TSTP Solution File: ARI655_1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ARI655_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 : n006.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 10:34:11 EDT 2023
% Result : Theorem 38.53s 16.50s
% Output : CNFRefutation 39.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 92 ( 61 unt; 6 typ; 0 def)
% Number of atoms : 125 ( 60 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 85 ( 46 ~; 36 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number arithmetic : 368 ( 59 atm; 207 fun; 58 num; 44 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 ( 6 usr; 8 con; 0-2 aty)
% Number of variables : 44 (; 44 !; 0 ?; 44 :)
% 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(b,type,
b: $int ).
tff(a,type,
a: $int ).
%Foreground operators:
tff(f_67,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_33,negated_conjecture,
~ $lesseq(0,$product($difference(a,b),$difference(c,d))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_002) ).
tff(f_90,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_31,axiom,
$lesseq(d,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_001) ).
tff(f_81,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_30,axiom,
$lesseq(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(f_65,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_73,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(c_15,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_67]) ).
tff(c_53,plain,
! [A_12: $int,B_13: $int,C_14: $int] : ( $product(A_12,$sum(B_13,C_14)) = $sum($product(A_12,B_13),$product(A_12,C_14)) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_15]) ).
tff(c_6,plain,
~ $lesseq(0,$product($sum($uminus(b),a),$sum($uminus(d),c))),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_32,plain,
$less($product($sum(a,$uminus(b)),$sum(c,$uminus(d))),0),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_6]) ).
tff(c_35,plain,
$less($product($sum($uminus(b),a),$sum($uminus(d),c)),0),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_32]) ).
tff(c_57,plain,
$less($sum($product($sum($uminus(b),a),$uminus(d)),$product($sum($uminus(b),a),c)),0),
inference(demodulation,[status(thm),theory(equality)],[c_53,c_35]) ).
tff(c_60,plain,
$less($sum($product($sum(a,$uminus(b)),c),$product($sum(a,$uminus(b)),$uminus(d))),0),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_57]) ).
tff(c_72,plain,
$product($sum(a,$uminus(b)),$uminus(d)) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_60]) ).
tff(c_75,plain,
$product($sum($uminus(b),a),$uminus(d)) = '#skE_2',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_72]) ).
tff(c_241,plain,
$product($sum($uminus(b),a),$uminus(d)) = '#skE_2',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_72]) ).
tff(c_38,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_90]) ).
tff(c_375,plain,
( $less(0,'#skE_2')
| ~ $less(0,$sum($uminus(b),a))
| ~ $less(0,$uminus(d)) ),
inference(superposition,[status(thm),theory(equality)],[c_241,c_38]) ).
tff(c_377,plain,
( $less(0,'#skE_2')
| ~ $less(b,a)
| ~ $less(d,0) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_375]) ).
tff(c_426,plain,
~ $less(d,0),
inference(splitLeft,[status(thm)],[c_377]) ).
tff(c_68,plain,
$product($sum(a,$uminus(b)),c) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_60]) ).
tff(c_80,plain,
$product($sum($uminus(b),a),c) = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_68]) ).
tff(c_205,plain,
( $less(0,'#skE_1')
| ~ $less(0,$sum($uminus(b),a))
| ~ $less(0,c) ),
inference(superposition,[status(thm),theory(equality)],[c_80,c_38]) ).
tff(c_207,plain,
( $less(0,'#skE_1')
| ~ $less(b,a)
| ~ $less(0,c) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_205]) ).
tff(c_421,plain,
~ $less(0,c),
inference(splitLeft,[status(thm)],[c_207]) ).
tff(c_71,plain,
$product($sum($uminus(b),a),c) = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_68]) ).
tff(c_323,plain,
( ( '#skE_2' = '#skE_1' )
| ( $uminus(d) != c ) ),
inference(superposition,[status(thm),theory(equality)],[c_241,c_71]) ).
tff(c_325,plain,
( ( '#skE_2' = '#skE_1' )
| ( d != $uminus(c) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_323]) ).
tff(c_415,plain,
d != $uminus(c),
inference(splitLeft,[status(thm)],[c_325]) ).
tff(c_3,plain,
$lesseq(d,c),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_36,plain,
~ $less(c,d),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_3]) ).
tff(c_427,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_426,c_421,c_415,c_36]) ).
tff(c_430,plain,
( ~ $less(b,a)
| $less(0,'#skE_2') ),
inference(splitRight,[status(thm)],[c_377]) ).
tff(c_433,plain,
~ $less(b,a),
inference(splitLeft,[status(thm)],[c_430]) ).
tff(c_39,plain,
! [B_24: $int] : ( $product(0,B_24) = 0 ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_236,plain,
( ( '#skE_1' = 0 )
| ( $sum($uminus(b),a) != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_39,c_80]) ).
tff(c_238,plain,
( ( '#skE_1' = 0 )
| ( b != a ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_236]) ).
tff(c_413,plain,
b != a,
inference(splitLeft,[status(thm)],[c_238]) ).
tff(c_1,plain,
$lesseq(b,a),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_37,plain,
~ $less(a,b),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_1]) ).
tff(c_434,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_433,c_413,c_37]) ).
tff(c_438,plain,
$less(b,a),
inference(splitRight,[status(thm)],[c_430]) ).
tff(c_46,plain,
! [A_12: $int,X_34: $int,B_13: $int,C_14: $int] :
( ( $product(A_12,X_34) = $sum($product(A_12,B_13),$product(A_12,C_14)) )
| ( X_34 != $sum(B_13,C_14) ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_15]) ).
tff(c_178,plain,
! [X_34: $int,C_14: $int] :
( ( $product($sum($uminus(b),a),X_34) = $sum('#skE_1',$product($sum($uminus(b),a),C_14)) )
| ( X_34 != $sum(c,C_14) ) ),
inference(superposition,[status(thm),theory(equality)],[c_80,c_46]) ).
tff(c_4215,plain,
! [C_856: $int,X_860: $int] :
( ( $sum('#skE_1',$product($sum(a,$uminus(b)),C_856)) = $product($sum(a,$uminus(b)),X_860) )
| ( X_860 != $sum(C_856,c) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_178]) ).
tff(c_4652,plain,
! [C_856: $int,X_860: $int] :
( $less(0,$sum('#skE_1',$product($sum(a,$uminus(b)),C_856)))
| ~ $less(0,$sum(a,$uminus(b)))
| ~ $less(0,X_860)
| ( X_860 != $sum(C_856,c) ) ),
inference(superposition,[status(thm),theory(equality)],[c_4215,c_38]) ).
tff(c_4655,plain,
! [C_856: $int,X_860: $int] :
( $less(0,$sum('#skE_1',$product($sum($uminus(b),a),C_856)))
| ~ $less(b,a)
| ~ $less(0,X_860)
| ( X_860 != $sum(c,C_856) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4652]) ).
tff(c_161963,plain,
! [C_856: $int,X_860: $int] :
( $less(0,$sum('#skE_1',$product($sum($uminus(b),a),C_856)))
| ~ $less(0,X_860)
| ( X_860 != $sum(c,C_856) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_438,c_4655]) ).
tff(c_161969,plain,
! [C_29048: $int,X_29050: $int] :
( $less(0,$sum('#skE_1',$product($sum(a,$uminus(b)),C_29048)))
| ~ $less(0,X_29050)
| ( X_29050 != $sum(C_29048,c) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_161963]) ).
tff(c_162718,plain,
( $less(0,$sum('#skE_1','#skE_2'))
| ~ $less(0,$sum($uminus(d),c))
| ( $sum($uminus(b),a) != $sum(a,$uminus(b)) ) ),
inference(superposition,[status(thm),theory(equality)],[c_75,c_161969]) ).
tff(c_162720,plain,
( $less(0,$sum('#skE_1','#skE_2'))
| ~ $less(d,c) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_162718]) ).
tff(c_162762,plain,
~ $less(d,c),
inference(splitLeft,[status(thm)],[c_162720]) ).
tff(c_47,plain,
! [B_7: $int,A_8: $int] : ( $product(B_7,A_8) = $product(A_8,B_7) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_42,plain,
! [A_17: $int,B_18: $int,X_33: $int] :
( ( $uminus($product(A_17,B_18)) = $product(X_33,B_18) )
| ( X_33 != $uminus(A_17) ) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_44,plain,
! [X_33: $int,B_18: $int,A_17: $int] :
( ( $uminus($product(X_33,B_18)) = $product(A_17,B_18) )
| ( X_33 != $uminus(A_17) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_42]) ).
tff(c_390,plain,
$product($uminus(d),$sum($uminus(b),a)) = '#skE_2',
inference(superposition,[status(thm),theory(equality)],[c_47,c_241]) ).
tff(c_661,plain,
$product($uminus(d),$sum(a,$uminus(b))) = '#skE_2',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_390]) ).
tff(c_743,plain,
$uminus($product($uminus($uminus(d)),$sum(a,$uminus(b)))) = '#skE_2',
inference(superposition,[status(thm),theory(equality)],[c_44,c_661]) ).
tff(c_857,plain,
$uminus($product($sum(a,$uminus(b)),$uminus($uminus(d)))) = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_47,c_743]) ).
tff(c_10761,plain,
$product($sum($uminus(b),a),d) = $uminus('#skE_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_857]) ).
tff(c_11140,plain,
( ( $uminus('#skE_2') = '#skE_1' )
| ( d != c ) ),
inference(superposition,[status(thm),theory(equality)],[c_10761,c_71]) ).
tff(c_11142,plain,
( ( '#skE_2' = $uminus('#skE_1') )
| ( d != c ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_11140]) ).
tff(c_11868,plain,
d != c,
inference(splitLeft,[status(thm)],[c_11142]) ).
tff(c_162764,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_162762,c_11868,c_36]) ).
tff(c_162767,plain,
$less(0,$sum('#skE_1','#skE_2')),
inference(splitRight,[status(thm)],[c_162720]) ).
tff(c_63,plain,
$product($sum(a,$uminus(b)),$uminus(d)) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_60]) ).
tff(c_62,plain,
$product($sum(a,$uminus(b)),c) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_60]) ).
tff(c_61,plain,
$less($sum($product($sum(a,$uminus(b)),c),$product($sum(a,$uminus(b)),$uminus(d))),0),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_57]) ).
tff(c_65,plain,
$less($sum('#skE_1','#skE_2'),0),
inference(demodulation,[status(thm),theory(equality)],[c_63,c_62,c_61]) ).
tff(c_77,plain,
$less($sum('#skE_2','#skE_1'),0),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_65]) ).
tff(c_162769,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_162767,c_77]) ).
tff(c_162772,plain,
'#skE_2' = $uminus('#skE_1'),
inference(splitRight,[status(thm)],[c_11142]) ).
tff(c_162949,plain,
$less($sum($uminus('#skE_1'),'#skE_1'),0),
inference(demodulation,[status(thm),theory(equality)],[c_162772,c_77]) ).
tff(c_162955,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_162949]) ).
tff(c_162959,plain,
b = a,
inference(splitRight,[status(thm)],[c_238]) ).
tff(c_162982,plain,
$product($sum($uminus(a),a),$uminus(d)) = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_162959,c_75]) ).
tff(c_162985,plain,
$product(0,$uminus(d)) = '#skE_2',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_162982]) ).
tff(c_162990,plain,
$product(0,$uminus(d)) = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_162985]) ).
tff(c_162992,plain,
'#skE_2' = 0,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_162990]) ).
tff(c_162958,plain,
'#skE_1' = 0,
inference(splitRight,[status(thm)],[c_238]) ).
tff(c_162966,plain,
$less($sum('#skE_2',0),0),
inference(demodulation,[status(thm),theory(equality)],[c_162958,c_77]) ).
tff(c_162979,plain,
$less('#skE_2',0),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_162966]) ).
tff(c_162993,plain,
$less(0,0),
inference(demodulation,[status(thm),theory(equality)],[c_162992,c_162979]) ).
tff(c_162996,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_162993]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ARI655_1 : TPTP v8.1.2. Released v6.3.0.
% 0.00/0.14 % 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 : n006.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 00:05:13 EDT 2023
% 0.13/0.35 % CPUTime :
% 38.53/16.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 38.53/16.52
% 38.53/16.52 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 39.14/16.61
% 39.14/16.61 Inference rules
% 39.14/16.61 ----------------------
% 39.14/16.61 #Ref : 0
% 39.14/16.61 #Sup : 22687
% 39.14/16.61 #Fact : 0
% 39.14/16.61 #Define : 2
% 39.14/16.61 #Split : 152
% 39.14/16.61 #Chain : 0
% 39.14/16.61 #Close : 9
% 39.14/16.61
% 39.14/16.61 Ordering : LPO
% 39.14/16.61
% 39.14/16.61 Simplification rules
% 39.14/16.61 ----------------------
% 39.14/16.61 #Subsume : 4371
% 39.14/16.61 #Demod : 4949
% 39.14/16.61 #Tautology : 6441
% 39.14/16.61 #SimpNegUnit : 1110
% 39.14/16.61 #BackRed : 28
% 39.14/16.61
% 39.14/16.61 #Partial instantiations: 0
% 39.14/16.61 #Strategies tried : 1
% 39.14/16.61
% 39.14/16.61 Timing (in seconds)
% 39.14/16.61 ----------------------
% 39.19/16.61 Preprocessing : 0.53
% 39.19/16.61 Parsing : 0.28
% 39.19/16.61 CNF conversion : 0.03
% 39.19/16.61 Main loop : 14.95
% 39.19/16.61 Inferencing : 1.19
% 39.19/16.61 Reduction : 6.07
% 39.19/16.61 Demodulation : 4.83
% 39.19/16.61 BG Simplification : 0.85
% 39.19/16.61 Subsumption : 3.08
% 39.19/16.61 Abstraction : 0.38
% 39.19/16.61 MUC search : 1.80
% 39.19/16.61 Cooper : 2.17
% 39.19/16.61 Total : 15.60
% 39.19/16.61 Index Insertion : 0.00
% 39.19/16.61 Index Deletion : 0.00
% 39.19/16.61 Index Matching : 0.00
% 39.19/16.61 BG Taut test : 0.00
%------------------------------------------------------------------------------