TSTP Solution File: ANA003-4 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ANA003-4 : TPTP v8.1.2. Released v1.0.0.
% 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 : n031.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 10:32:45 EDT 2023
% Result : Unsatisfiable 4.90s 2.18s
% Output : CNFRefutation 4.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 26
% Syntax : Number of formulae : 58 ( 13 unt; 14 typ; 0 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 82 ( 36 ~; 46 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 11 >; 3 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 50 (; 50 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ less_or_equal > minimum > add > #nlpp > xs > negate > half > g > f > delta_2 > delta_1 > absolute > n0 > epsilon_0 > a_real_number
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(minimum,type,
minimum: ( $i * $i ) > $i ).
tff(less_or_equal,type,
less_or_equal: ( $i * $i ) > $o ).
tff(epsilon_0,type,
epsilon_0: $i ).
tff(half,type,
half: $i > $i ).
tff(xs,type,
xs: $i > $i ).
tff(f,type,
f: $i > $i ).
tff(delta_2,type,
delta_2: $i > $i ).
tff(g,type,
g: $i > $i ).
tff(absolute,type,
absolute: $i > $i ).
tff(delta_1,type,
delta_1: $i > $i ).
tff(add,type,
add: ( $i * $i ) > $i ).
tff(n0,type,
n0: $i ).
tff(negate,type,
negate: $i > $i ).
tff(a_real_number,type,
a_real_number: $i ).
tff(f_94,axiom,
~ less_or_equal(epsilon_0,n0),
file(unknown,unknown) ).
tff(f_91,axiom,
! [Epsilon,Z] :
( less_or_equal(Epsilon,n0)
| ~ less_or_equal(absolute(add(Z,negate(a_real_number))),delta_2(Epsilon))
| less_or_equal(absolute(add(g(Z),negate(g(a_real_number)))),Epsilon) ),
file(unknown,unknown) ).
tff(f_57,axiom,
! [X,Z,Y] :
( ~ less_or_equal(X,half(Z))
| ~ less_or_equal(Y,half(Z))
| less_or_equal(add(X,Y),Z) ),
file(unknown,unknown) ).
tff(f_105,axiom,
! [Delta] :
( less_or_equal(Delta,n0)
| ~ less_or_equal(add(absolute(add(f(xs(Delta)),negate(f(a_real_number)))),absolute(add(g(xs(Delta)),negate(g(a_real_number))))),epsilon_0) ),
file(unknown,unknown) ).
tff(f_63,axiom,
! [X] :
( less_or_equal(X,n0)
| ~ less_or_equal(half(X),n0) ),
file(unknown,unknown) ).
tff(f_99,axiom,
! [Delta] :
( less_or_equal(Delta,n0)
| less_or_equal(absolute(add(xs(Delta),negate(a_real_number))),Delta) ),
file(unknown,unknown) ).
tff(f_34,axiom,
! [Z,X,Y] :
( ~ less_or_equal(Z,minimum(X,Y))
| less_or_equal(Z,X) ),
file(unknown,unknown) ).
tff(f_40,axiom,
! [Z,X,Y] :
( ~ less_or_equal(Z,minimum(X,Y))
| less_or_equal(Z,Y) ),
file(unknown,unknown) ).
tff(f_83,axiom,
! [Epsilon,Z] :
( less_or_equal(Epsilon,n0)
| ~ less_or_equal(absolute(add(Z,negate(a_real_number))),delta_1(Epsilon))
| less_or_equal(absolute(add(f(Z),negate(f(a_real_number)))),Epsilon) ),
file(unknown,unknown) ).
tff(f_48,axiom,
! [X,Y] :
( less_or_equal(X,n0)
| less_or_equal(Y,n0)
| ~ less_or_equal(minimum(X,Y),n0) ),
file(unknown,unknown) ).
tff(f_69,axiom,
! [Epsilon] :
( less_or_equal(Epsilon,n0)
| ~ less_or_equal(delta_1(Epsilon),n0) ),
file(unknown,unknown) ).
tff(f_75,axiom,
! [Epsilon] :
( less_or_equal(Epsilon,n0)
| ~ less_or_equal(delta_2(Epsilon),n0) ),
file(unknown,unknown) ).
tff(c_20,plain,
~ less_or_equal(epsilon_0,n0),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_18,plain,
! [Z_18,Epsilon_17] :
( less_or_equal(absolute(add(g(Z_18),negate(g(a_real_number)))),Epsilon_17)
| ~ less_or_equal(absolute(add(Z_18,negate(a_real_number))),delta_2(Epsilon_17))
| less_or_equal(Epsilon_17,n0) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_8,plain,
! [X_9,Y_11,Z_10] :
( less_or_equal(add(X_9,Y_11),Z_10)
| ~ less_or_equal(Y_11,half(Z_10))
| ~ less_or_equal(X_9,half(Z_10)) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_223,plain,
! [Delta_64] :
( ~ less_or_equal(add(absolute(add(f(xs(Delta_64)),negate(f(a_real_number)))),absolute(add(g(xs(Delta_64)),negate(g(a_real_number))))),epsilon_0)
| less_or_equal(Delta_64,n0) ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_681,plain,
! [Delta_115] :
( less_or_equal(Delta_115,n0)
| ~ less_or_equal(absolute(add(g(xs(Delta_115)),negate(g(a_real_number)))),half(epsilon_0))
| ~ less_or_equal(absolute(add(f(xs(Delta_115)),negate(f(a_real_number)))),half(epsilon_0)) ),
inference(resolution,[status(thm)],[c_8,c_223]) ).
tff(c_695,plain,
! [Delta_115] :
( less_or_equal(Delta_115,n0)
| ~ less_or_equal(absolute(add(f(xs(Delta_115)),negate(f(a_real_number)))),half(epsilon_0))
| ~ less_or_equal(absolute(add(xs(Delta_115),negate(a_real_number))),delta_2(half(epsilon_0)))
| less_or_equal(half(epsilon_0),n0) ),
inference(resolution,[status(thm)],[c_18,c_681]) ).
tff(c_1119,plain,
less_or_equal(half(epsilon_0),n0),
inference(splitLeft,[status(thm)],[c_695]) ).
tff(c_10,plain,
! [X_12] :
( ~ less_or_equal(half(X_12),n0)
| less_or_equal(X_12,n0) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_1122,plain,
less_or_equal(epsilon_0,n0),
inference(resolution,[status(thm)],[c_1119,c_10]) ).
tff(c_1126,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20,c_1122]) ).
tff(c_1128,plain,
~ less_or_equal(half(epsilon_0),n0),
inference(splitRight,[status(thm)],[c_695]) ).
tff(c_31,plain,
! [Delta_32] :
( less_or_equal(absolute(add(xs(Delta_32),negate(a_real_number))),Delta_32)
| less_or_equal(Delta_32,n0) ),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_2,plain,
! [Z_1,X_2,Y_3] :
( less_or_equal(Z_1,X_2)
| ~ less_or_equal(Z_1,minimum(X_2,Y_3)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_40,plain,
! [X_2,Y_3] :
( less_or_equal(absolute(add(xs(minimum(X_2,Y_3)),negate(a_real_number))),X_2)
| less_or_equal(minimum(X_2,Y_3),n0) ),
inference(resolution,[status(thm)],[c_31,c_2]) ).
tff(c_4,plain,
! [Z_4,Y_6,X_5] :
( less_or_equal(Z_4,Y_6)
| ~ less_or_equal(Z_4,minimum(X_5,Y_6)) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_41,plain,
! [X_5,Y_6] :
( less_or_equal(absolute(add(xs(minimum(X_5,Y_6)),negate(a_real_number))),Y_6)
| less_or_equal(minimum(X_5,Y_6),n0) ),
inference(resolution,[status(thm)],[c_31,c_4]) ).
tff(c_16,plain,
! [Z_16,Epsilon_15] :
( less_or_equal(absolute(add(f(Z_16),negate(f(a_real_number)))),Epsilon_15)
| ~ less_or_equal(absolute(add(Z_16,negate(a_real_number))),delta_1(Epsilon_15))
| less_or_equal(Epsilon_15,n0) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_1129,plain,
! [Delta_154] :
( less_or_equal(Delta_154,n0)
| ~ less_or_equal(absolute(add(f(xs(Delta_154)),negate(f(a_real_number)))),half(epsilon_0))
| ~ less_or_equal(absolute(add(xs(Delta_154),negate(a_real_number))),delta_2(half(epsilon_0))) ),
inference(splitRight,[status(thm)],[c_695]) ).
tff(c_1140,plain,
! [Delta_154] :
( less_or_equal(Delta_154,n0)
| ~ less_or_equal(absolute(add(xs(Delta_154),negate(a_real_number))),delta_2(half(epsilon_0)))
| ~ less_or_equal(absolute(add(xs(Delta_154),negate(a_real_number))),delta_1(half(epsilon_0)))
| less_or_equal(half(epsilon_0),n0) ),
inference(resolution,[status(thm)],[c_16,c_1129]) ).
tff(c_1189,plain,
! [Delta_160] :
( less_or_equal(Delta_160,n0)
| ~ less_or_equal(absolute(add(xs(Delta_160),negate(a_real_number))),delta_2(half(epsilon_0)))
| ~ less_or_equal(absolute(add(xs(Delta_160),negate(a_real_number))),delta_1(half(epsilon_0))) ),
inference(negUnitSimplification,[status(thm)],[c_1128,c_1140]) ).
tff(c_1291,plain,
! [X_161] :
( ~ less_or_equal(absolute(add(xs(minimum(X_161,delta_2(half(epsilon_0)))),negate(a_real_number))),delta_1(half(epsilon_0)))
| less_or_equal(minimum(X_161,delta_2(half(epsilon_0))),n0) ),
inference(resolution,[status(thm)],[c_41,c_1189]) ).
tff(c_1341,plain,
less_or_equal(minimum(delta_1(half(epsilon_0)),delta_2(half(epsilon_0))),n0),
inference(resolution,[status(thm)],[c_40,c_1291]) ).
tff(c_6,plain,
! [X_7,Y_8] :
( ~ less_or_equal(minimum(X_7,Y_8),n0)
| less_or_equal(Y_8,n0)
| less_or_equal(X_7,n0) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_1345,plain,
( less_or_equal(delta_2(half(epsilon_0)),n0)
| less_or_equal(delta_1(half(epsilon_0)),n0) ),
inference(resolution,[status(thm)],[c_1341,c_6]) ).
tff(c_1378,plain,
less_or_equal(delta_1(half(epsilon_0)),n0),
inference(splitLeft,[status(thm)],[c_1345]) ).
tff(c_12,plain,
! [Epsilon_13] :
( ~ less_or_equal(delta_1(Epsilon_13),n0)
| less_or_equal(Epsilon_13,n0) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_1381,plain,
less_or_equal(half(epsilon_0),n0),
inference(resolution,[status(thm)],[c_1378,c_12]) ).
tff(c_1385,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1128,c_1381]) ).
tff(c_1386,plain,
less_or_equal(delta_2(half(epsilon_0)),n0),
inference(splitRight,[status(thm)],[c_1345]) ).
tff(c_14,plain,
! [Epsilon_14] :
( ~ less_or_equal(delta_2(Epsilon_14),n0)
| less_or_equal(Epsilon_14,n0) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_1390,plain,
less_or_equal(half(epsilon_0),n0),
inference(resolution,[status(thm)],[c_1386,c_14]) ).
tff(c_1394,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1128,c_1390]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : ANA003-4 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.15 % 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
% 0.15/0.36 % Computer : n031.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 15:50:44 EDT 2023
% 0.15/0.37 % CPUTime :
% 4.90/2.18 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.90/2.19
% 4.90/2.19 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.90/2.22
% 4.90/2.22 Inference rules
% 4.90/2.22 ----------------------
% 4.90/2.23 #Ref : 0
% 4.90/2.23 #Sup : 302
% 4.90/2.23 #Fact : 0
% 4.90/2.23 #Define : 0
% 4.90/2.23 #Split : 3
% 4.90/2.23 #Chain : 0
% 4.90/2.23 #Close : 0
% 4.90/2.23
% 4.90/2.23 Ordering : KBO
% 4.90/2.23
% 4.90/2.23 Simplification rules
% 4.90/2.23 ----------------------
% 4.90/2.23 #Subsume : 0
% 4.90/2.23 #Demod : 0
% 4.90/2.23 #Tautology : 0
% 4.90/2.23 #SimpNegUnit : 4
% 4.90/2.23 #BackRed : 0
% 4.90/2.23
% 4.90/2.23 #Partial instantiations: 0
% 4.90/2.23 #Strategies tried : 1
% 4.90/2.23
% 4.90/2.23 Timing (in seconds)
% 4.90/2.23 ----------------------
% 4.90/2.23 Preprocessing : 0.44
% 4.90/2.23 Parsing : 0.24
% 4.90/2.23 CNF conversion : 0.02
% 4.90/2.23 Main loop : 0.71
% 4.90/2.23 Inferencing : 0.33
% 4.90/2.23 Reduction : 0.09
% 4.90/2.23 Demodulation : 0.04
% 4.90/2.23 BG Simplification : 0.03
% 4.90/2.23 Subsumption : 0.21
% 4.90/2.23 Abstraction : 0.03
% 4.90/2.23 MUC search : 0.00
% 4.90/2.23 Cooper : 0.00
% 4.90/2.23 Total : 1.21
% 4.90/2.23 Index Insertion : 0.00
% 4.90/2.23 Index Deletion : 0.00
% 4.90/2.23 Index Matching : 0.00
% 4.90/2.23 BG Taut test : 0.00
%------------------------------------------------------------------------------