TSTP Solution File: ARI633_1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ARI633_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 10:34:09 EDT 2023
% Result : Theorem 17.08s 6.12s
% Output : CNFRefutation 17.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 22
% Syntax : Number of formulae : 107 ( 69 unt; 9 typ; 0 def)
% Number of atoms : 137 ( 74 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 94 ( 55 ~; 32 |; 1 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 291 ( 55 atm; 116 fun; 66 num; 54 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 9 usr; 10 con; 0-2 aty)
% Number of variables : 54 (; 54 !; 0 ?; 54 :)
% 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(v,type,
v: $real ).
tff(w,type,
w: $real ).
%Foreground operators:
tff(f,type,
f: $real > $real ).
tff(f_93,axiom,
! [N: $real] : ( $product(0,N) = 0 ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas_real.p',mult_def_1) ).
tff(f_98,axiom,
! [A: $real,B: $real] : ( $product(A,B) = $product(B,A) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas_real.p',mult_comm) ).
tff(f_35,negated_conjecture,
~ $less($sum(u,$product(w,f(x))),$sum(v,w)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conclusion) ).
tff(f_86,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_123,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(f_33,hypothesis,
$greater(w,0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_01) ).
tff(f_127,axiom,
! [A: $real,B: $real,C: $real] : ( $product(A,$quotient(B,C)) = $quotient($product(A,B),C) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas_real.p',times_divide_eq_right) ).
tff(f_154,axiom,
! [A: $real,B: $real,C: $real] :
( ( B != 0 )
=> ( $quotient($product(C,A),$product(C,B)) = $quotient(A,B) ) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas_real.p',nonzero_mult_divide_mult_cancel_left) ).
tff(f_131,axiom,
! [A: $real,B: $real] : ( $quotient($uminus(A),B) = $uminus($quotient(A,B)) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas_real.p',divide_minus_left) ).
tff(f_106,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_180,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_32,hypothesis,
$less(u,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis) ).
tff(f_31,axiom,
! [Xa: $real] : $lesseq(f(Xa),1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_less_equal_1) ).
tff(c_22,plain,
! [N_15: $real] : ( $product(0,N_15) = 0 ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_24,plain,
! [N_16: $real] : ( $product(0,N_16) = 0 ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_22]) ).
tff(c_30,plain,
! [B_23: $real,A_24: $real] : ( $product(B_23,A_24) = $product(A_24,B_23) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_85,plain,
~ $less($sum(u,$product(w,f(x))),$sum(v,w)),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_110,plain,
f(x) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_85]) ).
tff(c_93,plain,
~ $less($sum(u,$product(w,f(x))),$sum(v,w)),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_113,plain,
~ $less($sum(u,$product(w,'#skE_1')),$sum(v,w)),
inference(demodulation,[status(thm),theory(equality)],[c_110,c_93]) ).
tff(c_121,plain,
~ $less($sum(u,$product('#skE_1',w)),$sum(v,w)),
inference(demodulation,[status(thm),theory(equality)],[c_30,c_113]) ).
tff(c_148,plain,
$product('#skE_1',w) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_121]) ).
tff(c_17,plain,
! [Y_11: $real,Z_12: $real] :
( ( $quotient($product(Y_11,Z_12),Y_11) = Z_12 )
| ( Y_11 = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_236,plain,
( ( $quotient('#skE_2','#skE_1') = w )
| ( '#skE_1' = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_148,c_17]) ).
tff(c_445,plain,
$quotient('#skE_2','#skE_1') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_236]) ).
tff(c_444,plain,
( ( $quotient('#skE_2','#skE_1') = w )
| ( '#skE_1' = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_148,c_17]) ).
tff(c_447,plain,
( ( w = '#skE_3' )
| ( '#skE_1' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_445,c_444]) ).
tff(c_451,plain,
'#skE_1' = 0,
inference(splitLeft,[status(thm)],[c_447]) ).
tff(c_145,plain,
$product('#skE_1',w) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_121]) ).
tff(c_460,plain,
$product(0,w) = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_451,c_145]) ).
tff(c_461,plain,
$product(0,w) = '#skE_2',
inference(backgroundSimplification,[status(thm),theory('LFA')],[c_460]) ).
tff(c_468,plain,
'#skE_2' = 0,
inference(demodulation,[status(thm),theory(equality)],[c_24,c_461]) ).
tff(c_47,plain,
! [A_41: $real,B_42: $real] :
( $less(0,$product(A_41,B_42))
| ~ $less(0,A_41)
| ~ $less(0,B_42) ),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_49,plain,
! [A_43: $real,B_44: $real] :
( ~ $lesseq($product(A_43,B_44),0)
| ~ $less(0,A_43)
| ~ $less(0,B_44) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_47]) ).
tff(c_256,plain,
( ~ $lesseq('#skE_2',0)
| ~ $less(0,'#skE_1')
| ~ $less(0,w) ),
inference(superposition,[status(thm),theory(equality)],[c_148,c_49]) ).
tff(c_437,plain,
~ $less(0,w),
inference(splitLeft,[status(thm)],[c_256]) ).
tff(c_6,plain,
$greater(w,0),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_7,plain,
~ $lesseq(w,0),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_6]) ).
tff(c_438,plain,
$false,
inference(close,[status(thm),theory('LFA')],[c_437,c_7]) ).
tff(c_439,plain,
( ~ $less(0,'#skE_1')
| ~ $lesseq('#skE_2',0) ),
inference(splitRight,[status(thm)],[c_256]) ).
tff(c_442,plain,
~ $lesseq('#skE_2',0),
inference(splitLeft,[status(thm)],[c_439]) ).
tff(c_471,plain,
~ $lesseq(0,0),
inference(demodulation,[status(thm),theory(equality)],[c_468,c_442]) ).
tff(c_476,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LFA')],[c_471]) ).
tff(c_477,plain,
w = '#skE_3',
inference(splitRight,[status(thm)],[c_447]) ).
tff(c_52,plain,
! [A_48: $real,B_49: $real,C_50: $real] : ( $quotient($product(A_48,B_49),C_50) = $product(A_48,$quotient(B_49,C_50)) ),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_64,plain,
! [C_74: $real,A_75: $real,B_76: $real] :
( ( $quotient($product(C_74,A_75),$product(C_74,B_76)) = $quotient(A_75,B_76) )
| ( B_76 = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_154]) ).
tff(c_210,plain,
! [A_75: $real] :
( ( $quotient($product('#skE_1',A_75),'#skE_2') = $quotient(A_75,w) )
| ( w = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_148,c_64]) ).
tff(c_267,plain,
! [A_75: $real] :
( ( $quotient(A_75,w) = $product('#skE_1',$quotient(A_75,'#skE_2')) )
| ( w = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_210]) ).
tff(c_6174,plain,
! [A_75: $real] :
( ( $quotient(A_75,'#skE_3') = $product('#skE_1',$quotient(A_75,'#skE_2')) )
| ( '#skE_3' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_477,c_477,c_267]) ).
tff(c_6176,plain,
'#skE_3' = 0,
inference(splitLeft,[status(thm)],[c_6174]) ).
tff(c_566,plain,
$quotient('#skE_2','#skE_1') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_236]) ).
tff(c_88,plain,
! [A_53: $real,B_54: $real,X_108: $real] :
( ( $uminus($quotient(A_53,B_54)) = $quotient(X_108,B_54) )
| ( X_108 != $uminus(A_53) ) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_4827,plain,
$quotient($uminus('#skE_2'),'#skE_1') = $uminus('#skE_3'),
inference(superposition,[status(thm),theory(equality)],[c_566,c_88]) ).
tff(c_450,plain,
$quotient('#skE_2','#skE_1') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_236]) ).
tff(c_4897,plain,
( ( $uminus('#skE_3') = '#skE_3' )
| ( $uminus('#skE_2') != '#skE_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_4827,c_450]) ).
tff(c_4898,plain,
( ( $uminus('#skE_3') = '#skE_3' )
| ( $uminus('#skE_2') != '#skE_2' ) ),
inference(backgroundSimplification,[status(thm),theory('LFA')],[c_4897]) ).
tff(c_4943,plain,
$uminus('#skE_2') != '#skE_2',
inference(splitLeft,[status(thm)],[c_4898]) ).
tff(c_275,plain,
$product(w,'#skE_1') = '#skE_2',
inference(superposition,[status(thm),theory(equality)],[c_30,c_148]) ).
tff(c_561,plain,
$product('#skE_3','#skE_1') = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_477,c_275]) ).
tff(c_286,plain,
$product(w,'#skE_1') = '#skE_2',
inference(superposition,[status(thm),theory(equality)],[c_30,c_148]) ).
tff(c_90,plain,
! [A_33: $real,B_34: $real,X_109: $real] :
( ( $uminus($product(A_33,B_34)) = $product(X_109,B_34) )
| ( X_109 != $uminus(A_33) ) ),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_400,plain,
! [A_33: $real] :
( ( $uminus($product(A_33,'#skE_1')) = '#skE_2' )
| ( w != $uminus(A_33) ) ),
inference(superposition,[status(thm),theory(equality)],[c_286,c_90]) ).
tff(c_5854,plain,
! [A_2307: $real] :
( ( $uminus($product(A_2307,'#skE_1')) = '#skE_2' )
| ( '#skE_3' != $uminus(A_2307) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_477,c_400]) ).
tff(c_5886,plain,
( ( $uminus('#skE_2') = '#skE_2' )
| ( $uminus('#skE_3') != '#skE_3' )
| ( '#skE_1' != '#skE_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_561,c_5854]) ).
tff(c_5933,plain,
$uminus('#skE_3') != '#skE_3',
inference(negUnitSimplification,[status(thm)],[c_4943,c_5886]) ).
tff(c_5934,plain,
$uminus('#skE_3') != '#skE_3',
inference(backgroundSimplification,[status(thm),theory('LFA')],[c_5933]) ).
tff(c_6182,plain,
$uminus(0) != 0,
inference(demodulation,[status(thm),theory(equality)],[c_6176,c_6176,c_5934]) ).
tff(c_6251,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LFA')],[c_6182]) ).
tff(c_6253,plain,
'#skE_3' != 0,
inference(splitRight,[status(thm)],[c_6174]) ).
tff(c_382,plain,
( ( $quotient('#skE_2',w) = '#skE_1' )
| ( w = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_286,c_17]) ).
tff(c_7963,plain,
( ( $quotient('#skE_2','#skE_3') = '#skE_1' )
| ( '#skE_3' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_477,c_477,c_382]) ).
tff(c_7968,plain,
$quotient('#skE_2','#skE_3') = '#skE_1',
inference(negUnitSimplification,[status(thm)],[c_6253,c_7963]) ).
tff(c_77,plain,
! [B_93: $real,A_92: $real] :
( $less(1,$quotient(B_93,A_92))
| ~ $less(0,A_92)
| ~ $less(A_92,B_93) ),
inference(cnfTransformation,[status(thm)],[f_180]) ).
tff(c_79,plain,
! [B_94: $real,A_95: $real] :
( ~ $lesseq($quotient(B_94,A_95),1)
| ~ $less(0,A_95)
| ~ $less(A_95,B_94) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_77]) ).
tff(c_8157,plain,
( ~ $lesseq('#skE_1',1)
| ~ $less(0,'#skE_3')
| ~ $less('#skE_3','#skE_2') ),
inference(superposition,[status(thm),theory(equality)],[c_7968,c_79]) ).
tff(c_9021,plain,
~ $less('#skE_3','#skE_2'),
inference(splitLeft,[status(thm)],[c_8157]) ).
tff(c_140,plain,
$product('#skE_1',w) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_121]) ).
tff(c_139,plain,
~ $less($sum(u,$product('#skE_1',w)),$sum(v,w)),
inference(demodulation,[status(thm),theory(equality)],[c_30,c_113]) ).
tff(c_142,plain,
~ $less($sum(u,'#skE_2'),$sum(v,w)),
inference(demodulation,[status(thm),theory(equality)],[c_140,c_139]) ).
tff(c_556,plain,
~ $less($sum(u,'#skE_2'),$sum(v,'#skE_3')),
inference(demodulation,[status(thm),theory(equality)],[c_477,c_142]) ).
tff(c_4,plain,
$less(u,v),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_5,plain,
~ $lesseq(v,u),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_4]) ).
tff(c_9023,plain,
$false,
inference(close,[status(thm),theory('LFA')],[c_9021,c_556,c_5]) ).
tff(c_9024,plain,
( ~ $less(0,'#skE_3')
| ~ $lesseq('#skE_1',1) ),
inference(splitRight,[status(thm)],[c_8157]) ).
tff(c_9028,plain,
~ $lesseq('#skE_1',1),
inference(splitLeft,[status(thm)],[c_9024]) ).
tff(c_124,plain,
f(x) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_85]) ).
tff(c_2,plain,
! [X_1a: $real] : $lesseq(f(X_1a),1),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_3,plain,
! [X_1a: $real] : ~ $less(1,f(X_1a)),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_2]) ).
tff(c_135,plain,
~ $less(1,'#skE_1'),
inference(superposition,[status(thm),theory(equality)],[c_124,c_3]) ).
tff(c_9029,plain,
$false,
inference(close,[status(thm),theory('LFA')],[c_9028,c_135]) ).
tff(c_9030,plain,
~ $less(0,'#skE_3'),
inference(splitRight,[status(thm)],[c_9024]) ).
tff(c_557,plain,
~ $lesseq('#skE_3',0),
inference(demodulation,[status(thm),theory(equality)],[c_477,c_7]) ).
tff(c_9033,plain,
$false,
inference(close,[status(thm),theory('LFA')],[c_9030,c_557]) ).
tff(c_9034,plain,
$uminus('#skE_3') = '#skE_3',
inference(splitRight,[status(thm)],[c_4898]) ).
tff(c_9127,plain,
$false,
inference(close,[status(thm),theory('LFA')],[c_9034,c_557]) ).
tff(c_9129,plain,
$lesseq('#skE_2',0),
inference(splitRight,[status(thm)],[c_439]) ).
tff(c_9130,plain,
~ $less(0,'#skE_2'),
inference(backgroundSimplification,[status(thm),theory('LFA')],[c_9129]) ).
tff(c_9131,plain,
$false,
inference(close,[status(thm),theory('LFA')],[c_9130,c_142,c_5,c_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ARI633_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 : n022.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 00:07:33 EDT 2023
% 0.14/0.35 % CPUTime :
% 17.08/6.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.08/6.13
% 17.08/6.13 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 17.36/6.18
% 17.36/6.18 Inference rules
% 17.36/6.18 ----------------------
% 17.36/6.18 #Ref : 0
% 17.36/6.18 #Sup : 1422
% 17.36/6.18 #Fact : 0
% 17.36/6.18 #Define : 4
% 17.36/6.18 #Split : 36
% 17.36/6.18 #Chain : 0
% 17.36/6.18 #Close : 15
% 17.36/6.18
% 17.36/6.18 Ordering : LPO
% 17.36/6.18
% 17.36/6.18 Simplification rules
% 17.36/6.18 ----------------------
% 17.36/6.18 #Subsume : 196
% 17.36/6.18 #Demod : 548
% 17.36/6.18 #Tautology : 215
% 17.36/6.18 #SimpNegUnit : 89
% 17.36/6.18 #BackRed : 66
% 17.36/6.18
% 17.36/6.18 #Partial instantiations: 0
% 17.36/6.18 #Strategies tried : 1
% 17.36/6.18
% 17.36/6.18 Timing (in seconds)
% 17.36/6.18 ----------------------
% 17.36/6.18 Preprocessing : 0.65
% 17.36/6.18 Parsing : 0.31
% 17.36/6.18 CNF conversion : 0.03
% 17.36/6.19 Main loop : 4.45
% 17.36/6.19 Inferencing : 0.40
% 17.36/6.19 Reduction : 0.60
% 17.36/6.19 Demodulation : 0.44
% 17.36/6.19 BG Simplification : 0.19
% 17.36/6.19 Subsumption : 0.31
% 17.36/6.19 Abstraction : 0.12
% 17.36/6.19 MUC search : 2.11
% 17.36/6.19 Cooper : 0.00
% 17.36/6.19 Total : 5.18
% 17.36/6.19 Index Insertion : 0.00
% 17.36/6.19 Index Deletion : 0.00
% 17.36/6.19 Index Matching : 0.00
% 17.36/6.19 BG Taut test : 0.00
%------------------------------------------------------------------------------