%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ARI636_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 : n002.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 6.61s 3.20s
% Output : CNFRefutation 6.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 68 ( 44 unt; 0 typ; 0 def)
% Number of atoms : 101 ( 34 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 83 ( 50 ~; 26 |; 1 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 175 ( 60 atm; 46 fun; 39 num; 30 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 9 usr; 10 con; 0-2 aty)
% Number of variables : 30 ( 30 !; 0 ?; 30 :)
% 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(y,type,
y: $real ).
tff(v,type,
v: $real ).
%Foreground operators:
tff(f,type,
f: $real > $real ).
tff(f_38,negated_conjecture,
~ $less($sum(f(x),u),$sum($product(v,v),f(y))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conclusion) ).
tff(f_120,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_140,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_207,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_34,hypothesis,
$less(u,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis) ).
tff(f_33,axiom,
! [Xa: $real,Ya: $real] :
( $greatereq(Xa,Ya)
=> $greatereq(f(Xa),f(Ya)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_non_decreasing) ).
tff(f_36,hypothesis,
$lesseq(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_02) ).
tff(f_35,hypothesis,
$greater(v,1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_01) ).
tff(f_157,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(c_86,plain,
~ $less($sum(f(x),u),$sum($product(v,v),f(y))),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_186,plain,
$product(v,v) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_86]) ).
tff(c_18,plain,
! [Y_12: $real,Z_13: $real] :
( ( $quotient($product(Y_12,Z_13),Y_12) = Z_13 )
| ( Y_12 = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_275,plain,
( ( $quotient('#skE_2',v) = v )
| ( v = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_186,c_18]) ).
tff(c_443,plain,
$quotient('#skE_2',v) = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_275]) ).
tff(c_442,plain,
( ( $quotient('#skE_2',v) = v )
| ( v = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_186,c_18]) ).
tff(c_445,plain,
( ( v = '#skE_4' )
| ( v = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_443,c_442]) ).
tff(c_553,plain,
v = 0,
inference(splitLeft,[status(thm)],[c_445]) ).
tff(c_122,plain,
$product(v,v) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_86]) ).
tff(c_91,plain,
! [A_34: $real,B_35: $real,X_112: $real] :
( ( $uminus($product(A_34,B_35)) = $product(X_112,B_35) )
| ( X_112 != $uminus(A_34) ) ),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_383,plain,
! [A_197: $real] :
( ( $uminus($product(A_197,v)) = '#skE_2' )
| ( v != $uminus(A_197) ) ),
inference(superposition,[status(thm),theory(equality)],[c_91,c_186]) ).
tff(c_426,plain,
( ( $uminus('#skE_2') = '#skE_2' )
| ( $uminus(v) != v ) ),
inference(superposition,[status(thm),theory(equality)],[c_122,c_383]) ).
tff(c_427,plain,
( ( $uminus('#skE_2') = '#skE_2' )
| ( $uminus(v) != v ) ),
inference(backgroundSimplification,[status(thm),theory('LFA')],[c_426]) ).
tff(c_440,plain,
$uminus(v) != v,
inference(splitLeft,[status(thm)],[c_427]) ).
tff(c_558,plain,
$uminus(0) != 0,
inference(demodulation,[status(thm),theory(equality)],[c_553,c_553,c_440]) ).
tff(c_572,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LFA')],[c_558]) ).
tff(c_573,plain,
v = '#skE_4',
inference(splitRight,[status(thm)],[c_445]) ).
tff(c_451,plain,
$quotient('#skE_2',v) = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_275]) ).
tff(c_75,plain,
! [B_88: $real,A_87: $real] :
( ~ $lesseq(1,$quotient(B_88,A_87))
| ~ $less(0,A_87)
| $lesseq(A_87,B_88) ),
inference(cnfTransformation,[status(thm)],[f_207]) ).
tff(c_77,plain,
! [B_91: $real,A_92: $real] :
( ~ $lesseq(1,$quotient(B_91,A_92))
| ~ $less(0,A_92)
| ~ $less(B_91,A_92) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_75]) ).
tff(c_542,plain,
( ~ $lesseq(1,'#skE_4')
| ~ $less(0,v)
| ~ $less('#skE_2',v) ),
inference(superposition,[status(thm),theory(equality)],[c_451,c_77]) ).
tff(c_735,plain,
( ~ $lesseq(1,'#skE_4')
| ~ $less(0,'#skE_4')
| ~ $less('#skE_2','#skE_4') ),
inference(demodulation,[status(thm),theory(equality)],[c_573,c_573,c_542]) ).
tff(c_736,plain,
~ $less('#skE_2','#skE_4'),
inference(splitLeft,[status(thm)],[c_735]) ).
tff(c_3,plain,
$less(u,v),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_4,plain,
~ $lesseq(v,u),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_3]) ).
tff(c_591,plain,
~ $lesseq('#skE_4',u),
inference(demodulation,[status(thm),theory(equality)],[c_573,c_4]) ).
tff(c_120,plain,
f(x) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_86]) ).
tff(c_152,plain,
f(y) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_86]) ).
tff(c_1,plain,
! [X_1a: $real,Y_2a: $real] :
( $greatereq(f(X_1a),f(Y_2a))
| ~ $greatereq(X_1a,Y_2a) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_2,plain,
! [X_1a: $real,Y_2a: $real] :
( ~ $less(f(X_1a),f(Y_2a))
| ~ $lesseq(Y_2a,X_1a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_1]) ).
tff(c_329,plain,
! [Y_190a: $real] :
( ~ $less('#skE_3',f(Y_190a))
| ~ $lesseq(Y_190a,y) ),
inference(superposition,[status(thm),theory(equality)],[c_152,c_2]) ).
tff(c_338,plain,
( ~ $less('#skE_3','#skE_1')
| ~ $lesseq(x,y) ),
inference(superposition,[status(thm),theory(equality)],[c_120,c_329]) ).
tff(c_339,plain,
~ $lesseq(x,y),
inference(splitLeft,[status(thm)],[c_338]) ).
tff(c_7,plain,
$lesseq(x,y),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_8,plain,
~ $less(y,x),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_7]) ).
tff(c_340,plain,
$false,
inference(close,[status(thm),theory('LFA')],[c_339,c_8]) ).
tff(c_341,plain,
~ $less('#skE_3','#skE_1'),
inference(splitRight,[status(thm)],[c_338]) ).
tff(c_113,plain,
f(y) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_86]) ).
tff(c_112,plain,
$product(v,v) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_86]) ).
tff(c_111,plain,
f(x) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_86]) ).
tff(c_94,plain,
~ $less($sum(f(x),u),$sum($product(v,v),f(y))),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_115,plain,
~ $less($sum('#skE_1',u),$sum('#skE_2','#skE_3')),
inference(demodulation,[status(thm),theory(equality)],[c_113,c_112,c_111,c_94]) ).
tff(c_737,plain,
$false,
inference(close,[status(thm),theory('LFA')],[c_736,c_591,c_341,c_115]) ).
tff(c_738,plain,
( ~ $less(0,'#skE_4')
| ~ $lesseq(1,'#skE_4') ),
inference(splitRight,[status(thm)],[c_735]) ).
tff(c_805,plain,
~ $lesseq(1,'#skE_4'),
inference(splitLeft,[status(thm)],[c_738]) ).
tff(c_5,plain,
$greater(v,1),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_6,plain,
~ $lesseq(v,1),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_5]) ).
tff(c_590,plain,
~ $lesseq('#skE_4',1),
inference(demodulation,[status(thm),theory(equality)],[c_573,c_6]) ).
tff(c_806,plain,
$false,
inference(close,[status(thm),theory('LFA')],[c_805,c_590]) ).
tff(c_807,plain,
~ $less(0,'#skE_4'),
inference(splitRight,[status(thm)],[c_738]) ).
tff(c_810,plain,
$false,
inference(close,[status(thm),theory('LFA')],[c_807,c_590]) ).
tff(c_811,plain,
$uminus('#skE_2') = '#skE_2',
inference(splitRight,[status(thm)],[c_427]) ).
tff(c_48,plain,
! [A_42: $real,B_43: $real] :
( $less(0,$product(A_42,B_43))
| ~ $less(0,A_42)
| ~ $less(0,B_43) ),
inference(cnfTransformation,[status(thm)],[f_157]) ).
tff(c_50,plain,
! [A_44: $real,B_45: $real] :
( ~ $lesseq($product(A_44,B_45),0)
| ~ $less(0,A_44)
| ~ $less(0,B_45) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_48]) ).
tff(c_295,plain,
( ~ $lesseq('#skE_2',0)
| ~ $less(0,v) ),
inference(superposition,[status(thm),theory(equality)],[c_186,c_50]) ).
tff(c_322,plain,
~ $less(0,v),
inference(splitLeft,[status(thm)],[c_295]) ).
tff(c_323,plain,
$false,
inference(close,[status(thm),theory('LFA')],[c_322,c_6]) ).
tff(c_324,plain,
~ $lesseq('#skE_2',0),
inference(splitRight,[status(thm)],[c_295]) ).
tff(c_813,plain,
$false,
inference(close,[status(thm),theory('LFA')],[c_811,c_324]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ARI636_1 : TPTP v9.0.0. Released v6.3.0.
% 0.13/0.13 % 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 : n002.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 15:15:31 EDT 2025
% 0.13/0.34 % CPUTime :
% 6.61/3.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.61/3.22
% 6.61/3.22 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------