TSTP Solution File: SWW662_2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWW662_2 : TPTP v8.1.2. Released v6.1.0.
% 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 : n029.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 11:07:54 EDT 2023
% Result : Theorem 12.44s 4.04s
% Output : CNFRefutation 12.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 72
% Syntax : Number of formulae : 180 ( 79 unt; 58 typ; 0 def)
% Number of atoms : 174 ( 80 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 113 ( 61 ~; 38 |; 4 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number arithmetic : 384 ( 74 atm; 83 fun; 162 num; 65 var)
% Number of types : 8 ( 6 usr; 1 ari)
% Number of type conns : 64 ( 29 >; 35 *; 0 +; 0 <<)
% Number of predicates : 6 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 57 ( 50 usr; 26 con; 0-5 aty)
% Number of variables : 65 (; 64 !; 1 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
%$ sort1 > is_power_of_21 > set > set2 > match_bool1 > get > sum3 > sum2 > mk_array1 > make1 > get2 > const > power1 > mod1 > map > length1 > elts > div1 > #nlpp > witness1 > tb2t2 > tb2t1 > tb2t > t2tb2 > t2tb1 > t2tb > array > abs1 > tuple03 > tuple0 > true1 > real > qtmark > int > false1 > bool > #skF_1 > #skF_2
%Foreground sorts:
tff(map_int_int,type,
map_int_int: $tType ).
tff(tuple02,type,
tuple02: $tType ).
tff(bool1,type,
bool1: $tType ).
tff(array_int,type,
array_int: $tType ).
tff(ty,type,
ty: $tType ).
tff(uni,type,
uni: $tType ).
%Background operators:
tff('#skE_7',type,
'#skE_7': $int ).
tff('#skE_11',type,
'#skE_11': $int ).
tff('#skE_12',type,
'#skE_12': $int ).
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skE_6',type,
'#skE_6': $int ).
tff('#skE_13',type,
'#skE_13': $int ).
tff('#skE_10',type,
'#skE_10': $int ).
tff('#skE_5',type,
'#skE_5': $int ).
tff('#skE_8',type,
'#skE_8': $int ).
tff('#skE_4',type,
'#skE_4': $int ).
tff('#skF_3',type,
'#skF_3': $int ).
tff('#skE_3',type,
'#skE_3': $int ).
tff('#skE_9',type,
'#skE_9': $int ).
tff('#skE_14',type,
'#skE_14': $int ).
%Foreground operators:
tff(tb2t1,type,
tb2t1: uni > map_int_int ).
tff(mod1,type,
mod1: ( $int * $int ) > $int ).
tff(length1,type,
length1: ( ty * uni ) > $int ).
tff(div1,type,
div1: ( $int * $int ) > $int ).
tff(get2,type,
get2: ( ty * uni * $int ) > uni ).
tff(true1,type,
true1: bool1 ).
tff(is_power_of_21,type,
is_power_of_21: $int > $o ).
tff(const,type,
const: ( ty * ty * uni ) > uni ).
tff(elts,type,
elts: ( ty * uni ) > uni ).
tff(int,type,
int: ty ).
tff(false1,type,
false1: bool1 ).
tff(tb2t,type,
tb2t: uni > $int ).
tff(tb2t2,type,
tb2t2: uni > array_int ).
tff(sort1,type,
sort1: ( ty * uni ) > $o ).
tff(t2tb,type,
t2tb: $int > uni ).
tff(witness1,type,
witness1: ty > uni ).
tff(real,type,
real: ty ).
tff('#skF_1',type,
'#skF_1': ( map_int_int * map_int_int * $int * $int ) > $int ).
tff(t2tb2,type,
t2tb2: array_int > uni ).
tff(set,type,
set: ( ty * ty * uni * uni * uni ) > uni ).
tff(match_bool1,type,
match_bool1: ( ty * bool1 * uni * uni ) > uni ).
tff(array,type,
array: ty > ty ).
tff(make1,type,
make1: ( ty * $int * uni ) > uni ).
tff('#skF_2',type,
'#skF_2': $int > $int ).
tff(tuple0,type,
tuple0: ty ).
tff(qtmark,type,
qtmark: ty ).
tff(sum2,type,
sum2: ( map_int_int * $int * $int ) > $int ).
tff(bool,type,
bool: ty ).
tff(t2tb1,type,
t2tb1: map_int_int > uni ).
tff(get,type,
get: ( ty * ty * uni * uni ) > uni ).
tff(tuple03,type,
tuple03: tuple02 ).
tff(power1,type,
power1: ( $int * $int ) > $int ).
tff(map,type,
map: ( ty * ty ) > ty ).
tff(set2,type,
set2: ( ty * uni * $int * uni ) > uni ).
tff(sum3,type,
sum3: ( array_int * $int * $int ) > $int ).
tff(mk_array1,type,
mk_array1: ( ty * $int * uni ) > uni ).
tff(abs1,type,
abs1: $int > $int ).
tff(f_124,axiom,
! [Xa: $int] : ( div1(Xa,1) = Xa ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',div_1) ).
tff(f_76,axiom,
! [Xa: $int,Ya: $int] :
( ( Ya != 0 )
=> ( Xa = $sum($product(Ya,div1(Xa,Ya)),mod1(Xa,Ya)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',div_mod) ).
tff(f_126,axiom,
! [Xa: $int] : ( mod1(Xa,1) = 0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod_1) ).
tff(f_2967,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(f_299,negated_conjecture,
~ ! [Xa: $int] :
( is_power_of_21(Xa)
=> ( $less(1,Xa)
=> ( $product(2,div1(Xa,2)) = Xa ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',is_power_of_2_1) ).
tff(f_2970,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_122,axiom,
! [Xa: $int,Ya: $int] :
( ( Ya != 0 )
=> $lesseq(abs1($product(div1(Xa,Ya),Ya)),abs1(Xa)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rounds_toward_zero) ).
tff(f_63,axiom,
! [Xa: $int] :
( ( $lesseq(0,Xa)
=> ( abs1(Xa) = Xa ) )
& ( ~ $lesseq(0,Xa)
=> ( abs1(Xa) = $uminus(Xa) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abs_def) ).
tff(f_132,axiom,
! [Xa: $int,Ya: $int] :
( ( $lesseq(0,Xa)
& $less(Xa,Ya) )
=> ( div1(Xa,Ya) = 0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',div_inf) ).
tff(f_292,axiom,
! [Xa: $int] :
( is_power_of_21(Xa)
<=> ? [Ka: $int] :
( $lesseq(0,Ka)
& ( Xa = power1(2,Ka) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',is_power_of_2_def) ).
tff(f_164,axiom,
! [Xa: $int,Na: $int] :
( $less(0,Na)
=> ( power1(Xa,Na) = $product(Xa,power1(Xa,$difference(Na,1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_s_alt) ).
tff(f_156,axiom,
! [Xa: $int] : ( power1(Xa,0) = 1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_0) ).
tff(f_285,axiom,
! [Xa: $int] :
( $lesseq(0,Xa)
=> ( $lesseq($product(2,div1(Xa,2)),Xa)
& $lesseq($difference(Xa,1),$product(2,div1(Xa,2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',div_mod_2) ).
tff(f_71,axiom,
! [Xa: $int] : $lesseq(0,abs1(Xa)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abs_pos) ).
tff(c_246,plain,
! [X_37a: $int] : ( div1(X_37a,1) = X_37a ),
inference(cnfTransformation,[status(thm)],[f_124]) ).
tff(c_30,plain,
! [Y_22a: $int,X_21a: $int] :
( ( $sum($product(Y_22a,div1(X_21a,Y_22a)),mod1(X_21a,Y_22a)) = X_21a )
| ( Y_22a = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_6266,plain,
! [X_1245a: $int,Y_1246a: $int] :
( ( mod1(X_1245a,Y_1246a) = $sum(X_1245a,$uminus($product(Y_1246a,div1(X_1245a,Y_1246a)))) )
| ( Y_1246a = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_30]) ).
tff(c_245,plain,
! [X_38a: $int] : ( mod1(X_38a,1) = 0 ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_6294,plain,
! [X_1245a: $int] :
( ( $sum(X_1245a,$uminus($product(1,div1(X_1245a,1)))) = 0 )
| ( 1 = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_6266,c_245]) ).
tff(c_6320,plain,
! [X_1245a: $int] :
( ( $sum(X_1245a,$uminus($product(1,X_1245a))) = 0 )
| ( 1 = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_246,c_6294]) ).
tff(c_6335,plain,
! [X_1247a: $int] : ( $product(1,X_1247a) = X_1247a ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6320]) ).
tff(c_276,plain,
! [X_207: $int,N_164: $int,M_163: $int] :
( ( $product(X_207,N_164) = $sum(N_164,$product(M_163,N_164)) )
| ( X_207 != $sum(1,M_163) ) ),
inference(cnfTransformation,[status(thm)],[f_2967]) ).
tff(c_6420,plain,
! [X_1247a: $int] : ( $product($sum(1,1),X_1247a) = $sum(X_1247a,X_1247a) ),
inference(superposition,[status(thm),theory(equality)],[c_6335,c_276]) ).
tff(c_6422,plain,
! [X_1247a: $int] : ( $product(2,X_1247a) = $product(2,X_1247a) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6420]) ).
tff(c_191,plain,
$product(2,div1('#skF_3',2)) != '#skF_3',
inference(cnfTransformation,[status(thm)],[f_299]) ).
tff(c_331,plain,
div1('#skF_3',2) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_191]) ).
tff(c_274,plain,
! [B_167: $int,A_168: $int] : ( $product(B_167,A_168) = $product(A_168,B_167) ),
inference(cnfTransformation,[status(thm)],[f_2970]) ).
tff(c_47,plain,
! [X_35a: $int,Y_36a: $int] :
( $lesseq(abs1($product(div1(X_35a,Y_36a),Y_36a)),abs1(X_35a))
| ( Y_36a = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_247,plain,
! [X_35a: $int,Y_36a: $int] :
( ~ $less(abs1(X_35a),abs1($product(div1(X_35a,Y_36a),Y_36a)))
| ( Y_36a = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_47]) ).
tff(c_1501,plain,
! [X_662a: $int,Y_663a: $int] :
( ~ $less(abs1(X_662a),abs1($product(Y_663a,div1(X_662a,Y_663a))))
| ( Y_663a = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_274,c_247]) ).
tff(c_1543,plain,
( ~ $less(abs1('#skF_3'),abs1($product(2,'#skE_1')))
| ( 2 = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_331,c_1501]) ).
tff(c_1546,plain,
~ $less(abs1('#skF_3'),abs1($product(2,'#skE_1'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1543]) ).
tff(c_4658,plain,
abs1('#skF_3') = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_1546]) ).
tff(c_17,plain,
! [X_17a: $int] :
( ( abs1(X_17a) = X_17a )
| ~ $lesseq(0,X_17a) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_263,plain,
! [X_17a: $int] :
( ( abs1(X_17a) = X_17a )
| $less(X_17a,0) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_17]) ).
tff(c_4738,plain,
( ( '#skF_3' = '#skE_6' )
| $less('#skF_3',0) ),
inference(superposition,[status(thm),theory(equality)],[c_4658,c_263]) ).
tff(c_4753,plain,
$less('#skF_3',0),
inference(splitLeft,[status(thm)],[c_4738]) ).
tff(c_53,plain,
! [X_39a: $int,Y_40a: $int] :
( ( div1(X_39a,Y_40a) = 0 )
| ~ $lesseq(0,X_39a)
| ~ $less(X_39a,Y_40a) ),
inference(cnfTransformation,[status(thm)],[f_132]) ).
tff(c_1279,plain,
! [X_636a: $int,Y_637a: $int] :
( ( div1(X_636a,Y_637a) = 0 )
| $less(X_636a,0)
| ~ $less(X_636a,Y_637a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_53]) ).
tff(c_1304,plain,
( ( '#skE_1' = 0 )
| $less('#skF_3',0)
| ~ $less('#skF_3',2) ),
inference(superposition,[status(thm),theory(equality)],[c_1279,c_331]) ).
tff(c_1312,plain,
~ $less('#skF_3',2),
inference(splitLeft,[status(thm)],[c_1304]) ).
tff(c_4894,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_4753,c_1312]) ).
tff(c_4897,plain,
'#skF_3' = '#skE_6',
inference(splitRight,[status(thm)],[c_4738]) ).
tff(c_186,plain,
is_power_of_21('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_299]) ).
tff(c_153,plain,
! [X_157a: $int] :
( $lesseq(0,'#skF_2'(X_157a))
| ~ is_power_of_21(X_157a) ),
inference(cnfTransformation,[status(thm)],[f_292]) ).
tff(c_473,plain,
! [X_334a: $int] :
( ~ $less('#skF_2'(X_334a),0)
| ~ is_power_of_21(X_334a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_153]) ).
tff(c_479,plain,
~ $less('#skF_2'('#skF_3'),0),
inference(resolution,[status(thm)],[c_186,c_473]) ).
tff(c_494,plain,
'#skF_2'('#skF_3') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_479]) ).
tff(c_4971,plain,
'#skF_2'('#skE_6') = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_4897,c_494]) ).
tff(c_4955,plain,
is_power_of_21('#skE_6'),
inference(demodulation,[status(thm),theory(equality)],[c_4897,c_186]) ).
tff(c_193,plain,
! [X_157a: $int] :
( ( power1(2,'#skF_2'(X_157a)) = X_157a )
| ~ is_power_of_21(X_157a) ),
inference(cnfTransformation,[status(thm)],[f_292]) ).
tff(c_4964,plain,
power1(2,'#skF_2'('#skE_6')) = '#skE_6',
inference(resolution,[status(thm)],[c_4955,c_193]) ).
tff(c_5545,plain,
power1(2,'#skE_2') = '#skE_6',
inference(demodulation,[status(thm),theory(equality)],[c_4971,c_4964]) ).
tff(c_8258,plain,
! [X_1609a: $int,N_1610a: $int] :
( ( $product(X_1609a,power1(X_1609a,$sum($uminus(1),N_1610a))) = power1(X_1609a,N_1610a) )
| ~ $less(0,N_1610a) ),
inference(cnfTransformation,[status(thm)],[f_164]) ).
tff(c_8568,plain,
( ( $product(2,power1(2,$sum($uminus(1),'#skE_2'))) = '#skE_6' )
| ~ $less(0,'#skE_2') ),
inference(superposition,[status(thm),theory(equality)],[c_5545,c_8258]) ).
tff(c_8639,plain,
power1(2,$sum($uminus(1),'#skE_2')) = '#skE_14',
inference(define,[status(thm),theory(equality)],[c_8568]) ).
tff(c_8464,plain,
( ( $product(2,power1(2,$sum($uminus(1),'#skE_2'))) = '#skE_6' )
| ~ $less(0,'#skE_2') ),
inference(superposition,[status(thm),theory(equality)],[c_8258,c_5545]) ).
tff(c_8820,plain,
( ( '#skE_6' = $product(2,'#skE_14') )
| ~ $less(0,'#skE_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_6422,c_8639,c_8464]) ).
tff(c_8822,plain,
~ $less(0,'#skE_2'),
inference(splitLeft,[status(thm)],[c_8820]) ).
tff(c_240,plain,
! [X_49a: $int] : ( power1(X_49a,0) = 1 ),
inference(cnfTransformation,[status(thm)],[f_156]) ).
tff(c_148,plain,
! [K_160a: $int] :
( is_power_of_21(power1(2,K_160a))
| ~ $lesseq(0,K_160a) ),
inference(cnfTransformation,[status(thm)],[f_292]) ).
tff(c_538,plain,
! [K_399a: $int] :
( is_power_of_21(power1(2,K_399a))
| $less(K_399a,0) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_148]) ).
tff(c_546,plain,
( is_power_of_21(1)
| $less(0,0) ),
inference(superposition,[status(thm),theory(equality)],[c_240,c_538]) ).
tff(c_550,plain,
is_power_of_21(1),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_546]) ).
tff(c_192,plain,
! [X_157a: $int] :
( ~ $less('#skF_2'(X_157a),0)
| ~ is_power_of_21(X_157a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_153]) ).
tff(c_561,plain,
~ $less('#skF_2'(1),0),
inference(resolution,[status(thm)],[c_550,c_192]) ).
tff(c_598,plain,
'#skF_2'(1) = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_561]) ).
tff(c_610,plain,
( ( '#skE_4' = '#skE_2' )
| ( '#skF_3' != 1 ) ),
inference(superposition,[status(thm),theory(equality)],[c_598,c_494]) ).
tff(c_615,plain,
'#skF_3' != 1,
inference(splitLeft,[status(thm)],[c_610]) ).
tff(c_497,plain,
'#skF_2'('#skF_3') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_479]) ).
tff(c_616,plain,
! [X_514a: $int] :
( ( power1(2,'#skF_2'(X_514a)) = X_514a )
| ~ is_power_of_21(X_514a) ),
inference(cnfTransformation,[status(thm)],[f_292]) ).
tff(c_625,plain,
power1(2,'#skF_2'('#skF_3')) = '#skF_3',
inference(resolution,[status(thm)],[c_186,c_616]) ).
tff(c_646,plain,
power1(2,'#skE_2') = '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_497,c_625]) ).
tff(c_661,plain,
( ( '#skF_3' = 1 )
| ( '#skE_2' != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_646,c_240]) ).
tff(c_682,plain,
'#skE_2' != 0,
inference(negUnitSimplification,[status(thm)],[c_615,c_661]) ).
tff(c_488,plain,
'#skF_2'('#skF_3') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_479]) ).
tff(c_487,plain,
~ $less('#skF_2'('#skF_3'),0),
inference(resolution,[status(thm)],[c_186,c_473]) ).
tff(c_495,plain,
~ $less('#skE_2',0),
inference(demodulation,[status(thm),theory(equality)],[c_488,c_487]) ).
tff(c_8823,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_8822,c_682,c_495]) ).
tff(c_8826,plain,
'#skE_6' = $product(2,'#skE_14'),
inference(splitRight,[status(thm)],[c_8820]) ).
tff(c_4948,plain,
div1('#skE_6',2) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_4897,c_331]) ).
tff(c_143,plain,
! [X_156a: $int] :
( $lesseq($difference(X_156a,1),$product(2,div1(X_156a,2)))
| ~ $lesseq(0,X_156a) ),
inference(cnfTransformation,[status(thm)],[f_285]) ).
tff(c_5612,plain,
! [X_1102a: $int] :
( ~ $less($sum(1,$product(2,div1(X_1102a,2))),X_1102a)
| $less(X_1102a,0) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_143]) ).
tff(c_5621,plain,
( ~ $less($sum(1,$product(2,'#skE_1')),'#skE_6')
| $less('#skE_6',0) ),
inference(superposition,[status(thm),theory(equality)],[c_4948,c_5612]) ).
tff(c_6462,plain,
~ $less($sum(1,$product(2,'#skE_1')),'#skE_6'),
inference(splitLeft,[status(thm)],[c_5621]) ).
tff(c_8866,plain,
~ $less($sum(1,$product(2,'#skE_1')),$product(2,'#skE_14')),
inference(demodulation,[status(thm),theory(equality)],[c_8826,c_6462]) ).
tff(c_8920,plain,
~ $less('#skE_1','#skE_14'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_8866]) ).
tff(c_145,plain,
! [X_156a: $int] :
( $lesseq($product(2,div1(X_156a,2)),X_156a)
| ~ $lesseq(0,X_156a) ),
inference(cnfTransformation,[status(thm)],[f_285]) ).
tff(c_1384,plain,
! [X_648a: $int] :
( ~ $less(X_648a,$product(2,div1(X_648a,2)))
| $less(X_648a,0) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_145]) ).
tff(c_1395,plain,
( ~ $less('#skF_3',$product(2,'#skE_1'))
| $less('#skF_3',0) ),
inference(superposition,[status(thm),theory(equality)],[c_331,c_1384]) ).
tff(c_1397,plain,
~ $less('#skF_3',$product(2,'#skE_1')),
inference(splitLeft,[status(thm)],[c_1395]) ).
tff(c_4937,plain,
~ $less('#skE_6',$product(2,'#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_4897,c_1397]) ).
tff(c_8877,plain,
~ $less($product(2,'#skE_14'),$product(2,'#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_8826,c_4937]) ).
tff(c_8926,plain,
~ $less('#skE_14','#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_8877]) ).
tff(c_325,plain,
div1('#skF_3',2) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_191]) ).
tff(c_278,plain,
$product(2,div1('#skF_3',2)) != '#skF_3',
inference(cnfTransformation,[status(thm)],[f_299]) ).
tff(c_332,plain,
'#skF_3' != $product(2,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_325,c_278]) ).
tff(c_4949,plain,
'#skE_6' != $product(2,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_4897,c_332]) ).
tff(c_8895,plain,
$product(2,'#skE_14') != $product(2,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_8826,c_4949]) ).
tff(c_8936,plain,
'#skE_14' != '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_8895]) ).
tff(c_8959,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_8920,c_8926,c_8936]) ).
tff(c_8962,plain,
$less('#skE_6',0),
inference(splitRight,[status(thm)],[c_5621]) ).
tff(c_4641,plain,
$product(2,'#skE_1') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_1546]) ).
tff(c_4640,plain,
abs1('#skF_3') = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_1546]) ).
tff(c_1611,plain,
~ $less(abs1('#skF_3'),abs1($product(2,'#skE_1'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1543]) ).
tff(c_4655,plain,
~ $less('#skE_6',abs1('#skE_7')),
inference(demodulation,[status(thm),theory(equality)],[c_4641,c_4640,c_1611]) ).
tff(c_6160,plain,
abs1('#skE_7') = '#skE_9',
inference(define,[status(thm),theory(equality)],[c_4655]) ).
tff(c_28,plain,
! [X_20a: $int] : $lesseq(0,abs1(X_20a)),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_258,plain,
! [X_20a: $int] : ~ $less(abs1(X_20a),0),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_28]) ).
tff(c_6255,plain,
~ $less('#skE_9',0),
inference(superposition,[status(thm),theory(equality)],[c_6160,c_258]) ).
tff(c_6150,plain,
abs1('#skE_7') = '#skE_9',
inference(define,[status(thm),theory(equality)],[c_4655]) ).
tff(c_6149,plain,
~ $less('#skE_6',abs1('#skE_7')),
inference(demodulation,[status(thm),theory(equality)],[c_4641,c_4640,c_1611]) ).
tff(c_6157,plain,
~ $less('#skE_6','#skE_9'),
inference(demodulation,[status(thm),theory(equality)],[c_6150,c_6149]) ).
tff(c_9009,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_8962,c_6255,c_6157]) ).
tff(c_9012,plain,
$less('#skF_3',0),
inference(splitRight,[status(thm)],[c_1395]) ).
tff(c_9014,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_9012,c_1312]) ).
tff(c_9018,plain,
$less('#skF_3',2),
inference(splitRight,[status(thm)],[c_1304]) ).
tff(c_187,plain,
$less(1,'#skF_3'),
inference(cnfTransformation,[status(thm)],[f_299]) ).
tff(c_9019,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_9018,c_187]) ).
tff(c_9023,plain,
'#skF_3' = 1,
inference(splitRight,[status(thm)],[c_610]) ).
tff(c_9040,plain,
$less(1,1),
inference(demodulation,[status(thm),theory(equality)],[c_9023,c_187]) ).
tff(c_9047,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_9040]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW662_2 : TPTP v8.1.2. Released v6.1.0.
% 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 : n029.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 : Thu Aug 3 19:35:37 EDT 2023
% 0.14/0.35 % CPUTime :
% 12.44/4.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.44/4.05
% 12.44/4.05 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.44/4.10
% 12.44/4.10 Inference rules
% 12.44/4.10 ----------------------
% 12.44/4.10 #Ref : 0
% 12.44/4.10 #Sup : 1386
% 12.44/4.10 #Fact : 1
% 12.44/4.10 #Define : 16
% 12.44/4.10 #Split : 45
% 12.44/4.10 #Chain : 0
% 12.44/4.10 #Close : 11
% 12.44/4.10
% 12.44/4.10 Ordering : LPO
% 12.44/4.10
% 12.44/4.10 Simplification rules
% 12.44/4.10 ----------------------
% 12.44/4.10 #Subsume : 118
% 12.44/4.10 #Demod : 459
% 12.44/4.10 #Tautology : 588
% 12.44/4.10 #SimpNegUnit : 50
% 12.44/4.10 #BackRed : 80
% 12.44/4.10
% 12.44/4.10 #Partial instantiations: 167
% 12.44/4.10 #Strategies tried : 1
% 12.44/4.10
% 12.44/4.10 Timing (in seconds)
% 12.44/4.10 ----------------------
% 12.44/4.10 Preprocessing : 0.83
% 12.44/4.10 Parsing : 0.44
% 12.44/4.10 CNF conversion : 0.06
% 12.44/4.10 Main loop : 2.05
% 12.44/4.10 Inferencing : 0.42
% 12.44/4.10 Reduction : 0.52
% 12.44/4.10 Demodulation : 0.39
% 12.44/4.10 BG Simplification : 0.19
% 12.44/4.10 Subsumption : 0.39
% 12.44/4.10 Abstraction : 0.06
% 12.44/4.10 MUC search : 0.13
% 12.44/4.10 Cooper : 0.33
% 12.44/4.10 Total : 2.95
% 12.44/4.10 Index Insertion : 0.00
% 12.44/4.10 Index Deletion : 0.00
% 12.44/4.10 Index Matching : 0.00
% 12.44/4.10 BG Taut test : 0.00
%------------------------------------------------------------------------------