58))
| ~ less_than_or_equal(X_57,Y_58)
| less_than_or_equal(n0,f(X_57)) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_7382,plain,
! [X_162,X_163,Y_164] :
( ~ less_than_or_equal(X_162,k(X_163))
| less_than_or_equal(X_162,Y_164)
| ~ in_interval(lower_bound,X_163,upper_bound)
| ~ less_than_or_equal(n0,f(Y_164))
| ~ less_than_or_equal(X_163,Y_164)
| less_than_or_equal(n0,f(X_163)) ),
inference(resolution,[status(thm)],[c_392,c_8]) ).
tff(c_28589,plain,
! [Y_327,Y_328,X_329] :
( less_than_or_equal(Y_327,Y_328)
| ~ in_interval(lower_bound,X_329,upper_bound)
| ~ less_than_or_equal(n0,f(Y_328))
| ~ less_than_or_equal(X_329,Y_328)
| less_than_or_equal(n0,f(X_329))
| less_than_or_equal(k(X_329),Y_327) ),
inference(resolution,[status(thm)],[c_6,c_7382]) ).
tff(c_694583,plain,
! [Y_1700,X_1701,X_1702] :
( less_than_or_equal(Y_1700,X_1701)
| ~ in_interval(lower_bound,X_1702,upper_bound)
| ~ less_than_or_equal(X_1702,X_1701)
| less_than_or_equal(n0,f(X_1702))
| less_than_or_equal(k(X_1702),Y_1700)
| ~ less_than_or_equal(X_1701,upper_bound)
| less_than_or_equal(X_1701,l) ),
inference(resolution,[status(thm)],[c_191,c_28589]) ).
tff(c_696179,plain,
! [Y_1700] :
( less_than_or_equal(Y_1700,upper_bound)
| ~ in_interval(lower_bound,l,upper_bound)
| less_than_or_equal(n0,f(l))
| less_than_or_equal(k(l),Y_1700)
| ~ less_than_or_equal(upper_bound,upper_bound)
| less_than_or_equal(upper_bound,l) ),
inference(resolution,[status(thm)],[c_70,c_694583]) ).
tff(c_697875,plain,
! [Y_1700] :
( less_than_or_equal(Y_1700,upper_bound)
| less_than_or_equal(n0,f(l))
| less_than_or_equal(k(l),Y_1700)
| less_than_or_equal(upper_bound,l) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_91142,c_696179]) ).
tff(c_697893,plain,
! [Y_1703] :
( less_than_or_equal(Y_1703,upper_bound)
| less_than_or_equal(k(l),Y_1703) ),
inference(negUnitSimplification,[status(thm)],[c_21578,c_91657,c_697875]) ).
tff(c_10,plain,
! [X_10,Y_11] :
( less_than_or_equal(X_10,Y_11)
| ~ less_than_or_equal(X_10,q(Y_11,X_10)) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_702774,plain,
! [Y_1709] :
( less_than_or_equal(k(l),Y_1709)
| less_than_or_equal(q(Y_1709,k(l)),upper_bound) ),
inference(resolution,[status(thm)],[c_697893,c_10]) ).
tff(c_73,plain,
! [Y_31,X_32] :
( less_than_or_equal(Y_31,X_32)
| ~ less_than_or_equal(q(X_32,Y_31),X_32) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_82,plain,
! [Y_31,X_5] :
( less_than_or_equal(Y_31,X_5)
| less_than_or_equal(X_5,q(X_5,Y_31)) ),
inference(resolution,[status(thm)],[c_6,c_73]) ).
tff(c_8064,plain,
! [X_172,Y_173] :
( less_than_or_equal(k(X_172),Y_173)
| ~ in_interval(lower_bound,X_172,upper_bound)
| ~ less_than_or_equal(n0,f(q(Y_173,k(X_172))))
| ~ less_than_or_equal(X_172,q(Y_173,k(X_172)))
| less_than_or_equal(n0,f(X_172)) ),
inference(resolution,[status(thm)],[c_392,c_10]) ).
tff(c_54579,plain,
! [X_447,Y_448] :
( less_than_or_equal(k(X_447),Y_448)
| ~ in_interval(lower_bound,X_447,upper_bound)
| ~ less_than_or_equal(X_447,q(Y_448,k(X_447)))
| less_than_or_equal(n0,f(X_447))
| ~ less_than_or_equal(q(Y_448,k(X_447)),upper_bound)
| less_than_or_equal(q(Y_448,k(X_447)),l) ),
inference(resolution,[status(thm)],[c_191,c_8064]) ).
tff(c_54825,plain,
! [X_5] :
( ~ in_interval(lower_bound,X_5,upper_bound)
| less_than_or_equal(n0,f(X_5))
| ~ less_than_or_equal(q(X_5,k(X_5)),upper_bound)
| less_than_or_equal(q(X_5,k(X_5)),l)
| less_than_or_equal(k(X_5),X_5) ),
inference(resolution,[status(thm)],[c_82,c_54579]) ).
tff(c_702780,plain,
( ~ in_interval(lower_bound,l,upper_bound)
| less_than_or_equal(n0,f(l))
| less_than_or_equal(q(l,k(l)),l)
| less_than_or_equal(k(l),l) ),
inference(resolution,[status(thm)],[c_702774,c_54825]) ).
tff(c_703083,plain,
( less_than_or_equal(n0,f(l))
| less_than_or_equal(q(l,k(l)),l)
| less_than_or_equal(k(l),l) ),
inference(demodulation,[status(thm),theory(equality)],[c_91142,c_702780]) ).
tff(c_703084,plain,
( less_than_or_equal(q(l,k(l)),l)
| less_than_or_equal(k(l),l) ),
inference(negUnitSimplification,[status(thm)],[c_91657,c_703083]) ).
tff(c_719444,plain,
less_than_or_equal(k(l),l),
inference(splitLeft,[status(thm)],[c_703084]) ).
tff(c_18,plain,
! [X_17] :
( ~ in_interval(lower_bound,X_17,upper_bound)
| ~ less_than_or_equal(k(X_17),X_17)
| less_than_or_equal(n0,f(X_17)) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_719719,plain,
( ~ in_interval(lower_bound,l,upper_bound)
| less_than_or_equal(n0,f(l)) ),
inference(resolution,[status(thm)],[c_719444,c_18]) ).
tff(c_720004,plain,
less_than_or_equal(n0,f(l)),
inference(demodulation,[status(thm),theory(equality)],[c_91142,c_719719]) ).
tff(c_720006,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_91657,c_720004]) ).
tff(c_720008,plain,
~ less_than_or_equal(k(l),l),
inference(splitRight,[status(thm)],[c_703084]) ).
tff(c_720007,plain,
less_than_or_equal(q(l,k(l)),l),
inference(splitRight,[status(thm)],[c_703084]) ).
tff(c_12,plain,
! [Y_13,X_12] :
( less_than_or_equal(Y_13,X_12)
| ~ less_than_or_equal(q(X_12,Y_13),X_12) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_720649,plain,
less_than_or_equal(k(l),l),
inference(resolution,[status(thm)],[c_720007,c_12]) ).
tff(c_720930,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_720008,c_720649]) ).
tff(c_720932,plain,
~ less_than_or_equal(f(l),n0),
inference(splitRight,[status(thm)],[c_91141]) ).
tff(c_720931,plain,
less_than_or_equal(l,h(l)),
inference(splitRight,[status(thm)],[c_91141]) ).
tff(c_721020,plain,
( ~ in_interval(lower_bound,l,upper_bound)
| less_than_or_equal(f(l),n0) ),
inference(resolution,[status(thm)],[c_720931,c_14]) ).
tff(c_721104,plain,
less_than_or_equal(f(l),n0),
inference(demodulation,[status(thm),theory(equality)],[c_91142,c_721020]) ).
tff(c_721328,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_720932,c_721104]) ).
tff(c_721329,plain,
less_than_or_equal(f(upper_bound),n0),
inference(splitRight,[status(thm)],[c_21482]) ).
tff(c_721724,plain,
~ less_than_or_equal(n0,f(upper_bound)),
inference(resolution,[status(thm)],[c_721329,c_264]) ).
tff(c_721764,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_34,c_721724]) ).
tff(c_721765,plain,
less_than_or_equal(f(upper_bound),n0),
inference(splitRight,[status(thm)],[c_21239]) ).
tff(c_721807,plain,
~ less_than_or_equal(n0,f(upper_bound)),
inference(resolution,[status(thm)],[c_721765,c_264]) ).
tff(c_721850,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_34,c_721807]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ANA002-1 : TPTP v8.1.2. Bugfixed v1.0.1.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 15:50:24 EDT 2023
% 0.13/0.35 % CPUTime :
% 166.52/150.99 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 166.52/151.00
% 166.52/151.00 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 166.52/151.05
% 166.52/151.05 Inference rules
% 166.52/151.05 ----------------------
% 166.52/151.05 #Ref : 0
% 166.52/151.05 #Sup : 173655
% 166.52/151.05 #Fact : 326
% 166.52/151.05 #Define : 0
% 166.52/151.05 #Split : 53
% 166.52/151.05 #Chain : 0
% 166.52/151.05 #Close : 0
% 166.52/151.05
% 166.52/151.05 Ordering : KBO
% 166.52/151.05
% 166.52/151.05 Simplification rules
% 166.52/151.05 ----------------------
% 166.52/151.05 #Subsume : 92620
% 166.52/151.05 #Demod : 80671
% 166.52/151.05 #Tautology : 38289
% 166.52/151.05 #SimpNegUnit : 6017
% 166.52/151.05 #BackRed : 0
% 166.52/151.05
% 166.52/151.05 #Partial instantiations: 0
% 166.52/151.05 #Strategies tried : 1
% 166.52/151.05
% 166.52/151.05 Timing (in seconds)
% 166.52/151.05 ----------------------
% 166.52/151.05 Preprocessing : 0.44
% 166.52/151.05 Parsing : 0.24
% 166.52/151.05 CNF conversion : 0.03
% 166.52/151.05 Main loop : 149.55
% 166.52/151.06 Inferencing : 7.14
% 166.52/151.06 Reduction : 35.40
% 166.52/151.06 Demodulation : 25.36
% 166.52/151.06 BG Simplification : 0.44
% 166.52/151.06 Subsumption : 93.35
% 166.52/151.06 Abstraction : 1.01
% 166.52/151.06 MUC search : 0.00
% 166.52/151.06 Cooper : 0.00
% 166.52/151.06 Total : 150.07
% 166.52/151.06 Index Insertion : 0.00
% 166.52/151.06 Index Deletion : 0.00
% 166.52/151.06 Index Matching : 0.00
% 166.52/151.06 BG Taut test : 0.00
%------------------------------------------------------------------------------