TSTP Solution File: ARI669_1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ARI669_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 10:34:13 EDT 2023
% Result : Theorem 23.94s 9.66s
% Output : CNFRefutation 24.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 11
% Syntax : Number of formulae : 100 ( 57 unt; 6 typ; 0 def)
% Number of atoms : 139 ( 134 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 97 ( 52 ~; 43 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 292 ( 0 atm; 146 fun; 111 num; 35 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 6 usr; 8 con; 0-2 aty)
% Number of variables : 35 (; 35 !; 0 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
%$ #nlpp
%Foreground sorts:
%Background operators:
tff(c,type,
c: $int ).
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skE_3',type,
'#skE_3': $int ).
tff(b,type,
b: $int ).
tff(a,type,
a: $int ).
%Foreground operators:
tff(f_306,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_37,negated_conjecture,
~ ( ( $product($product($product(a,b),b),c) = 0 )
<=> ( ( c = 0 )
| ( b = 0 )
| ( a = 0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(f_322,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_308,axiom,
! [A: $int,B: $int,C: $int] : ( $product(A,$sum(B,C)) = $sum($product(A,B),$product(A,C)) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',mult_dist) ).
tff(f_303,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_64,plain,
! [B_7: $int,A_8: $int] : ( $product(B_7,A_8) = $product(A_8,B_7) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_46,plain,
( ( $product($product($product(a,b),b),c) != 0 )
| ( c != 0 ) ),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_82,plain,
( ( $product(c,$product(b,$product(a,b))) != 0 )
| ( c != 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_64,c_64,c_46]) ).
tff(c_100,plain,
$product(a,b) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_82]) ).
tff(c_56,plain,
! [B_24: $int] : ( $product(0,B_24) = 0 ),
inference(cnfTransformation,[status(thm)],[f_322]) ).
tff(c_214,plain,
( ( '#skE_1' = 0 )
| ( a != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_100,c_56]) ).
tff(c_261,plain,
a != 0,
inference(splitLeft,[status(thm)],[c_214]) ).
tff(c_84,plain,
$product(a,b) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_82]) ).
tff(c_83,plain,
( ( $product(c,$product(b,$product(a,b))) != 0 )
| ( c != 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_64,c_64,c_46]) ).
tff(c_87,plain,
( ( $product(c,$product(b,'#skE_1')) != 0 )
| ( c != 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_84,c_83]) ).
tff(c_97,plain,
( ( $product(c,$product('#skE_1',b)) != 0 )
| ( c != 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_64,c_87]) ).
tff(c_270,plain,
$product('#skE_1',b) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_97]) ).
tff(c_396,plain,
( ( '#skE_2' = 0 )
| ( '#skE_1' != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_270,c_56]) ).
tff(c_441,plain,
'#skE_1' != 0,
inference(splitLeft,[status(thm)],[c_396]) ).
tff(c_269,plain,
$product('#skE_1',b) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_97]) ).
tff(c_99,plain,
$product(a,b) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_82]) ).
tff(c_50,plain,
( ( $product($product($product(a,b),b),c) != 0 )
| ( b != 0 ) ),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_446,plain,
( ( $product('#skE_2',c) != 0 )
| ( b != 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_64,c_269,c_64,c_99,c_64,c_64,c_50]) ).
tff(c_448,plain,
$product('#skE_2',c) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_446]) ).
tff(c_447,plain,
( ( $product('#skE_2',c) != 0 )
| ( b != 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_64,c_269,c_64,c_99,c_64,c_64,c_50]) ).
tff(c_455,plain,
( ( '#skE_3' != 0 )
| ( b != 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_448,c_447]) ).
tff(c_457,plain,
b != 0,
inference(splitLeft,[status(thm)],[c_455]) ).
tff(c_246,plain,
$product('#skE_1',b) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_97]) ).
tff(c_245,plain,
( ( $product(c,$product('#skE_1',b)) != 0 )
| ( c != 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_64,c_87]) ).
tff(c_249,plain,
( ( $product(c,'#skE_2') != 0 )
| ( c != 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_246,c_245]) ).
tff(c_259,plain,
( ( $product('#skE_2',c) != 0 )
| ( c != 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_64,c_249]) ).
tff(c_430,plain,
$product('#skE_2',c) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_259]) ).
tff(c_429,plain,
( ( $product('#skE_2',c) != 0 )
| ( c != 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_64,c_249]) ).
tff(c_437,plain,
( ( '#skE_3' != 0 )
| ( c != 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_430,c_429]) ).
tff(c_439,plain,
c != 0,
inference(splitLeft,[status(thm)],[c_437]) ).
tff(c_57,plain,
! [C_23: $int] : ( $product(C_23,1) = C_23 ),
inference(cnfTransformation,[status(thm)],[f_322]) ).
tff(c_463,plain,
$product('#skE_2',c) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_259]) ).
tff(c_36,plain,
( ( $product($product($product(a,b),b),c) = 0 )
| ( c = 0 )
| ( b = 0 )
| ( a = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_634,plain,
( ( '#skE_3' = 0 )
| ( c = 0 )
| ( b = 0 )
| ( a = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_463,c_64,c_269,c_64,c_99,c_64,c_64,c_36]) ).
tff(c_636,plain,
'#skE_3' = 0,
inference(negUnitSimplification,[status(thm)],[c_261,c_457,c_439,c_634]) ).
tff(c_454,plain,
$product('#skE_2',c) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_446]) ).
tff(c_662,plain,
$product('#skE_2',c) = 0,
inference(demodulation,[status(thm),theory(equality)],[c_636,c_454]) ).
tff(c_17,plain,
! [A_9: $int,C_11: $int,B_10: $int] : ( $product(A_9,$sum(C_11,B_10)) = $sum($product(A_9,B_10),$product(A_9,C_11)) ),
inference(cnfTransformation,[status(thm)],[f_308]) ).
tff(c_63,plain,
! [A_12: $int,X_70: $int,B_13: $int,C_14: $int] :
( ( $product(A_12,X_70) = $sum($product(A_12,B_13),$product(A_12,C_14)) )
| ( X_70 != $sum(B_13,C_14) ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_17]) ).
tff(c_777,plain,
! [B_13: $int,X_70: $int] :
( ( $sum($product('#skE_2',B_13),0) = $product('#skE_2',X_70) )
| ( X_70 != $sum(B_13,c) ) ),
inference(superposition,[status(thm),theory(equality)],[c_662,c_63]) ).
tff(c_8795,plain,
! [X_1432: $int,B_1433: $int] :
( ( $product('#skE_2',X_1432) = $product('#skE_2',B_1433) )
| ( X_1432 != $sum(c,B_1433) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_777]) ).
tff(c_9952,plain,
$product('#skE_2',$sum(c,1)) = '#skE_2',
inference(superposition,[status(thm),theory(equality)],[c_57,c_8795]) ).
tff(c_44084,plain,
$product('#skE_2',$sum(1,c)) = '#skE_2',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_9952]) ).
tff(c_58,plain,
! [C_21: $int,B_22: $int] :
( ( $product(C_21,B_22) != C_21 )
| ( C_21 = 0 )
| ( B_22 = 1 ) ),
inference(cnfTransformation,[status(thm)],[f_322]) ).
tff(c_44967,plain,
( ( '#skE_2' = 0 )
| ( $sum(1,c) = 1 ) ),
inference(superposition,[status(thm),theory(equality)],[c_44084,c_58]) ).
tff(c_44969,plain,
( ( '#skE_2' = 0 )
| ( c = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_44967]) ).
tff(c_45261,plain,
'#skE_2' = 0,
inference(negUnitSimplification,[status(thm)],[c_439,c_44969]) ).
tff(c_66,plain,
! [X_71: $int,N_4: $int,M_3: $int] :
( ( $product(X_71,N_4) = $sum(N_4,$product(M_3,N_4)) )
| ( X_71 != $sum(1,M_3) ) ),
inference(cnfTransformation,[status(thm)],[f_303]) ).
tff(c_361,plain,
$product($sum(1,'#skE_1'),b) = $sum(b,'#skE_2'),
inference(superposition,[status(thm),theory(equality)],[c_270,c_66]) ).
tff(c_4143,plain,
$product($sum(1,'#skE_1'),b) = $sum('#skE_2',b),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_361]) ).
tff(c_4373,plain,
$product(b,$sum(1,'#skE_1')) = $sum('#skE_2',b),
inference(superposition,[status(thm),theory(equality)],[c_4143,c_64]) ).
tff(c_4376,plain,
$product(b,$sum(1,'#skE_1')) = $sum(b,'#skE_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4373]) ).
tff(c_106948,plain,
$product(b,$sum(1,'#skE_1')) = $sum(b,0),
inference(demodulation,[status(thm),theory(equality)],[c_45261,c_4376]) ).
tff(c_106953,plain,
$product(b,$sum(1,'#skE_1')) = b,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_106948]) ).
tff(c_108663,plain,
( ( b = 0 )
| ( $sum(1,'#skE_1') = 1 ) ),
inference(superposition,[status(thm),theory(equality)],[c_106953,c_58]) ).
tff(c_108665,plain,
( ( b = 0 )
| ( '#skE_1' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_108663]) ).
tff(c_109255,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_441,c_457,c_108665]) ).
tff(c_109259,plain,
b = 0,
inference(splitRight,[status(thm)],[c_455]) ).
tff(c_91,plain,
$product(a,b) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_82]) ).
tff(c_109281,plain,
$product(a,0) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_109259,c_91]) ).
tff(c_109366,plain,
! [X_70: $int,C_14: $int] :
( ( $product(a,X_70) = $sum('#skE_1',$product(a,C_14)) )
| ( X_70 != $sum(0,C_14) ) ),
inference(superposition,[status(thm),theory(equality)],[c_109281,c_63]) ).
tff(c_109368,plain,
! [X_70: $int] : ( $sum('#skE_1',$product(a,X_70)) = $product(a,X_70) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_109366]) ).
tff(c_109370,plain,
'#skE_1' = 0,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_109368]) ).
tff(c_109410,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_441,c_109370]) ).
tff(c_109414,plain,
'#skE_1' = 0,
inference(splitRight,[status(thm)],[c_396]) ).
tff(c_109604,plain,
( ( $product(c,$product(b,$product(a,b))) != 0 )
| ( b != 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_64,c_64,c_50]) ).
tff(c_109606,plain,
$product(a,b) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_109604]) ).
tff(c_109605,plain,
( ( $product(c,$product(b,$product(a,b))) != 0 )
| ( b != 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_64,c_64,c_50]) ).
tff(c_109609,plain,
( ( $product(c,$product(b,'#skE_1')) != 0 )
| ( b != 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_109606,c_109605]) ).
tff(c_109620,plain,
b != 0,
inference(demodulation,[status(thm),theory(equality)],[c_56,c_64,c_56,c_109414,c_64,c_109609]) ).
tff(c_180,plain,
$product($sum(1,a),b) = $sum(b,'#skE_1'),
inference(superposition,[status(thm),theory(equality)],[c_100,c_66]) ).
tff(c_183,plain,
$product($sum(1,a),b) = $sum('#skE_1',b),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_180]) ).
tff(c_112292,plain,
$product($sum(1,a),b) = $sum(0,b),
inference(demodulation,[status(thm),theory(equality)],[c_109414,c_183]) ).
tff(c_112297,plain,
$product($sum(1,a),b) = b,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_112292]) ).
tff(c_124729,plain,
$product(b,$sum(1,a)) = b,
inference(superposition,[status(thm),theory(equality)],[c_64,c_112297]) ).
tff(c_125273,plain,
( ( b = 0 )
| ( $sum(1,a) = 1 ) ),
inference(superposition,[status(thm),theory(equality)],[c_124729,c_58]) ).
tff(c_125275,plain,
( ( b = 0 )
| ( a = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_125273]) ).
tff(c_125464,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_261,c_109620,c_125275]) ).
tff(c_125467,plain,
'#skE_3' != 0,
inference(splitRight,[status(thm)],[c_437]) ).
tff(c_125468,plain,
c = 0,
inference(splitRight,[status(thm)],[c_437]) ).
tff(c_436,plain,
$product('#skE_2',c) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_259]) ).
tff(c_125491,plain,
$product('#skE_2',0) = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_125468,c_436]) ).
tff(c_125596,plain,
! [C_14: $int,X_70: $int] :
( ( $sum('#skE_3',$product('#skE_2',C_14)) = $product('#skE_2',X_70) )
| ( X_70 != $sum(0,C_14) ) ),
inference(superposition,[status(thm),theory(equality)],[c_125491,c_63]) ).
tff(c_125598,plain,
! [X_70: $int] : ( $sum($uminus('#skE_3'),$product('#skE_2',X_70)) = $product('#skE_2',X_70) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_125596]) ).
tff(c_125600,plain,
'#skE_3' = 0,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_125598]) ).
tff(c_125651,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_125467,c_125600]) ).
tff(c_125655,plain,
a = 0,
inference(splitRight,[status(thm)],[c_214]) ).
tff(c_54,plain,
( ( $product($product($product(a,b),b),c) != 0 )
| ( a != 0 ) ),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_125972,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_125655,c_56,c_64,c_56,c_64,c_56,c_125655,c_64,c_64,c_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ARI669_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
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 4 00:10:04 EDT 2023
% 0.13/0.34 % CPUTime :
% 23.94/9.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.94/9.67
% 23.94/9.67 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 24.52/9.77
% 24.52/9.77 Inference rules
% 24.52/9.77 ----------------------
% 24.52/9.77 #Ref : 0
% 24.52/9.77 #Sup : 21588
% 24.52/9.77 #Fact : 0
% 24.52/9.77 #Define : 7
% 24.52/9.77 #Split : 134
% 24.52/9.77 #Chain : 0
% 24.52/9.77 #Close : 1
% 24.52/9.77
% 24.52/9.77 Ordering : LPO
% 24.52/9.77
% 24.52/9.77 Simplification rules
% 24.52/9.77 ----------------------
% 24.52/9.77 #Subsume : 7090
% 24.52/9.77 #Demod : 4752
% 24.52/9.77 #Tautology : 8134
% 24.52/9.77 #SimpNegUnit : 3020
% 24.52/9.77 #BackRed : 53
% 24.52/9.77
% 24.52/9.77 #Partial instantiations: 0
% 24.52/9.77 #Strategies tried : 1
% 24.52/9.77
% 24.52/9.77 Timing (in seconds)
% 24.52/9.77 ----------------------
% 24.52/9.77 Preprocessing : 0.52
% 24.52/9.77 Parsing : 0.27
% 24.52/9.77 CNF conversion : 0.03
% 24.52/9.77 Main loop : 8.08
% 24.52/9.77 Inferencing : 0.99
% 24.52/9.77 Reduction : 3.33
% 24.52/9.77 Demodulation : 2.53
% 24.52/9.77 BG Simplification : 0.48
% 24.52/9.77 Subsumption : 1.96
% 24.52/9.78 Abstraction : 0.23
% 24.52/9.78 MUC search : 0.02
% 24.52/9.78 Cooper : 0.10
% 24.52/9.78 Total : 8.73
% 24.52/9.78 Index Insertion : 0.00
% 24.52/9.78 Index Deletion : 0.00
% 24.52/9.78 Index Matching : 0.00
% 24.52/9.78 BG Taut test : 0.00
%------------------------------------------------------------------------------