TSTP Solution File: ARI680_1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ARI680_1 : TPTP v8.1.2. Released v6.3.0.
% 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 : n020.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 10:34:14 EDT 2023
% Result : Theorem 15.48s 4.91s
% Output : CNFRefutation 15.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 37 ( 24 unt; 4 typ; 0 def)
% Number of atoms : 49 ( 13 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 36 ( 20 ~; 14 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 149 ( 33 atm; 49 fun; 52 num; 15 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 4 usr; 10 con; 0-2 aty)
% Number of variables : 15 (; 15 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
%$ #nlpp
%Foreground sorts:
%Background operators:
tff(y,type,
y: $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff(a,type,
a: $int ).
tff(x,type,
x: $int ).
%Foreground operators:
tff(f_71,axiom,
! [M: $int,N: $int] : ( $product($sum(1,M),N) = $sum(N,$product(M,N)) ),
file('/export/starexec/sandbox/solver/bin/lemmas/mult_lemmas.p',mult_def_2) ).
tff(f_30,axiom,
$greater(4,$sum($product($product(3,x),y),$product(7,a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(f_99,axiom,
! [A: $int,B: $int] :
( ( $less(0,A)
& $less(0,B) )
=> $less(0,$product(A,B)) ),
file('/export/starexec/sandbox/solver/bin/lemmas/mult_lemmas.p',mult_nonneg_nonneg) ).
tff(f_32,axiom,
$less(1,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_002) ).
tff(f_31,axiom,
$less(3,$product(2,x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_001) ).
tff(f_34,negated_conjecture,
~ $greater(0,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_003) ).
tff(c_50,plain,
! [X_37: $int,N_4: $int,M_3: $int] :
( ( $product(X_37,N_4) = $sum(N_4,$product(M_3,N_4)) )
| ( X_37 != $sum(1,M_3) ) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_2,plain,
$greater(4,$sum($product($product(3,x),y),$product(7,a))),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_38,plain,
$less($sum($product(7,a),$product(3,$product(x,y))),4),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_2]) ).
tff(c_67,plain,
$product(x,y) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_38]) ).
tff(c_187,plain,
! [M_3: $int] :
( ( $sum(y,$product(M_3,y)) = '#skE_1' )
| ( x != $sum(1,M_3) ) ),
inference(superposition,[status(thm),theory(equality)],[c_50,c_67]) ).
tff(c_1424,plain,
! [M_283: $int] :
( ( $product(M_283,y) = $sum($uminus(y),'#skE_1') )
| ( x != $sum(1,M_283) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_187]) ).
tff(c_39,plain,
! [A_27: $int,B_28: $int] :
( $less(0,$product(A_27,B_28))
| ~ $less(0,A_27)
| ~ $less(0,B_28) ),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_1616,plain,
! [M_283: $int] :
( $less(0,$sum($uminus(y),'#skE_1'))
| ~ $less(0,M_283)
| ~ $less(0,y)
| ( x != $sum(1,M_283) ) ),
inference(superposition,[status(thm),theory(equality)],[c_1424,c_39]) ).
tff(c_1618,plain,
! [M_283: $int] :
( $less(y,'#skE_1')
| ~ $less(0,M_283)
| ~ $less(0,y)
| ( x != $sum(1,M_283) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1616]) ).
tff(c_47219,plain,
~ $less(0,y),
inference(splitLeft,[status(thm)],[c_1618]) ).
tff(c_33,plain,
$less(1,y),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_47220,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_47219,c_33]) ).
tff(c_47223,plain,
! [M_283: $int] :
( ~ $less(0,M_283)
| ( x != $sum(1,M_283) )
| $less(y,'#skE_1') ),
inference(splitRight,[status(thm)],[c_1618]) ).
tff(c_48284,plain,
! [M_283: $int] :
( ~ $less(0,M_283)
| ( x != $sum(1,M_283) ) ),
inference(splitLeft,[status(thm)],[c_47223]) ).
tff(c_48285,plain,
$lesseq(x,1),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_48284]) ).
tff(c_48287,plain,
~ $less(1,x),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_48285]) ).
tff(c_4,plain,
$less(3,$product(2,x)),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_34,plain,
$less(1,x),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_4]) ).
tff(c_48288,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_48287,c_34]) ).
tff(c_48290,plain,
$less(y,'#skE_1'),
inference(splitRight,[status(thm)],[c_47223]) ).
tff(c_56,plain,
$product(x,y) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_38]) ).
tff(c_51,plain,
$less($sum($product(7,a),$product(3,$product(x,y))),4),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_2]) ).
tff(c_58,plain,
$less($sum($product(7,a),$product(3,'#skE_1')),4),
inference(demodulation,[status(thm),theory(equality)],[c_56,c_51]) ).
tff(c_64,plain,
$less($sum($product(3,'#skE_1'),$product(7,a)),4),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_58]) ).
tff(c_7,plain,
~ $greater(0,a),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_32,plain,
~ $less(a,0),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_7]) ).
tff(c_48291,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_48290,c_64,c_33,c_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : ARI680_1 : TPTP v8.1.2. Released v6.3.0.
% 0.00/0.15 % 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
% 0.18/0.37 % Computer : n020.cluster.edu
% 0.18/0.37 % Model : x86_64 x86_64
% 0.18/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.37 % Memory : 8042.1875MB
% 0.18/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.37 % CPULimit : 300
% 0.18/0.37 % WCLimit : 300
% 0.18/0.37 % DateTime : Fri Aug 4 00:06:52 EDT 2023
% 0.18/0.37 % CPUTime :
% 15.48/4.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.48/4.92
% 15.48/4.92 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.83/5.00
% 15.83/5.00 Inference rules
% 15.83/5.00 ----------------------
% 15.83/5.00 #Ref : 0
% 15.83/5.00 #Sup : 7723
% 15.83/5.00 #Fact : 0
% 15.83/5.00 #Define : 1
% 15.83/5.00 #Split : 32
% 15.83/5.00 #Chain : 0
% 15.83/5.00 #Close : 10
% 15.83/5.00
% 15.83/5.00 Ordering : LPO
% 15.83/5.00
% 15.83/5.00 Simplification rules
% 15.83/5.00 ----------------------
% 15.83/5.00 #Subsume : 1803
% 15.83/5.00 #Demod : 926
% 15.83/5.00 #Tautology : 4542
% 15.83/5.00 #SimpNegUnit : 549
% 15.83/5.00 #BackRed : 0
% 15.83/5.00
% 15.83/5.00 #Partial instantiations: 0
% 15.83/5.00 #Strategies tried : 1
% 15.83/5.00
% 15.83/5.00 Timing (in seconds)
% 15.83/5.00 ----------------------
% 15.83/5.00 Preprocessing : 0.54
% 15.83/5.00 Parsing : 0.29
% 15.83/5.00 CNF conversion : 0.03
% 15.83/5.00 Main loop : 3.32
% 15.83/5.00 Inferencing : 0.60
% 15.83/5.00 Reduction : 1.19
% 15.83/5.00 Demodulation : 0.89
% 15.83/5.00 BG Simplification : 0.29
% 15.83/5.00 Subsumption : 0.77
% 15.83/5.00 Abstraction : 0.11
% 15.83/5.00 MUC search : 0.08
% 15.83/5.00 Cooper : 0.15
% 15.83/5.00 Total : 3.96
% 15.83/5.00 Index Insertion : 0.00
% 15.83/5.00 Index Deletion : 0.00
% 15.83/5.00 Index Matching : 0.00
% 15.83/5.00 BG Taut test : 0.00
%------------------------------------------------------------------------------