TSTP Solution File: ARI616_1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ARI616_1 : TPTP v8.1.2. Released v5.1.0.
% 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 : n016.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 10:34:07 EDT 2023
% Result : Theorem 3.02s 1.73s
% Output : CNFRefutation 3.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 10 unt; 6 typ; 0 def)
% Number of atoms : 24 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 4 |; 2 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 56 ( 14 atm; 22 fun; 0 num; 20 var)
% Number of types : 2 ( 0 usr; 1 ari)
% Number of type conns : 3 ( 1 >; 2 *; 0 +; 0 <<)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 20 (; 19 !; 1 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
%$ p > #nlpp
%Foreground sorts:
%Background operators:
tff('#skF_5',type,
'#skF_5': $int ).
tff('#skF_4',type,
'#skF_4': $int ).
tff('#skF_2',type,
'#skF_2': $int ).
tff('#skF_3',type,
'#skF_3': $int ).
tff('#skF_1',type,
'#skF_1': $int ).
%Foreground operators:
tff(p,type,
p: ( $int * $int * $int ) > $o ).
tff(f_42,negated_conjecture,
~ ( ! [Xa: $int,Ya: $int,Za: $int] :
( ( $lesseq($sum(Ya,$uminus(Za)),Xa)
& $lesseq(Xa,$sum(Ya,Za)) )
<=> p(Xa,Ya,Za) )
=> ! [Y1a: $int,Z1a: $int,Y2a: $int,Z2a: $int] :
( ? [Xa: $int] :
( p(Xa,Y1a,Z1a)
& p(Xa,Y2a,Z2a) )
=> $lesseq($sum(Y1a,$uminus(Y2a)),$sum(Z1a,Z2a)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_of_radii_gt_distance_of_centers) ).
tff(c_45,plain,
p('#skF_5','#skF_3','#skF_4'),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_9,plain,
! [X_1a: $int,Y_2a: $int,Z_3a: $int] :
( ~ p(X_1a,Y_2a,Z_3a)
| $lesseq(X_1a,$sum(Y_2a,Z_3a)) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_14,plain,
! [X_1a: $int,Y_2a: $int,Z_3a: $int] :
( ~ p(X_1a,Y_2a,Z_3a)
| ~ $less($sum(Y_2a,Z_3a),X_1a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_9]) ).
tff(c_55,plain,
~ $less($sum('#skF_3','#skF_4'),'#skF_5'),
inference(resolution,[status(thm)],[c_45,c_14]) ).
tff(c_57,plain,
~ $less($sum('#skF_4','#skF_3'),'#skF_5'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_55]) ).
tff(c_32,plain,
p('#skF_5','#skF_1','#skF_2'),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_11,plain,
! [X_1a: $int,Y_2a: $int,Z_3a: $int] :
( ~ p(X_1a,Y_2a,Z_3a)
| $lesseq($sum(Y_2a,$uminus(Z_3a)),X_1a) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_13,plain,
! [X_1a: $int,Y_2a: $int,Z_3a: $int] :
( ~ p(X_1a,Y_2a,Z_3a)
| ~ $less($sum(X_1a,Z_3a),Y_2a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_11]) ).
tff(c_39,plain,
~ $less($sum('#skF_5','#skF_2'),'#skF_1'),
inference(resolution,[status(thm)],[c_32,c_13]) ).
tff(c_41,plain,
~ $less($sum('#skF_2','#skF_5'),'#skF_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_39]) ).
tff(c_1,plain,
~ $lesseq($sum('#skF_1',$uminus('#skF_3')),$sum('#skF_2','#skF_4')),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_2,plain,
$less($sum('#skF_4',$sum('#skF_3','#skF_2')),'#skF_1'),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_1]) ).
tff(c_25,plain,
$less($sum('#skF_2',$sum('#skF_3','#skF_4')),'#skF_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2]) ).
tff(c_58,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_57,c_41,c_25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ARI616_1 : TPTP v8.1.2. Released v5.1.0.
% 0.00/0.13 % 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
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 4 00:40:08 EDT 2023
% 0.14/0.34 % CPUTime :
% 3.02/1.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.02/1.73
% 3.02/1.73 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.02/1.76
% 3.02/1.76 Inference rules
% 3.02/1.76 ----------------------
% 3.02/1.76 #Ref : 0
% 3.02/1.76 #Sup : 4
% 3.02/1.76 #Fact : 0
% 3.02/1.76 #Define : 0
% 3.02/1.76 #Split : 0
% 3.02/1.76 #Chain : 0
% 3.02/1.76 #Close : 1
% 3.02/1.76
% 3.02/1.76 Ordering : LPO
% 3.02/1.76
% 3.02/1.76 Simplification rules
% 3.02/1.76 ----------------------
% 3.02/1.76 #Subsume : 0
% 3.02/1.76 #Demod : 0
% 3.02/1.76 #Tautology : 0
% 3.02/1.76 #SimpNegUnit : 0
% 3.02/1.76 #BackRed : 0
% 3.02/1.76
% 3.02/1.76 #Partial instantiations: 0
% 3.02/1.76 #Strategies tried : 1
% 3.02/1.76
% 3.02/1.76 Timing (in seconds)
% 3.02/1.76 ----------------------
% 3.02/1.76 Preprocessing : 0.50
% 3.02/1.76 Parsing : 0.27
% 3.02/1.76 CNF conversion : 0.03
% 3.02/1.76 Main loop : 0.17
% 3.02/1.76 Inferencing : 0.04
% 3.02/1.76 Reduction : 0.03
% 3.02/1.76 Demodulation : 0.03
% 3.02/1.76 BG Simplification : 0.02
% 3.02/1.76 Subsumption : 0.03
% 3.02/1.76 Abstraction : 0.01
% 3.02/1.76 MUC search : 0.01
% 3.02/1.76 Cooper : 0.05
% 3.02/1.76 Total : 0.73
% 3.02/1.76 Index Insertion : 0.00
% 3.02/1.76 Index Deletion : 0.00
% 3.02/1.76 Index Matching : 0.00
% 3.02/1.77 BG Taut test : 0.00
%------------------------------------------------------------------------------