%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ARI682_1 : TPTP v9.0.0. 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 : n023.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 : Wed Apr 9 05:40:50 PM UTC 2025
% Result : Theorem 3.74s 2.07s
% Output : CNFRefutation 4.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 7 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 102 ( 30 atm; 26 fun; 39 num; 7 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 : 7 ( 3 usr; 5 con; 0-2 aty)
% Number of variables : 7 ( 7 !; 0 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
%$ #nlpp
%Foreground sorts:
%Background operators:
tff('#skE_1',type,
'#skE_1': $int ).
tff(b,type,
b: $int ).
tff(a,type,
a: $int ).
%Foreground operators:
tff(f_33,negated_conjecture,
~ $lesseq($sum(a,1),$sum($product(a,b),b)),
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_30,axiom,
$less(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(f_31,axiom,
$lesseq(0,a),
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(c_5,plain,
~ $lesseq($sum(a,1),$sum($product(a,b),b)),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_33,plain,
$less($sum(b,$product(a,b)),$sum(1,a)),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_5]) ).
tff(c_64,plain,
$product(a,b) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_33]) ).
tff(c_36,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_180,plain,
( $less(0,'#skE_1')
| ~ $less(0,a)
| ~ $less(0,b) ),
inference(superposition,[status(thm),theory(equality)],[c_64,c_36]) ).
tff(c_387,plain,
~ $less(0,b),
inference(splitLeft,[status(thm)],[c_180]) ).
tff(c_35,plain,
$less(a,b),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_2,plain,
$lesseq(0,a),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_34,plain,
~ $less(a,0),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_2]) ).
tff(c_388,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_387,c_35,c_34]) ).
tff(c_391,plain,
( ~ $less(0,a)
| $less(0,'#skE_1') ),
inference(splitRight,[status(thm)],[c_180]) ).
tff(c_394,plain,
~ $less(0,a),
inference(splitLeft,[status(thm)],[c_391]) ).
tff(c_37,plain,
! [B_24: $int] : ( $product(0,B_24) = 0 ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_178,plain,
( ( '#skE_1' = 0 )
| ( a != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_64,c_37]) ).
tff(c_209,plain,
a != 0,
inference(splitLeft,[status(thm)],[c_178]) ).
tff(c_572,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_394,c_209,c_34]) ).
tff(c_575,plain,
$less(0,'#skE_1'),
inference(splitRight,[status(thm)],[c_391]) ).
tff(c_53,plain,
$product(a,b) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_33]) ).
tff(c_48,plain,
$less($sum(b,$product(a,b)),$sum(1,a)),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_5]) ).
tff(c_55,plain,
$less($sum(b,'#skE_1'),$sum(1,a)),
inference(demodulation,[status(thm),theory(equality)],[c_53,c_48]) ).
tff(c_61,plain,
$less($sum('#skE_1',b),$sum(1,a)),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_55]) ).
tff(c_577,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_575,c_61,c_35]) ).
tff(c_581,plain,
a = 0,
inference(splitRight,[status(thm)],[c_178]) ).
tff(c_580,plain,
'#skE_1' = 0,
inference(splitRight,[status(thm)],[c_178]) ).
tff(c_587,plain,
$less($sum(0,b),$sum(1,a)),
inference(demodulation,[status(thm),theory(equality)],[c_580,c_61]) ).
tff(c_593,plain,
$less(b,$sum(1,a)),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_587]) ).
tff(c_603,plain,
$less(b,$sum(1,0)),
inference(demodulation,[status(thm),theory(equality)],[c_581,c_593]) ).
tff(c_605,plain,
$less(b,1),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_603]) ).
tff(c_599,plain,
$less(0,b),
inference(demodulation,[status(thm),theory(equality)],[c_581,c_35]) ).
tff(c_606,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_605,c_599]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ARI682_1 : TPTP v9.0.0. Released v6.3.0.
% 0.12/0.13 % 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 : n023.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 : Mon Apr 7 15:16:39 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.74/2.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.74/2.07
% 3.74/2.07 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------