TSTP Solution File: ARI676_1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ARI676_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 : n027.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 10:34:13 EDT 2023
% Result : Theorem 6.81s 2.75s
% Output : CNFRefutation 6.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 27 unt; 2 typ; 0 def)
% Number of atoms : 48 ( 22 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 13 ~; 9 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 124 ( 22 atm; 50 fun; 33 num; 19 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 : 8 ( 2 usr; 5 con; 0-2 aty)
% Number of variables : 19 (; 19 !; 0 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
%$ #nlpp
%Foreground sorts:
%Background operators:
tff('#skE_1',type,
'#skE_1': $int ).
tff(a,type,
a: $int ).
%Foreground operators:
tff(f_59,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_67,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_31,negated_conjecture,
~ $lesseq(0,$sum($product(a,a),10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(f_84,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_75,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(c_40,plain,
! [B_7: $int,A_8: $int] : ( $product(B_7,A_8) = $product(A_8,B_7) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_35,plain,
! [A_17: $int,B_18: $int,X_33: $int] :
( ( $uminus($product(A_17,B_18)) = $product(X_33,B_18) )
| ( X_33 != $uminus(A_17) ) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_37,plain,
! [X_33: $int,B_18: $int,A_17: $int] :
( ( $uminus($product(X_33,B_18)) = $product(A_17,B_18) )
| ( X_33 != $uminus(A_17) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_35]) ).
tff(c_2,plain,
~ $lesseq(0,$sum($product(a,a),10)),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_30,plain,
$less($product(a,a),$uminus(10)),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_2]) ).
tff(c_58,plain,
$product(a,a) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_30]) ).
tff(c_122,plain,
$uminus($product($uminus(a),a)) = '#skE_1',
inference(superposition,[status(thm),theory(equality)],[c_37,c_58]) ).
tff(c_194,plain,
$uminus($product(a,$uminus(a))) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_40,c_122]) ).
tff(c_212,plain,
$product(a,$uminus(a)) = $uminus('#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_194]) ).
tff(c_327,plain,
$uminus($product($uminus(a),$uminus(a))) = $uminus('#skE_1'),
inference(superposition,[status(thm),theory(equality)],[c_212,c_37]) ).
tff(c_8078,plain,
$product($uminus(a),$uminus(a)) = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_327]) ).
tff(c_31,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_84]) ).
tff(c_8480,plain,
( $less(0,'#skE_1')
| ~ $less(0,$uminus(a)) ),
inference(superposition,[status(thm),theory(equality)],[c_8078,c_31]) ).
tff(c_8482,plain,
( $less(0,'#skE_1')
| ~ $less(a,0) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_8480]) ).
tff(c_8602,plain,
~ $less(a,0),
inference(splitLeft,[status(thm)],[c_8482]) ).
tff(c_175,plain,
( $less(0,'#skE_1')
| ~ $less(0,a) ),
inference(superposition,[status(thm),theory(equality)],[c_58,c_31]) ).
tff(c_207,plain,
~ $less(0,a),
inference(splitLeft,[status(thm)],[c_175]) ).
tff(c_32,plain,
! [B_24: $int] : ( $product(0,B_24) = 0 ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_173,plain,
( ( '#skE_1' = 0 )
| ( a != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_58,c_32]) ).
tff(c_205,plain,
a != 0,
inference(splitLeft,[status(thm)],[c_173]) ).
tff(c_8603,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_8602,c_207,c_205]) ).
tff(c_8606,plain,
$less(0,'#skE_1'),
inference(splitRight,[status(thm)],[c_8482]) ).
tff(c_48,plain,
$product(a,a) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_30]) ).
tff(c_43,plain,
$less($product(a,a),$uminus(10)),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_2]) ).
tff(c_55,plain,
$less('#skE_1',$uminus(10)),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_43]) ).
tff(c_8610,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_8606,c_55]) ).
tff(c_8613,plain,
$less(0,'#skE_1'),
inference(splitRight,[status(thm)],[c_175]) ).
tff(c_8615,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_8613,c_55]) ).
tff(c_8618,plain,
'#skE_1' = 0,
inference(splitRight,[status(thm)],[c_173]) ).
tff(c_8630,plain,
$less(0,$uminus(10)),
inference(demodulation,[status(thm),theory(equality)],[c_8618,c_55]) ).
tff(c_8632,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_8630]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ARI676_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
% 0.14/0.34 % Computer : n027.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 00:32:24 EDT 2023
% 0.14/0.34 % CPUTime :
% 6.81/2.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.81/2.75
% 6.81/2.75 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.81/2.78
% 6.81/2.78 Inference rules
% 6.81/2.78 ----------------------
% 6.81/2.78 #Ref : 0
% 6.81/2.78 #Sup : 1308
% 6.81/2.78 #Fact : 0
% 6.81/2.78 #Define : 1
% 6.81/2.78 #Split : 14
% 6.81/2.78 #Chain : 0
% 6.81/2.78 #Close : 3
% 6.81/2.78
% 6.81/2.78 Ordering : LPO
% 6.81/2.78
% 6.81/2.78 Simplification rules
% 6.81/2.78 ----------------------
% 6.81/2.78 #Subsume : 248
% 6.81/2.78 #Demod : 318
% 6.81/2.78 #Tautology : 691
% 6.81/2.78 #SimpNegUnit : 9
% 6.81/2.78 #BackRed : 1
% 6.81/2.78
% 6.81/2.78 #Partial instantiations: 0
% 6.81/2.78 #Strategies tried : 1
% 6.81/2.78
% 6.81/2.78 Timing (in seconds)
% 6.81/2.78 ----------------------
% 7.26/2.79 Preprocessing : 0.53
% 7.26/2.79 Parsing : 0.29
% 7.26/2.79 CNF conversion : 0.03
% 7.26/2.79 Main loop : 1.11
% 7.26/2.79 Inferencing : 0.25
% 7.26/2.79 Reduction : 0.38
% 7.26/2.79 Demodulation : 0.28
% 7.26/2.79 BG Simplification : 0.16
% 7.26/2.79 Subsumption : 0.19
% 7.26/2.79 Abstraction : 0.06
% 7.26/2.79 MUC search : 0.01
% 7.26/2.79 Cooper : 0.04
% 7.26/2.79 Total : 1.70
% 7.26/2.79 Index Insertion : 0.00
% 7.26/2.79 Index Deletion : 0.00
% 7.26/2.79 Index Matching : 0.00
% 7.26/2.79 BG Taut test : 0.00
%------------------------------------------------------------------------------