TSTP Solution File: ARI182_1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ARI182_1 : TPTP v8.1.2. Released v5.0.0.
% 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 : n008.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 10:33:20 EDT 2023
% Result : Theorem 2.83s 1.67s
% Output : CNFRefutation 2.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 19 unt; 5 typ; 0 def)
% Number of atoms : 21 ( 5 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 3 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 59 ( 15 atm; 30 fun; 9 num; 5 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 5 (; 5 !; 0 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
%$ #nlpp > f
%Foreground sorts:
%Background operators:
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skF_2',type,
'#skF_2': $int ).
tff('#skF_1',type,
'#skF_1': $int ).
%Foreground operators:
tff(f,type,
f: $int > $int ).
tff(f_34,negated_conjecture,
~ ( ! [Ua: $int] : $greater(f(Ua),Ua)
=> ! [Va: $int,Wa: $int] : $greatereq(f($sum(f(Va),Wa)),$sum($sum(Va,Wa),2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(c_2,plain,
~ $greatereq(f($sum('#skF_2',f('#skF_1'))),$sum($sum('#skF_2','#skF_1'),2)),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_11,plain,
$less(f($sum('#skF_2',f('#skF_1'))),$sum(2,$sum('#skF_1','#skF_2'))),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_2]) ).
tff(c_15,plain,
f('#skF_1') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_11]) ).
tff(c_13,plain,
$less(f($sum('#skF_2',f('#skF_1'))),$sum(2,$sum('#skF_1','#skF_2'))),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_2]) ).
tff(c_23,plain,
$less(f($sum('#skF_2','#skE_1')),$sum(2,$sum('#skF_1','#skF_2'))),
inference(demodulation,[status(thm),theory(equality)],[c_15,c_13]) ).
tff(c_26,plain,
$less(f($sum('#skE_1','#skF_2')),$sum(2,$sum('#skF_2','#skF_1'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_23]) ).
tff(c_49,plain,
f($sum('#skE_1','#skF_2')) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_26]) ).
tff(c_48,plain,
$less(f($sum('#skE_1','#skF_2')),$sum(2,$sum('#skF_2','#skF_1'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_23]) ).
tff(c_51,plain,
$less('#skE_2',$sum(2,$sum('#skF_2','#skF_1'))),
inference(demodulation,[status(thm),theory(equality)],[c_49,c_48]) ).
tff(c_58,plain,
$less('#skE_2',$sum(2,$sum('#skF_1','#skF_2'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_51]) ).
tff(c_53,plain,
f($sum('#skE_1','#skF_2')) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_26]) ).
tff(c_61,plain,
f($sum('#skF_2','#skE_1')) = '#skE_2',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_53]) ).
tff(c_5,plain,
! [U_1a: $int] : $greater(f(U_1a),U_1a),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_7,plain,
! [U_1a: $int] : $less(U_1a,f(U_1a)),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_5]) ).
tff(c_83,plain,
$less($sum('#skF_2','#skE_1'),'#skE_2'),
inference(superposition,[status(thm),theory(equality)],[c_61,c_7]) ).
tff(c_85,plain,
$less($sum('#skE_1','#skF_2'),'#skE_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_83]) ).
tff(c_29,plain,
f('#skF_1') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_11]) ).
tff(c_43,plain,
$less('#skF_1','#skE_1'),
inference(superposition,[status(thm),theory(equality)],[c_29,c_7]) ).
tff(c_92,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_58,c_85,c_43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ARI182_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.13 % 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
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 4 00:14:03 EDT 2023
% 0.13/0.34 % CPUTime :
% 2.83/1.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.83/1.67
% 2.83/1.67 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.83/1.71
% 2.83/1.71 Inference rules
% 2.83/1.71 ----------------------
% 2.83/1.71 #Ref : 0
% 2.83/1.71 #Sup : 8
% 2.83/1.71 #Fact : 0
% 2.83/1.71 #Define : 2
% 2.83/1.71 #Split : 0
% 2.83/1.71 #Chain : 0
% 2.83/1.71 #Close : 1
% 2.83/1.71
% 2.83/1.71 Ordering : LPO
% 2.83/1.71
% 2.83/1.71 Simplification rules
% 2.83/1.71 ----------------------
% 2.83/1.71 #Subsume : 0
% 2.83/1.71 #Demod : 2
% 2.83/1.71 #Tautology : 4
% 2.83/1.71 #SimpNegUnit : 0
% 2.83/1.71 #BackRed : 0
% 2.83/1.71
% 2.83/1.71 #Partial instantiations: 0
% 2.83/1.71 #Strategies tried : 1
% 2.83/1.71
% 2.83/1.71 Timing (in seconds)
% 2.83/1.71 ----------------------
% 2.83/1.71 Preprocessing : 0.47
% 2.83/1.71 Parsing : 0.26
% 2.83/1.71 CNF conversion : 0.03
% 2.83/1.71 Main loop : 0.19
% 2.83/1.71 Inferencing : 0.04
% 2.83/1.71 Reduction : 0.04
% 2.83/1.71 Demodulation : 0.03
% 2.83/1.71 BG Simplification : 0.03
% 2.83/1.71 Subsumption : 0.04
% 2.83/1.71 Abstraction : 0.01
% 2.83/1.71 MUC search : 0.00
% 2.83/1.71 Cooper : 0.04
% 2.83/1.71 Total : 0.72
% 2.83/1.71 Index Insertion : 0.00
% 2.83/1.71 Index Deletion : 0.00
% 2.83/1.71 Index Matching : 0.00
% 2.83/1.71 BG Taut test : 0.00
%------------------------------------------------------------------------------