TSTP Solution File: ARI656_1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ARI656_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/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 10:34:12 EDT 2023
% Result : Theorem 19.64s 6.69s
% Output : CNFRefutation 20.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 76 ( 50 unt; 5 typ; 0 def)
% Number of atoms : 99 ( 49 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 63 ( 35 ~; 25 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 214 ( 44 atm; 89 fun; 47 num; 34 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 5 usr; 7 con; 0-2 aty)
% Number of variables : 34 (; 34 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
%$ #nlpp
%Foreground sorts:
%Background operators:
tff(c,type,
c: $int ).
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff(b,type,
b: $int ).
tff(a,type,
a: $int ).
%Foreground operators:
tff(f_65,axiom,
! [A: $int,B: $int] : ( $product(A,B) = $product(B,A) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',mult_comm) ).
tff(f_33,negated_conjecture,
~ $lesseq($product(a,c),$product(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_002) ).
tff(f_73,axiom,
! [A: $int,B: $int] : ( $uminus($product(A,B)) = $product($uminus(A),B) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',minus_mult_left) ).
tff(f_90,axiom,
! [A: $int,B: $int] :
( ( $less(0,A)
& $less(0,B) )
=> $less(0,$product(A,B)) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',mult_nonneg_nonneg) ).
tff(f_81,axiom,
! [C: $int,B: $int] :
( ( $product(C,B) = C )
<=> ( ( C = 0 )
| ( B = 1 ) ) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',mult_cancel_right1) ).
tff(f_31,axiom,
$lesseq(0,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_001) ).
tff(f_67,axiom,
! [A: $int,B: $int,C: $int] : ( $product(A,$sum(B,C)) = $sum($product(A,B),$product(A,C)) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',mult_dist) ).
tff(f_30,axiom,
$lesseq(c,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(c_46,plain,
! [B_7: $int,A_8: $int] : ( $product(B_7,A_8) = $product(A_8,B_7) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_6,plain,
~ $lesseq($product(a,c),$product(a,b)),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_34,plain,
$less($product(a,b),$product(a,c)),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_6]) ).
tff(c_69,plain,
$product(a,b) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_34]) ).
tff(c_385,plain,
$product(b,a) = '#skE_1',
inference(superposition,[status(thm),theory(equality)],[c_46,c_69]) ).
tff(c_41,plain,
! [A_17: $int,B_18: $int,X_37: $int] :
( ( $uminus($product(A_17,B_18)) = $product(X_37,B_18) )
| ( X_37 != $uminus(A_17) ) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_43,plain,
! [X_37: $int,B_18: $int,A_17: $int] :
( ( $uminus($product(X_37,B_18)) = $product(A_17,B_18) )
| ( X_37 != $uminus(A_17) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_41]) ).
tff(c_423,plain,
$uminus($product($uminus(b),a)) = '#skE_1',
inference(superposition,[status(thm),theory(equality)],[c_385,c_43]) ).
tff(c_508,plain,
$uminus($product(a,$uminus(b))) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_46,c_423]) ).
tff(c_18745,plain,
$product(a,$uminus(b)) = $uminus('#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_508]) ).
tff(c_37,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_90]) ).
tff(c_19325,plain,
( $less(0,$uminus('#skE_1'))
| ~ $less(0,a)
| ~ $less(0,$uminus(b)) ),
inference(superposition,[status(thm),theory(equality)],[c_18745,c_37]) ).
tff(c_19327,plain,
( $less('#skE_1',0)
| ~ $less(0,a)
| ~ $less(b,0) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_19325]) ).
tff(c_20292,plain,
~ $less(b,0),
inference(splitLeft,[status(thm)],[c_19327]) ).
tff(c_185,plain,
( $less(0,'#skE_1')
| ~ $less(0,a)
| ~ $less(0,b) ),
inference(superposition,[status(thm),theory(equality)],[c_69,c_37]) ).
tff(c_758,plain,
~ $less(0,b),
inference(splitLeft,[status(thm)],[c_185]) ).
tff(c_38,plain,
! [B_24: $int] : ( $product(0,B_24) = 0 ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_550,plain,
( ( '#skE_1' = 0 )
| ( b != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_38,c_385]) ).
tff(c_556,plain,
b != 0,
inference(splitLeft,[status(thm)],[c_550]) ).
tff(c_21065,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_20292,c_758,c_556]) ).
tff(c_21068,plain,
( ~ $less(0,a)
| $less('#skE_1',0) ),
inference(splitRight,[status(thm)],[c_19327]) ).
tff(c_21071,plain,
~ $less(0,a),
inference(splitLeft,[status(thm)],[c_21068]) ).
tff(c_213,plain,
$product(a,c) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_34]) ).
tff(c_366,plain,
( ( '#skE_2' = 0 )
| ( a != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_38,c_213]) ).
tff(c_370,plain,
a != 0,
inference(splitLeft,[status(thm)],[c_366]) ).
tff(c_3,plain,
$lesseq(0,a),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_35,plain,
~ $less(a,0),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_3]) ).
tff(c_21072,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_21071,c_370,c_35]) ).
tff(c_21076,plain,
$less(0,a),
inference(splitRight,[status(thm)],[c_21068]) ).
tff(c_62,plain,
$product(a,b) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_34]) ).
tff(c_15,plain,
! [A_9: $int,C_11: $int,B_10: $int] : ( $product(A_9,$sum(C_11,B_10)) = $sum($product(A_9,B_10),$product(A_9,C_11)) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_45,plain,
! [A_12: $int,X_38: $int,B_13: $int,C_14: $int] :
( ( $product(A_12,X_38) = $sum($product(A_12,B_13),$product(A_12,C_14)) )
| ( X_38 != $sum(B_13,C_14) ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_15]) ).
tff(c_316,plain,
! [X_38: $int,C_14: $int] :
( ( $product(a,X_38) = $sum('#skE_2',$product(a,C_14)) )
| ( X_38 != $sum(c,C_14) ) ),
inference(superposition,[status(thm),theory(equality)],[c_213,c_45]) ).
tff(c_6719,plain,
! [C_1088: $int,X_1085: $int] :
( ( $sum('#skE_2',$product(a,C_1088)) = $product(a,X_1085) )
| ( X_1085 != $sum(C_1088,c) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_316]) ).
tff(c_7480,plain,
! [C_1088: $int] :
( ( $sum('#skE_2',$product(a,C_1088)) = '#skE_1' )
| ( $sum(C_1088,c) != b ) ),
inference(superposition,[status(thm),theory(equality)],[c_62,c_6719]) ).
tff(c_7482,plain,
$product(a,$sum($uminus(c),b)) = $sum($uminus('#skE_2'),'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7480]) ).
tff(c_73392,plain,
$product(a,$sum(b,$uminus(c))) = $sum('#skE_1',$uminus('#skE_2')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7482]) ).
tff(c_73780,plain,
( $less(0,$sum('#skE_1',$uminus('#skE_2')))
| ~ $less(0,a)
| ~ $less(0,$sum(b,$uminus(c))) ),
inference(superposition,[status(thm),theory(equality)],[c_73392,c_37]) ).
tff(c_74508,plain,
( $less(0,$sum('#skE_1',$uminus('#skE_2')))
| ~ $less(0,$sum(b,$uminus(c))) ),
inference(demodulation,[status(thm),theory(equality)],[c_21076,c_73780]) ).
tff(c_74510,plain,
( $less('#skE_2','#skE_1')
| ~ $less(c,b) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_74508]) ).
tff(c_77509,plain,
~ $less(c,b),
inference(splitLeft,[status(thm)],[c_74510]) ).
tff(c_295,plain,
( ( '#skE_2' = '#skE_1' )
| ( c != b ) ),
inference(superposition,[status(thm),theory(equality)],[c_213,c_62]) ).
tff(c_297,plain,
( ( '#skE_2' = '#skE_1' )
| ( c != b ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_295]) ).
tff(c_374,plain,
c != b,
inference(splitLeft,[status(thm)],[c_297]) ).
tff(c_1,plain,
$lesseq(c,b),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_36,plain,
~ $less(b,c),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_1]) ).
tff(c_77512,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_77509,c_374,c_36]) ).
tff(c_77515,plain,
$less('#skE_2','#skE_1'),
inference(splitRight,[status(thm)],[c_74510]) ).
tff(c_55,plain,
$product(a,c) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_34]) ).
tff(c_54,plain,
$product(a,b) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_34]) ).
tff(c_49,plain,
$less($product(a,b),$product(a,c)),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_6]) ).
tff(c_66,plain,
$less('#skE_1','#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_55,c_54,c_49]) ).
tff(c_77517,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_77515,c_66]) ).
tff(c_77520,plain,
'#skE_2' = '#skE_1',
inference(splitRight,[status(thm)],[c_297]) ).
tff(c_77527,plain,
$less('#skE_1','#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_77520,c_66]) ).
tff(c_77533,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_77527]) ).
tff(c_77537,plain,
a = 0,
inference(splitRight,[status(thm)],[c_366]) ).
tff(c_210,plain,
( ( '#skE_1' = 0 )
| ( a != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_38,c_69]) ).
tff(c_77562,plain,
'#skE_1' = 0,
inference(demodulation,[status(thm),theory(equality)],[c_77537,c_210]) ).
tff(c_77536,plain,
'#skE_2' = 0,
inference(splitRight,[status(thm)],[c_366]) ).
tff(c_77548,plain,
$less('#skE_1',0),
inference(demodulation,[status(thm),theory(equality)],[c_77536,c_66]) ).
tff(c_77563,plain,
$less(0,0),
inference(demodulation,[status(thm),theory(equality)],[c_77562,c_77548]) ).
tff(c_77566,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_77563]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ARI656_1 : TPTP v8.1.2. Released v6.3.0.
% 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
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 4 00:40:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 19.64/6.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.64/6.69
% 19.64/6.69 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 20.02/6.78
% 20.02/6.78 Inference rules
% 20.02/6.78 ----------------------
% 20.02/6.78 #Ref : 0
% 20.02/6.78 #Sup : 12016
% 20.02/6.78 #Fact : 0
% 20.02/6.78 #Define : 2
% 20.02/6.78 #Split : 110
% 20.02/6.78 #Chain : 0
% 20.02/6.78 #Close : 6
% 20.02/6.78
% 20.02/6.78 Ordering : LPO
% 20.02/6.78
% 20.02/6.78 Simplification rules
% 20.02/6.78 ----------------------
% 20.02/6.78 #Subsume : 3349
% 20.02/6.78 #Demod : 1451
% 20.02/6.78 #Tautology : 4628
% 20.02/6.78 #SimpNegUnit : 1039
% 20.02/6.78 #BackRed : 6
% 20.02/6.78
% 20.02/6.78 #Partial instantiations: 0
% 20.02/6.78 #Strategies tried : 1
% 20.02/6.78
% 20.02/6.78 Timing (in seconds)
% 20.02/6.78 ----------------------
% 20.02/6.78 Preprocessing : 0.52
% 20.02/6.78 Parsing : 0.28
% 20.02/6.78 CNF conversion : 0.03
% 20.02/6.78 Main loop : 5.13
% 20.02/6.78 Inferencing : 0.72
% 20.02/6.78 Reduction : 1.92
% 20.02/6.78 Demodulation : 1.39
% 20.02/6.78 BG Simplification : 0.43
% 20.02/6.78 Subsumption : 1.26
% 20.02/6.78 Abstraction : 0.15
% 20.02/6.78 MUC search : 0.13
% 20.02/6.78 Cooper : 0.22
% 20.02/6.78 Total : 5.76
% 20.02/6.78 Index Insertion : 0.00
% 20.02/6.78 Index Deletion : 0.00
% 20.02/6.78 Index Matching : 0.00
% 20.02/6.78 BG Taut test : 0.00
%------------------------------------------------------------------------------