TSTP Solution File: ARI670_1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ARI670_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 : n015.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 7.15s 2.82s
% Output : CNFRefutation 7.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 35 unt; 4 typ; 0 def)
% Number of atoms : 74 ( 34 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 49 ( 26 ~; 20 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 178 ( 35 atm; 67 fun; 46 num; 30 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 : 9 ( 4 usr; 6 con; 0-2 aty)
% Number of variables : 30 (; 30 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
%$ #nlpp
%Foreground sorts:
%Background operators:
tff(c,type,
c: $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff(b,type,
b: $int ).
tff(a,type,
a: $int ).
%Foreground operators:
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_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_31,negated_conjecture,
~ $lesseq(a,$product(a,a)),
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(f_56,axiom,
! [M: $int,N: $int] : ( $product($sum(1,M),N) = $sum(N,$product(M,N)) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',mult_def_2) ).
tff(c_35,plain,
! [A_17: $int,B_18: $int,X_35: $int] :
( ( $uminus($product(A_17,B_18)) = $product(X_35,B_18) )
| ( X_35 != $uminus(A_17) ) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_37,plain,
! [X_35: $int,B_18: $int,A_17: $int] :
( ( $uminus($product(X_35,B_18)) = $product(A_17,B_18) )
| ( X_35 != $uminus(A_17) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_35]) ).
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_2,plain,
~ $lesseq(a,$product(a,a)),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_30,plain,
$less($product(a,a),a),
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_90,plain,
$uminus($product($uminus(a),a)) = '#skE_1',
inference(superposition,[status(thm),theory(equality)],[c_58,c_37]) ).
tff(c_164,plain,
$uminus($product(a,$uminus(a))) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_40,c_90]) ).
tff(c_212,plain,
$product(a,$uminus(a)) = $uminus('#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_164]) ).
tff(c_361,plain,
$uminus($product($uminus(a),$uminus(a))) = $uminus('#skE_1'),
inference(superposition,[status(thm),theory(equality)],[c_37,c_212]) ).
tff(c_558,plain,
$product($uminus(a),$uminus(a)) = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_361]) ).
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_707,plain,
( $less(0,'#skE_1')
| ~ $less(0,$uminus(a)) ),
inference(superposition,[status(thm),theory(equality)],[c_558,c_31]) ).
tff(c_709,plain,
( $less(0,'#skE_1')
| ~ $less(a,0) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_707]) ).
tff(c_1424,plain,
~ $less(a,0),
inference(splitLeft,[status(thm)],[c_709]) ).
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_1425,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1424,c_207,c_205]) ).
tff(c_1428,plain,
$less(0,'#skE_1'),
inference(splitRight,[status(thm)],[c_709]) ).
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),a),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_2]) ).
tff(c_55,plain,
$less('#skE_1',a),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_43]) ).
tff(c_1430,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1428,c_207,c_55]) ).
tff(c_1434,plain,
$less(0,a),
inference(splitRight,[status(thm)],[c_175]) ).
tff(c_42,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_56]) ).
tff(c_134,plain,
! [M_3: $int] :
( ( $sum(a,$product(M_3,a)) = '#skE_1' )
| ( a != $sum(1,M_3) ) ),
inference(superposition,[status(thm),theory(equality)],[c_58,c_42]) ).
tff(c_2219,plain,
! [M_428: $int] :
( ( $product(M_428,a) = $sum($uminus(a),'#skE_1') )
| ( a != $sum(1,M_428) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_134]) ).
tff(c_2284,plain,
! [M_428: $int] :
( $less(0,$sum($uminus(a),'#skE_1'))
| ~ $less(0,M_428)
| ~ $less(0,a)
| ( a != $sum(1,M_428) ) ),
inference(superposition,[status(thm),theory(equality)],[c_2219,c_31]) ).
tff(c_2393,plain,
! [M_428: $int] :
( $less(0,$sum($uminus(a),'#skE_1'))
| ~ $less(0,M_428)
| ( a != $sum(1,M_428) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1434,c_2284]) ).
tff(c_2395,plain,
! [M_428: $int] :
( $less(a,'#skE_1')
| ~ $less(0,M_428)
| ( a != $sum(1,M_428) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2393]) ).
tff(c_9516,plain,
! [M_428: $int] :
( ~ $less(0,M_428)
| ( a != $sum(1,M_428) ) ),
inference(splitLeft,[status(thm)],[c_2395]) ).
tff(c_9517,plain,
$lesseq(a,1),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_9516]) ).
tff(c_9519,plain,
~ $less(1,a),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_9517]) ).
tff(c_1433,plain,
$less(0,'#skE_1'),
inference(splitRight,[status(thm)],[c_175]) ).
tff(c_9520,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_9519,c_1433,c_55]) ).
tff(c_9522,plain,
$less(a,'#skE_1'),
inference(splitRight,[status(thm)],[c_2395]) ).
tff(c_9523,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_9522,c_55]) ).
tff(c_9527,plain,
a = 0,
inference(splitRight,[status(thm)],[c_173]) ).
tff(c_9526,plain,
'#skE_1' = 0,
inference(splitRight,[status(thm)],[c_173]) ).
tff(c_9538,plain,
$less(0,a),
inference(demodulation,[status(thm),theory(equality)],[c_9526,c_55]) ).
tff(c_9539,plain,
$less(0,0),
inference(demodulation,[status(thm),theory(equality)],[c_9527,c_9538]) ).
tff(c_9543,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_9539]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ARI670_1 : TPTP v8.1.2. Released v6.3.0.
% 0.00/0.14 % 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
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 4 00:27:59 EDT 2023
% 0.13/0.35 % CPUTime :
% 7.15/2.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.15/2.83
% 7.15/2.83 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.15/2.87
% 7.15/2.87 Inference rules
% 7.15/2.87 ----------------------
% 7.15/2.87 #Ref : 0
% 7.15/2.87 #Sup : 1413
% 7.15/2.87 #Fact : 0
% 7.15/2.87 #Define : 1
% 7.15/2.87 #Split : 25
% 7.15/2.87 #Chain : 0
% 7.15/2.87 #Close : 5
% 7.15/2.87
% 7.15/2.87 Ordering : LPO
% 7.15/2.87
% 7.15/2.87 Simplification rules
% 7.15/2.87 ----------------------
% 7.15/2.87 #Subsume : 311
% 7.15/2.87 #Demod : 340
% 7.15/2.87 #Tautology : 641
% 7.15/2.87 #SimpNegUnit : 16
% 7.15/2.87 #BackRed : 3
% 7.15/2.87
% 7.15/2.87 #Partial instantiations: 0
% 7.15/2.87 #Strategies tried : 1
% 7.15/2.87
% 7.15/2.87 Timing (in seconds)
% 7.15/2.87 ----------------------
% 7.36/2.92 Preprocessing : 0.51
% 7.36/2.92 Parsing : 0.27
% 7.36/2.92 CNF conversion : 0.03
% 7.36/2.92 Main loop : 1.26
% 7.36/2.92 Inferencing : 0.25
% 7.36/2.92 Reduction : 0.40
% 7.36/2.92 Demodulation : 0.31
% 7.36/2.92 BG Simplification : 0.17
% 7.36/2.92 Subsumption : 0.22
% 7.36/2.92 Abstraction : 0.07
% 7.36/2.92 MUC search : 0.05
% 7.36/2.92 Cooper : 0.10
% 7.36/2.92 Total : 1.83
% 7.36/2.92 Index Insertion : 0.00
% 7.36/2.92 Index Deletion : 0.00
% 7.36/2.92 Index Matching : 0.00
% 7.36/2.92 BG Taut test : 0.00
%------------------------------------------------------------------------------