%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ARI640_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 : n027.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 05:40:45 PM UTC 2025
% Result : Theorem 6.03s 2.80s
% Output : CNFRefutation 6.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 59 ( 23 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 41 ( 25 ~; 12 |; 0 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 113 ( 31 atm; 39 fun; 27 num; 16 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 3 usr; 5 con; 0-2 aty)
% Number of variables : 16 ( 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
%$ #nlpp
%Foreground sorts:
%Background operators:
tff('#skE_1',type,
'#skE_1': $real ).
tff(x,type,
x: $real ).
tff(y,type,
y: $real ).
%Foreground operators:
tff(f_32,hypothesis,
$greater($product(x,y),$sum(x,y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_03) ).
tff(f_74,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_94,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_161,axiom,
! [A: $real,B: $real] :
( $less(0,A)
=> ( $lesseq(1,$quotient(B,A))
<=> $lesseq(A,B) ) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas_real.p',le_divide_eq_1_pos) ).
tff(f_30,hypothesis,
$greater(y,0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_01) ).
tff(f_31,hypothesis,
$less(y,1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_02) ).
tff(f_29,hypothesis,
$greater(x,0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis) ).
tff(c_8,plain,
$greater($product(x,y),$sum(x,y)),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_87,plain,
~ $lesseq($product(x,y),$sum(x,y)),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_8]) ).
tff(c_119,plain,
$product(x,y) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_87]) ).
tff(c_19,plain,
! [Y_10: $real,Z_11: $real] :
( ( $quotient($product(Y_10,Z_11),Y_10) = Z_11 )
| ( Y_10 = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_207,plain,
( ( $quotient('#skE_1',x) = y )
| ( x = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_119,c_19]) ).
tff(c_669,plain,
x = 0,
inference(splitLeft,[status(thm)],[c_207]) ).
tff(c_92,plain,
! [A_32: $real,B_33: $real,X_106: $real] :
( ( $uminus($product(A_32,B_33)) = $product(X_106,B_33) )
| ( X_106 != $uminus(A_32) ) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_415,plain,
$product($uminus(x),y) = $uminus('#skE_1'),
inference(superposition,[status(thm),theory(equality)],[c_119,c_92]) ).
tff(c_116,plain,
$product(x,y) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_87]) ).
tff(c_514,plain,
( ( $uminus('#skE_1') = '#skE_1' )
| ( $uminus(x) != x ) ),
inference(superposition,[status(thm),theory(equality)],[c_415,c_116]) ).
tff(c_515,plain,
( ( $uminus('#skE_1') = '#skE_1' )
| ( $uminus(x) != x ) ),
inference(backgroundSimplification,[status(thm),theory('LFA')],[c_514]) ).
tff(c_663,plain,
$uminus(x) != x,
inference(splitLeft,[status(thm)],[c_515]) ).
tff(c_752,plain,
$uminus(0) != 0,
inference(demodulation,[status(thm),theory(equality)],[c_669,c_669,c_663]) ).
tff(c_778,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LFA')],[c_752]) ).
tff(c_785,plain,
$quotient('#skE_1',x) = y,
inference(splitRight,[status(thm)],[c_207]) ).
tff(c_73,plain,
! [B_86: $real,A_85: $real] :
( $lesseq(1,$quotient(B_86,A_85))
| ~ $less(0,A_85)
| ~ $lesseq(A_85,B_86) ),
inference(cnfTransformation,[status(thm)],[f_161]) ).
tff(c_75,plain,
! [B_87: $real,A_88: $real] :
( ~ $less($quotient(B_87,A_88),1)
| ~ $less(0,A_88)
| ~ $lesseq(A_88,B_87) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_73]) ).
tff(c_871,plain,
( ~ $less(y,1)
| ~ $less(0,x)
| ~ $lesseq(x,'#skE_1') ),
inference(superposition,[status(thm),theory(equality)],[c_785,c_75]) ).
tff(c_883,plain,
~ $lesseq(x,'#skE_1'),
inference(splitLeft,[status(thm)],[c_871]) ).
tff(c_111,plain,
$product(x,y) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_87]) ).
tff(c_95,plain,
~ $lesseq($product(x,y),$sum(x,y)),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_8]) ).
tff(c_113,plain,
~ $lesseq('#skE_1',$sum(x,y)),
inference(demodulation,[status(thm),theory(equality)],[c_111,c_95]) ).
tff(c_3,plain,
$greater(y,0),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_4,plain,
~ $lesseq(y,0),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_3]) ).
tff(c_884,plain,
$false,
inference(close,[status(thm),theory('LFA')],[c_883,c_113,c_4]) ).
tff(c_885,plain,
( ~ $less(0,x)
| ~ $less(y,1) ),
inference(splitRight,[status(thm)],[c_871]) ).
tff(c_1081,plain,
~ $less(y,1),
inference(splitLeft,[status(thm)],[c_885]) ).
tff(c_5,plain,
$less(y,1),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_6,plain,
~ $lesseq(1,y),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_5]) ).
tff(c_1082,plain,
$false,
inference(close,[status(thm),theory('LFA')],[c_1081,c_6]) ).
tff(c_1083,plain,
~ $less(0,x),
inference(splitRight,[status(thm)],[c_885]) ).
tff(c_1,plain,
$greater(x,0),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_2,plain,
~ $lesseq(x,0),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_1]) ).
tff(c_1087,plain,
$false,
inference(close,[status(thm),theory('LFA')],[c_1083,c_2]) ).
tff(c_1088,plain,
$uminus('#skE_1') = '#skE_1',
inference(splitRight,[status(thm)],[c_515]) ).
tff(c_1096,plain,
$false,
inference(close,[status(thm),theory('LFA')],[c_1088,c_113,c_4,c_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ARI640_1 : TPTP v9.0.0. Released v6.3.0.
% 0.03/0.13 % 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 : n027.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 15:15:36 EDT 2025
% 0.13/0.34 % CPUTime :
% 6.03/2.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.03/2.81
% 6.03/2.81 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------