TSTP Solution File: ARI681_1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ARI681_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 : n005.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 37.67s 15.45s
% Output : CNFRefutation 38.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 185 ( 129 unt; 8 typ; 0 def)
% Number of atoms : 249 ( 99 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 169 ( 97 ~; 69 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 491 ( 130 atm; 163 fun; 166 num; 32 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 : 12 ( 8 usr; 10 con; 0-2 aty)
% Number of variables : 32 (; 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
%$ #nlpp
%Foreground sorts:
%Background operators:
tff(c,type,
c: $int ).
tff(d,type,
d: $int ).
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skE_4',type,
'#skE_4': $int ).
tff('#skE_3',type,
'#skE_3': $int ).
tff(b,type,
b: $int ).
tff(a,type,
a: $int ).
%Foreground operators:
tff(f_68,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_34,negated_conjecture,
~ $less(0,$product(b,d)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_003) ).
tff(f_76,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_93,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_32,axiom,
$less(0,$product(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_002) ).
tff(f_84,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,
$less(0,$product(c,d)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_001) ).
tff(f_30,axiom,
$less(0,$product(a,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(c_57,plain,
! [B_7: $int,A_8: $int] : ( $product(B_7,A_8) = $product(A_8,B_7) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_35,plain,
~ $less(0,$product(b,d)),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_71,plain,
$product(b,d) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_35]) ).
tff(c_60,plain,
~ $less(0,$product(b,d)),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_78,plain,
~ $less(0,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_71,c_60]) ).
tff(c_81,plain,
$product(b,d) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_35]) ).
tff(c_52,plain,
! [A_17: $int,B_18: $int,X_45: $int] :
( ( $uminus($product(A_17,B_18)) = $product(X_45,B_18) )
| ( X_45 != $uminus(A_17) ) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_54,plain,
! [X_45: $int,B_18: $int,A_17: $int] :
( ( $uminus($product(X_45,B_18)) = $product(A_17,B_18) )
| ( X_45 != $uminus(A_17) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_52]) ).
tff(c_1635,plain,
! [A_328: $int] :
( ( $product(A_328,d) = $uminus('#skE_1') )
| ( b != $uminus(A_328) ) ),
inference(superposition,[status(thm),theory(equality)],[c_81,c_54]) ).
tff(c_7286,plain,
! [A_885: $int] :
( ( $product(d,A_885) = $uminus('#skE_1') )
| ( b != $uminus(A_885) ) ),
inference(superposition,[status(thm),theory(equality)],[c_1635,c_57]) ).
tff(c_7638,plain,
! [A_17: $int,A_885: $int] :
( ( $product(A_17,A_885) = $uminus($uminus('#skE_1')) )
| ( d != $uminus(A_17) )
| ( b != $uminus(A_885) ) ),
inference(superposition,[status(thm),theory(equality)],[c_7286,c_54]) ).
tff(c_149592,plain,
! [A_18129: $int,A_18130: $int] :
( ( $product(A_18129,A_18130) = '#skE_1' )
| ( d != $uminus(A_18129) )
| ( b != $uminus(A_18130) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7638]) ).
tff(c_48,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_93]) ).
tff(c_149947,plain,
! [A_18129: $int,A_18130: $int] :
( $less(0,'#skE_1')
| ~ $less(0,A_18129)
| ~ $less(0,A_18130)
| ( d != $uminus(A_18129) )
| ( b != $uminus(A_18130) ) ),
inference(superposition,[status(thm),theory(equality)],[c_149592,c_48]) ).
tff(c_150494,plain,
! [A_18129: $int,A_18130: $int] :
( ~ $less(0,A_18129)
| ~ $less(0,A_18130)
| ( d != $uminus(A_18129) )
| ( b != $uminus(A_18130) ) ),
inference(negUnitSimplification,[status(thm)],[c_78,c_149947]) ).
tff(c_150732,plain,
! [A_18130: $int] :
( ~ $less(0,A_18130)
| ( b != $uminus(A_18130) ) ),
inference(splitLeft,[status(thm)],[c_150494]) ).
tff(c_150733,plain,
$lesseq(0,b),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_150732]) ).
tff(c_150735,plain,
~ $less(b,0),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_150733]) ).
tff(c_39,plain,
$less(0,$product(a,b)),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_790,plain,
$product(a,b) = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_39]) ).
tff(c_929,plain,
$uminus($product($uminus(a),b)) = '#skE_4',
inference(superposition,[status(thm),theory(equality)],[c_790,c_54]) ).
tff(c_2432,plain,
$product($uminus(a),b) = $uminus('#skE_4'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_929]) ).
tff(c_2650,plain,
( $less(0,$uminus('#skE_4'))
| ~ $less(0,$uminus(a))
| ~ $less(0,b) ),
inference(superposition,[status(thm),theory(equality)],[c_2432,c_48]) ).
tff(c_2652,plain,
( $less('#skE_4',0)
| ~ $less(a,0)
| ~ $less(0,b) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2650]) ).
tff(c_33414,plain,
~ $less(0,b),
inference(splitLeft,[status(thm)],[c_2652]) ).
tff(c_49,plain,
! [B_24: $int] : ( $product(0,B_24) = 0 ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_195,plain,
( ( '#skE_1' = 0 )
| ( b != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_81,c_49]) ).
tff(c_236,plain,
b != 0,
inference(splitLeft,[status(thm)],[c_195]) ).
tff(c_150736,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_150735,c_33414,c_236]) ).
tff(c_150738,plain,
! [A_18129: $int] :
( ~ $less(0,A_18129)
| ( d != $uminus(A_18129) ) ),
inference(splitRight,[status(thm)],[c_150494]) ).
tff(c_150739,plain,
$lesseq(0,d),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_150738]) ).
tff(c_150741,plain,
~ $less(d,0),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_150739]) ).
tff(c_418,plain,
$product(d,b) = '#skE_1',
inference(superposition,[status(thm),theory(equality)],[c_57,c_81]) ).
tff(c_550,plain,
( ( '#skE_1' = 0 )
| ( d != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_418,c_49]) ).
tff(c_589,plain,
d != 0,
inference(splitLeft,[status(thm)],[c_550]) ).
tff(c_127,plain,
( $less(0,'#skE_1')
| ~ $less(0,b)
| ~ $less(0,d) ),
inference(superposition,[status(thm),theory(equality)],[c_81,c_48]) ).
tff(c_199,plain,
( ~ $less(0,b)
| ~ $less(0,d) ),
inference(negUnitSimplification,[status(thm)],[c_78,c_127]) ).
tff(c_242,plain,
~ $less(0,d),
inference(splitLeft,[status(thm)],[c_199]) ).
tff(c_150742,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_150741,c_589,c_242]) ).
tff(c_150746,plain,
$less(0,b),
inference(splitRight,[status(thm)],[c_2652]) ).
tff(c_494,plain,
$uminus($product($uminus(d),b)) = '#skE_1',
inference(superposition,[status(thm),theory(equality)],[c_54,c_418]) ).
tff(c_578,plain,
$uminus($product(b,$uminus(d))) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_57,c_494]) ).
tff(c_157873,plain,
$product(b,$uminus(d)) = $uminus('#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578]) ).
tff(c_158088,plain,
( $less(0,$uminus('#skE_1'))
| ~ $less(0,b)
| ~ $less(0,$uminus(d)) ),
inference(superposition,[status(thm),theory(equality)],[c_157873,c_48]) ).
tff(c_158528,plain,
( $less(0,$uminus('#skE_1'))
| ~ $less(0,$uminus(d)) ),
inference(demodulation,[status(thm),theory(equality)],[c_150746,c_158088]) ).
tff(c_158530,plain,
( $less('#skE_1',0)
| ~ $less(d,0) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_158528]) ).
tff(c_158721,plain,
~ $less(d,0),
inference(splitLeft,[status(thm)],[c_158530]) ).
tff(c_158722,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_158721,c_589,c_242]) ).
tff(c_158726,plain,
$less(d,0),
inference(splitRight,[status(thm)],[c_158530]) ).
tff(c_43,plain,
$less(0,$product(c,d)),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_592,plain,
$product(c,d) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_43]) ).
tff(c_987,plain,
$product(d,c) = '#skE_3',
inference(superposition,[status(thm),theory(equality)],[c_57,c_592]) ).
tff(c_1034,plain,
$uminus($product($uminus(d),c)) = '#skE_3',
inference(superposition,[status(thm),theory(equality)],[c_987,c_54]) ).
tff(c_1136,plain,
$uminus($product(c,$uminus(d))) = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_57,c_1034]) ).
tff(c_159742,plain,
$product(c,$uminus(d)) = $uminus('#skE_3'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1136]) ).
tff(c_160412,plain,
( $less(0,$uminus('#skE_3'))
| ~ $less(0,c)
| ~ $less(0,$uminus(d)) ),
inference(superposition,[status(thm),theory(equality)],[c_159742,c_48]) ).
tff(c_160414,plain,
( $less('#skE_3',0)
| ~ $less(0,c)
| ~ $less(d,0) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_160412]) ).
tff(c_162468,plain,
( $less('#skE_3',0)
| ~ $less(0,c) ),
inference(demodulation,[status(thm),theory(equality)],[c_158726,c_160414]) ).
tff(c_162470,plain,
~ $less(0,c),
inference(splitLeft,[status(thm)],[c_162468]) ).
tff(c_47,plain,
$less(0,$product(a,c)),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_245,plain,
$product(a,c) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_47]) ).
tff(c_1396,plain,
$product(c,a) = '#skE_2',
inference(superposition,[status(thm),theory(equality)],[c_57,c_245]) ).
tff(c_1502,plain,
$uminus($product($uminus(c),a)) = '#skE_2',
inference(superposition,[status(thm),theory(equality)],[c_54,c_1396]) ).
tff(c_1607,plain,
$uminus($product(a,$uminus(c))) = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_57,c_1502]) ).
tff(c_156226,plain,
$product(a,$uminus(c)) = $uminus('#skE_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1607]) ).
tff(c_156858,plain,
( $less(0,$uminus('#skE_2'))
| ~ $less(0,a)
| ~ $less(0,$uminus(c)) ),
inference(superposition,[status(thm),theory(equality)],[c_156226,c_48]) ).
tff(c_156860,plain,
( $less('#skE_2',0)
| ~ $less(0,a)
| ~ $less(c,0) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_156858]) ).
tff(c_159618,plain,
~ $less(c,0),
inference(splitLeft,[status(thm)],[c_156860]) ).
tff(c_731,plain,
( ( '#skE_3' = 0 )
| ( c != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_592,c_49]) ).
tff(c_770,plain,
c != 0,
inference(splitLeft,[status(thm)],[c_731]) ).
tff(c_162472,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_162470,c_159618,c_770]) ).
tff(c_162475,plain,
$less('#skE_3',0),
inference(splitRight,[status(thm)],[c_162468]) ).
tff(c_408,plain,
$product(c,d) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_43]) ).
tff(c_62,plain,
$less(0,$product(c,d)),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_415,plain,
$less(0,'#skE_3'),
inference(demodulation,[status(thm),theory(equality)],[c_408,c_62]) ).
tff(c_162477,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_162475,c_415]) ).
tff(c_162480,plain,
( ~ $less(0,a)
| $less('#skE_2',0) ),
inference(splitRight,[status(thm)],[c_156860]) ).
tff(c_162483,plain,
~ $less(0,a),
inference(splitLeft,[status(thm)],[c_162480]) ).
tff(c_150745,plain,
( ~ $less(a,0)
| $less('#skE_4',0) ),
inference(splitRight,[status(thm)],[c_2652]) ).
tff(c_150802,plain,
~ $less(a,0),
inference(splitLeft,[status(thm)],[c_150745]) ).
tff(c_397,plain,
( ( '#skE_2' = 0 )
| ( a != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_49,c_245]) ).
tff(c_403,plain,
a != 0,
inference(splitLeft,[status(thm)],[c_397]) ).
tff(c_162484,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_162483,c_150802,c_403]) ).
tff(c_162487,plain,
$less('#skE_2',0),
inference(splitRight,[status(thm)],[c_162480]) ).
tff(c_227,plain,
$product(a,c) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_47]) ).
tff(c_63,plain,
$less(0,$product(a,c)),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_234,plain,
$less(0,'#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_227,c_63]) ).
tff(c_162489,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_162487,c_234]) ).
tff(c_162492,plain,
$less('#skE_4',0),
inference(splitRight,[status(thm)],[c_150745]) ).
tff(c_772,plain,
$product(a,b) = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_39]) ).
tff(c_61,plain,
$less(0,$product(a,b)),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_779,plain,
$less(0,'#skE_4'),
inference(demodulation,[status(thm),theory(equality)],[c_772,c_61]) ).
tff(c_162495,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_162492,c_779]) ).
tff(c_162498,plain,
'#skE_3' = 0,
inference(splitRight,[status(thm)],[c_731]) ).
tff(c_162505,plain,
$less(0,0),
inference(demodulation,[status(thm),theory(equality)],[c_162498,c_415]) ).
tff(c_162517,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_162505]) ).
tff(c_162521,plain,
d = 0,
inference(splitRight,[status(thm)],[c_550]) ).
tff(c_414,plain,
$product(c,d) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_43]) ).
tff(c_162552,plain,
$product(c,0) = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_162521,c_414]) ).
tff(c_162554,plain,
'#skE_3' = 0,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_162552]) ).
tff(c_162555,plain,
$less(0,0),
inference(demodulation,[status(thm),theory(equality)],[c_162554,c_415]) ).
tff(c_162558,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_162555]) ).
tff(c_162561,plain,
'#skE_2' = 0,
inference(splitRight,[status(thm)],[c_397]) ).
tff(c_162568,plain,
$less(0,0),
inference(demodulation,[status(thm),theory(equality)],[c_162561,c_234]) ).
tff(c_162580,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_162568]) ).
tff(c_162584,plain,
$less(0,d),
inference(splitRight,[status(thm)],[c_199]) ).
tff(c_217,plain,
$uminus($product($uminus(b),d)) = '#skE_1',
inference(superposition,[status(thm),theory(equality)],[c_54,c_81]) ).
tff(c_165362,plain,
$product($uminus(b),d) = $uminus('#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_217]) ).
tff(c_165442,plain,
( $less(0,$uminus('#skE_1'))
| ~ $less(0,$uminus(b))
| ~ $less(0,d) ),
inference(superposition,[status(thm),theory(equality)],[c_165362,c_48]) ).
tff(c_165589,plain,
( $less(0,$uminus('#skE_1'))
| ~ $less(0,$uminus(b)) ),
inference(demodulation,[status(thm),theory(equality)],[c_162584,c_165442]) ).
tff(c_165591,plain,
( $less('#skE_1',0)
| ~ $less(b,0) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_165589]) ).
tff(c_165663,plain,
~ $less(b,0),
inference(splitLeft,[status(thm)],[c_165591]) ).
tff(c_162583,plain,
~ $less(0,b),
inference(splitRight,[status(thm)],[c_199]) ).
tff(c_165664,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_165663,c_162583,c_236]) ).
tff(c_165668,plain,
$less(b,0),
inference(splitRight,[status(thm)],[c_165591]) ).
tff(c_162882,plain,
$product(a,b) = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_39]) ).
tff(c_163402,plain,
$product(b,a) = '#skE_4',
inference(superposition,[status(thm),theory(equality)],[c_57,c_162882]) ).
tff(c_163494,plain,
$uminus($product($uminus(b),a)) = '#skE_4',
inference(superposition,[status(thm),theory(equality)],[c_54,c_163402]) ).
tff(c_163582,plain,
$uminus($product(a,$uminus(b))) = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_57,c_163494]) ).
tff(c_193887,plain,
$product(a,$uminus(b)) = $uminus('#skE_4'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_163582]) ).
tff(c_194577,plain,
( $less(0,$uminus('#skE_4'))
| ~ $less(0,a)
| ~ $less(0,$uminus(b)) ),
inference(superposition,[status(thm),theory(equality)],[c_193887,c_48]) ).
tff(c_194579,plain,
( $less('#skE_4',0)
| ~ $less(0,a)
| ~ $less(b,0) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_194577]) ).
tff(c_194829,plain,
( $less('#skE_4',0)
| ~ $less(0,a) ),
inference(demodulation,[status(thm),theory(equality)],[c_165668,c_194579]) ).
tff(c_194831,plain,
~ $less(0,a),
inference(splitLeft,[status(thm)],[c_194829]) ).
tff(c_162727,plain,
$product(a,c) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_47]) ).
tff(c_162862,plain,
$uminus($product($uminus(a),c)) = '#skE_2',
inference(superposition,[status(thm),theory(equality)],[c_54,c_162727]) ).
tff(c_164292,plain,
$product($uminus(a),c) = $uminus('#skE_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_162862]) ).
tff(c_164480,plain,
( $less(0,$uminus('#skE_2'))
| ~ $less(0,$uminus(a))
| ~ $less(0,c) ),
inference(superposition,[status(thm),theory(equality)],[c_164292,c_48]) ).
tff(c_164482,plain,
( $less('#skE_2',0)
| ~ $less(a,0)
| ~ $less(0,c) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_164480]) ).
tff(c_183058,plain,
~ $less(0,c),
inference(splitLeft,[status(thm)],[c_164482]) ).
tff(c_163048,plain,
$product(c,d) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_43]) ).
tff(c_163206,plain,
$uminus($product($uminus(c),d)) = '#skE_3',
inference(superposition,[status(thm),theory(equality)],[c_54,c_163048]) ).
tff(c_165078,plain,
$product($uminus(c),d) = $uminus('#skE_3'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_163206]) ).
tff(c_165155,plain,
( $less(0,$uminus('#skE_3'))
| ~ $less(0,$uminus(c))
| ~ $less(0,d) ),
inference(superposition,[status(thm),theory(equality)],[c_165078,c_48]) ).
tff(c_165298,plain,
( $less(0,$uminus('#skE_3'))
| ~ $less(0,$uminus(c)) ),
inference(demodulation,[status(thm),theory(equality)],[c_162584,c_165155]) ).
tff(c_165300,plain,
( $less('#skE_3',0)
| ~ $less(c,0) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_165298]) ).
tff(c_165660,plain,
~ $less(c,0),
inference(splitLeft,[status(thm)],[c_165300]) ).
tff(c_164047,plain,
! [A_19908: $int] :
( ( $product(A_19908,d) = $uminus('#skE_3') )
| ( c != $uminus(A_19908) ) ),
inference(superposition,[status(thm),theory(equality)],[c_163048,c_54]) ).
tff(c_163042,plain,
$product(c,d) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_43]) ).
tff(c_164185,plain,
( ( $uminus('#skE_3') = '#skE_3' )
| ( $uminus(c) != c ) ),
inference(superposition,[status(thm),theory(equality)],[c_164047,c_163042]) ).
tff(c_164187,plain,
( ( '#skE_3' = 0 )
| ( c != 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_164185]) ).
tff(c_164288,plain,
c != 0,
inference(splitLeft,[status(thm)],[c_164187]) ).
tff(c_183059,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_183058,c_165660,c_164288]) ).
tff(c_183062,plain,
( ~ $less(a,0)
| $less('#skE_2',0) ),
inference(splitRight,[status(thm)],[c_164482]) ).
tff(c_183065,plain,
~ $less(a,0),
inference(splitLeft,[status(thm)],[c_183062]) ).
tff(c_233,plain,
$product(a,c) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_47]) ).
tff(c_164433,plain,
( ( $uminus('#skE_2') = '#skE_2' )
| ( $uminus(a) != a ) ),
inference(superposition,[status(thm),theory(equality)],[c_164292,c_233]) ).
tff(c_164435,plain,
( ( '#skE_2' = 0 )
| ( a != 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_164433]) ).
tff(c_164533,plain,
a != 0,
inference(splitLeft,[status(thm)],[c_164435]) ).
tff(c_194832,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_194831,c_183065,c_164533]) ).
tff(c_194835,plain,
$less('#skE_4',0),
inference(splitRight,[status(thm)],[c_194829]) ).
tff(c_162868,plain,
$product(a,b) = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_39]) ).
tff(c_162875,plain,
$less(0,'#skE_4'),
inference(demodulation,[status(thm),theory(equality)],[c_162868,c_61]) ).
tff(c_194837,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_194835,c_162875]) ).
tff(c_194840,plain,
$less('#skE_2',0),
inference(splitRight,[status(thm)],[c_183062]) ).
tff(c_194842,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_194840,c_234]) ).
tff(c_194845,plain,
$less('#skE_3',0),
inference(splitRight,[status(thm)],[c_165300]) ).
tff(c_163036,plain,
$product(c,d) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_43]) ).
tff(c_163043,plain,
$less(0,'#skE_3'),
inference(demodulation,[status(thm),theory(equality)],[c_163036,c_62]) ).
tff(c_194847,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_194845,c_163043]) ).
tff(c_194850,plain,
'#skE_2' = 0,
inference(splitRight,[status(thm)],[c_164435]) ).
tff(c_194872,plain,
$less(0,0),
inference(demodulation,[status(thm),theory(equality)],[c_194850,c_234]) ).
tff(c_194885,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_194872]) ).
tff(c_194888,plain,
'#skE_3' = 0,
inference(splitRight,[status(thm)],[c_164187]) ).
tff(c_194910,plain,
$less(0,0),
inference(demodulation,[status(thm),theory(equality)],[c_194888,c_163043]) ).
tff(c_194924,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_194910]) ).
tff(c_194928,plain,
b = 0,
inference(splitRight,[status(thm)],[c_195]) ).
tff(c_195374,plain,
$less(0,$product(0,a)),
inference(demodulation,[status(thm),theory(equality)],[c_57,c_194928,c_39]) ).
tff(c_195376,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_195374]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ARI681_1 : TPTP v8.1.2. Released v6.3.0.
% 0.13/0.14 % 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 : n005.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 00:10:42 EDT 2023
% 0.13/0.35 % CPUTime :
% 37.67/15.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 37.67/15.47
% 37.67/15.47 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 38.02/15.59
% 38.02/15.59 Inference rules
% 38.02/15.59 ----------------------
% 38.02/15.59 #Ref : 0
% 38.02/15.59 #Sup : 29188
% 38.02/15.59 #Fact : 0
% 38.02/15.59 #Define : 7
% 38.02/15.59 #Split : 196
% 38.02/15.59 #Chain : 0
% 38.02/15.59 #Close : 16
% 38.02/15.59
% 38.02/15.59 Ordering : LPO
% 38.02/15.59
% 38.02/15.59 Simplification rules
% 38.02/15.59 ----------------------
% 38.02/15.59 #Subsume : 9686
% 38.02/15.59 #Demod : 5605
% 38.02/15.59 #Tautology : 8070
% 38.02/15.59 #SimpNegUnit : 254
% 38.02/15.59 #BackRed : 21
% 38.02/15.59
% 38.02/15.59 #Partial instantiations: 0
% 38.02/15.59 #Strategies tried : 1
% 38.02/15.59
% 38.02/15.59 Timing (in seconds)
% 38.02/15.59 ----------------------
% 38.02/15.59 Preprocessing : 0.54
% 38.02/15.59 Parsing : 0.29
% 38.02/15.59 CNF conversion : 0.03
% 38.02/15.59 Main loop : 13.85
% 38.02/15.59 Inferencing : 1.38
% 38.02/15.59 Reduction : 5.25
% 38.02/15.59 Demodulation : 3.83
% 38.02/15.59 BG Simplification : 0.83
% 38.02/15.59 Subsumption : 3.90
% 38.02/15.59 Abstraction : 0.38
% 38.02/15.59 MUC search : 0.23
% 38.02/15.59 Cooper : 0.35
% 38.02/15.59 Total : 14.55
% 38.02/15.59 Index Insertion : 0.00
% 38.02/15.59 Index Deletion : 0.00
% 38.02/15.59 Index Matching : 0.00
% 38.02/15.59 BG Taut test : 0.00
%------------------------------------------------------------------------------