TSTP Solution File: ARI635_1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ARI635_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 : n022.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 10:34:10 EDT 2023
% Result : Theorem 12.38s 4.70s
% Output : CNFRefutation 12.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 22
% Syntax : Number of formulae : 88 ( 54 unt; 11 typ; 0 def)
% Number of atoms : 108 ( 35 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 82 ( 51 ~; 24 |; 1 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 199 ( 66 atm; 56 fun; 47 num; 30 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 11 usr; 15 con; 0-2 aty)
% Number of variables : 30 (; 30 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
%$ #nlpp > f
%Foreground sorts:
%Background operators:
tff('#skE_1',type,
'#skE_1': $real ).
tff(u,type,
u: $real ).
tff(x,type,
x: $real ).
tff('#skE_2',type,
'#skE_2': $real ).
tff('#skE_4',type,
'#skE_4': $real ).
tff('#skE_3',type,
'#skE_3': $real ).
tff(y,type,
y: $real ).
tff(v,type,
v: $real ).
tff(w,type,
w: $real ).
tff(s,type,
s: $real ).
%Foreground operators:
tff(f,type,
f: $real > $real ).
tff(f_40,negated_conjecture,
~ $less($sum(f(x),u),$sum($product(v,v),f(y))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conclusion) ).
tff(f_126,axiom,
! [X: $real,Y: $real,Z: $real] :
( ( Y != 0 )
=> ( ( Z = $quotient(X,Y) )
<=> ( X = $product(Y,Z) ) ) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas_real.p',nonzero_eq_divide_eq) ).
tff(f_146,axiom,
! [A: $real,B: $real] : ( $uminus($product(A,B)) = $product($uminus(A),B) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas_real.p',minus_mult_left) ).
tff(f_37,hypothesis,
$less($product($quotient(1,3),$sum(w,s)),v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_03) ).
tff(f_220,axiom,
! [A: $real,B: $real] :
( $less(0,A)
=> ( $less(1,$quotient(B,A))
<=> $less(A,B) ) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas_real.p',less_divide_eq_1_pos) ).
tff(f_34,hypothesis,
$less(u,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis) ).
tff(f_33,axiom,
! [Xa: $real,Ya: $real] :
( $greatereq(Xa,Ya)
=> $greatereq(f(Xa),f(Ya)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_non_decreasing) ).
tff(f_38,hypothesis,
$lesseq(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_04) ).
tff(f_35,hypothesis,
$greater(w,1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_01) ).
tff(f_36,hypothesis,
$greater(s,2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_02) ).
tff(f_163,axiom,
! [A: $real,B: $real] :
( ( $less(0,A)
& $less(0,B) )
=> $less(0,$product(A,B)) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas_real.p',mult_nonneg_nonneg) ).
tff(c_90,plain,
~ $less($sum(f(x),u),$sum($product(v,v),f(y))),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_190,plain,
$product(v,v) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_90]) ).
tff(c_22,plain,
! [Y_12: $real,Z_13: $real] :
( ( $quotient($product(Y_12,Z_13),Y_12) = Z_13 )
| ( Y_12 = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_279,plain,
( ( $quotient('#skE_2',v) = v )
| ( v = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_190,c_22]) ).
tff(c_447,plain,
$quotient('#skE_2',v) = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_279]) ).
tff(c_446,plain,
( ( $quotient('#skE_2',v) = v )
| ( v = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_190,c_22]) ).
tff(c_449,plain,
( ( v = '#skE_4' )
| ( v = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_447,c_446]) ).
tff(c_453,plain,
v = 0,
inference(splitLeft,[status(thm)],[c_449]) ).
tff(c_126,plain,
$product(v,v) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_90]) ).
tff(c_95,plain,
! [A_34: $real,B_35: $real,X_112: $real] :
( ( $uminus($product(A_34,B_35)) = $product(X_112,B_35) )
| ( X_112 != $uminus(A_34) ) ),
inference(cnfTransformation,[status(thm)],[f_146]) ).
tff(c_387,plain,
! [A_197: $real] :
( ( $uminus($product(A_197,v)) = '#skE_2' )
| ( v != $uminus(A_197) ) ),
inference(superposition,[status(thm),theory(equality)],[c_95,c_190]) ).
tff(c_430,plain,
( ( $uminus('#skE_2') = '#skE_2' )
| ( $uminus(v) != v ) ),
inference(superposition,[status(thm),theory(equality)],[c_126,c_387]) ).
tff(c_431,plain,
( ( $uminus('#skE_2') = '#skE_2' )
| ( $uminus(v) != v ) ),
inference(backgroundSimplification,[status(thm),theory('LFA')],[c_430]) ).
tff(c_444,plain,
$uminus(v) != v,
inference(splitLeft,[status(thm)],[c_431]) ).
tff(c_454,plain,
$uminus(0) != 0,
inference(demodulation,[status(thm),theory(equality)],[c_453,c_453,c_444]) ).
tff(c_466,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LFA')],[c_454]) ).
tff(c_467,plain,
v = '#skE_4',
inference(splitRight,[status(thm)],[c_449]) ).
tff(c_9,plain,
$less($product(1/3,$sum(w,s)),v),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_10,plain,
~ $lesseq(v,$product(1/3,$sum(w,s))),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_9]) ).
tff(c_481,plain,
~ $lesseq('#skE_4',$product(1/3,$sum(w,s))),
inference(demodulation,[status(thm),theory(equality)],[c_467,c_10]) ).
tff(c_452,plain,
$quotient('#skE_2',v) = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_279]) ).
tff(c_494,plain,
$quotient('#skE_2','#skE_4') = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_467,c_452]) ).
tff(c_85,plain,
! [B_94: $real,A_93: $real] :
( ~ $less(1,$quotient(B_94,A_93))
| ~ $less(0,A_93)
| $less(A_93,B_94) ),
inference(cnfTransformation,[status(thm)],[f_220]) ).
tff(c_87,plain,
! [B_97: $real,A_98: $real] :
( ~ $less(1,$quotient(B_97,A_98))
| ~ $less(0,A_98)
| ~ $lesseq(B_97,A_98) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_85]) ).
tff(c_581,plain,
( ~ $less(1,'#skE_4')
| ~ $less(0,'#skE_4')
| ~ $lesseq('#skE_2','#skE_4') ),
inference(superposition,[status(thm),theory(equality)],[c_494,c_87]) ).
tff(c_1431,plain,
~ $lesseq('#skE_2','#skE_4'),
inference(splitLeft,[status(thm)],[c_581]) ).
tff(c_3,plain,
$less(u,v),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_4,plain,
~ $lesseq(v,u),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_3]) ).
tff(c_482,plain,
~ $lesseq('#skE_4',u),
inference(demodulation,[status(thm),theory(equality)],[c_467,c_4]) ).
tff(c_124,plain,
f(x) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_90]) ).
tff(c_156,plain,
f(y) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_90]) ).
tff(c_1,plain,
! [X_1a: $real,Y_2a: $real] :
( $greatereq(f(X_1a),f(Y_2a))
| ~ $greatereq(X_1a,Y_2a) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_2,plain,
! [X_1a: $real,Y_2a: $real] :
( ~ $less(f(X_1a),f(Y_2a))
| ~ $lesseq(Y_2a,X_1a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_1]) ).
tff(c_333,plain,
! [Y_190a: $real] :
( ~ $less('#skE_3',f(Y_190a))
| ~ $lesseq(Y_190a,y) ),
inference(superposition,[status(thm),theory(equality)],[c_156,c_2]) ).
tff(c_342,plain,
( ~ $less('#skE_3','#skE_1')
| ~ $lesseq(x,y) ),
inference(superposition,[status(thm),theory(equality)],[c_124,c_333]) ).
tff(c_343,plain,
~ $lesseq(x,y),
inference(splitLeft,[status(thm)],[c_342]) ).
tff(c_11,plain,
$lesseq(x,y),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_12,plain,
~ $less(y,x),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_11]) ).
tff(c_344,plain,
$false,
inference(close,[status(thm),theory('LFA')],[c_343,c_12]) ).
tff(c_345,plain,
~ $less('#skE_3','#skE_1'),
inference(splitRight,[status(thm)],[c_342]) ).
tff(c_117,plain,
f(y) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_90]) ).
tff(c_116,plain,
$product(v,v) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_90]) ).
tff(c_115,plain,
f(x) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_90]) ).
tff(c_98,plain,
~ $less($sum(f(x),u),$sum($product(v,v),f(y))),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_119,plain,
~ $less($sum('#skE_1',u),$sum('#skE_2','#skE_3')),
inference(demodulation,[status(thm),theory(equality)],[c_117,c_116,c_115,c_98]) ).
tff(c_1509,plain,
$false,
inference(close,[status(thm),theory('LFA')],[c_1431,c_482,c_345,c_119]) ).
tff(c_1510,plain,
( ~ $less(0,'#skE_4')
| ~ $less(1,'#skE_4') ),
inference(splitRight,[status(thm)],[c_581]) ).
tff(c_1513,plain,
~ $less(1,'#skE_4'),
inference(splitLeft,[status(thm)],[c_1510]) ).
tff(c_5,plain,
$greater(w,1),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_6,plain,
~ $lesseq(w,1),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_5]) ).
tff(c_7,plain,
$greater(s,2),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_8,plain,
~ $lesseq(s,2),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_7]) ).
tff(c_6203,plain,
$false,
inference(close,[status(thm),theory('LFA')],[c_481,c_1513,c_6,c_8]) ).
tff(c_6204,plain,
~ $less(0,'#skE_4'),
inference(splitRight,[status(thm)],[c_1510]) ).
tff(c_52,plain,
! [A_42: $real,B_43: $real] :
( $less(0,$product(A_42,B_43))
| ~ $less(0,A_42)
| ~ $less(0,B_43) ),
inference(cnfTransformation,[status(thm)],[f_163]) ).
tff(c_54,plain,
! [A_44: $real,B_45: $real] :
( ~ $lesseq($product(A_44,B_45),0)
| ~ $less(0,A_44)
| ~ $less(0,B_45) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_52]) ).
tff(c_299,plain,
( ~ $lesseq('#skE_2',0)
| ~ $less(0,v) ),
inference(superposition,[status(thm),theory(equality)],[c_190,c_54]) ).
tff(c_326,plain,
~ $less(0,v),
inference(splitLeft,[status(thm)],[c_299]) ).
tff(c_327,plain,
$false,
inference(close,[status(thm),theory('LFA')],[c_326,c_10,c_6,c_8]) ).
tff(c_329,plain,
$less(0,v),
inference(splitRight,[status(thm)],[c_299]) ).
tff(c_330,plain,
~ $lesseq(v,0),
inference(backgroundSimplification,[status(thm),theory('LFA')],[c_329]) ).
tff(c_475,plain,
~ $lesseq('#skE_4',0),
inference(demodulation,[status(thm),theory(equality)],[c_467,c_330]) ).
tff(c_6207,plain,
$false,
inference(close,[status(thm),theory('LFA')],[c_6204,c_475]) ).
tff(c_6208,plain,
$uminus('#skE_2') = '#skE_2',
inference(splitRight,[status(thm)],[c_431]) ).
tff(c_328,plain,
~ $lesseq('#skE_2',0),
inference(splitRight,[status(thm)],[c_299]) ).
tff(c_6210,plain,
$false,
inference(close,[status(thm),theory('LFA')],[c_6208,c_328]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ARI635_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
% 0.18/0.35 % Computer : n022.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Fri Aug 4 00:07:48 EDT 2023
% 0.18/0.35 % CPUTime :
% 12.38/4.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.38/4.72
% 12.38/4.72 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.47/4.76
% 12.47/4.76 Inference rules
% 12.47/4.76 ----------------------
% 12.47/4.76 #Ref : 0
% 12.47/4.76 #Sup : 953
% 12.47/4.76 #Fact : 0
% 12.47/4.76 #Define : 4
% 12.47/4.76 #Split : 20
% 12.47/4.76 #Chain : 0
% 12.47/4.76 #Close : 8
% 12.47/4.76
% 12.47/4.76 Ordering : LPO
% 12.47/4.76
% 12.47/4.76 Simplification rules
% 12.47/4.76 ----------------------
% 12.47/4.76 #Subsume : 117
% 12.47/4.76 #Demod : 441
% 12.47/4.76 #Tautology : 145
% 12.47/4.76 #SimpNegUnit : 66
% 12.47/4.76 #BackRed : 14
% 12.47/4.76
% 12.47/4.76 #Partial instantiations: 0
% 12.47/4.76 #Strategies tried : 1
% 12.47/4.76
% 12.47/4.76 Timing (in seconds)
% 12.47/4.76 ----------------------
% 12.47/4.76 Preprocessing : 0.66
% 12.47/4.76 Parsing : 0.31
% 12.47/4.76 CNF conversion : 0.03
% 12.47/4.76 Main loop : 3.02
% 12.47/4.76 Inferencing : 0.38
% 12.47/4.76 Reduction : 0.49
% 12.47/4.76 Demodulation : 0.37
% 12.47/4.76 BG Simplification : 0.16
% 12.47/4.76 Subsumption : 0.23
% 12.47/4.76 Abstraction : 0.12
% 12.47/4.76 MUC search : 1.11
% 12.47/4.76 Cooper : 0.00
% 12.47/4.76 Total : 3.75
% 12.47/4.76 Index Insertion : 0.00
% 12.47/4.76 Index Deletion : 0.00
% 12.47/4.76 Index Matching : 0.00
% 12.47/4.76 BG Taut test : 0.00
%------------------------------------------------------------------------------