%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ARI610_1 : TPTP v9.0.0. Released v5.1.0.
% 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 : n028.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 05:40:41 PM UTC 2025
% Result : Theorem 3.17s 1.80s
% Output : CNFRefutation 3.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 28 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 37 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 17 ( 8 ~; 6 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 65 ( 27 atm; 20 fun; 10 num; 8 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 : 10 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 8 ( 8 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
%$ #nlpp > f
%Foreground sorts:
%Background operators:
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skE_4',type,
'#skE_4': $int ).
tff('#skE_3',type,
'#skE_3': $int ).
tff(b,type,
b: $int ).
tff(a,type,
a: $int ).
%Foreground operators:
tff(f,type,
f: $int > $int ).
tff(f_36,negated_conjecture,
~ ( ( ! [Xa: $int,Ya: $int] :
( $lesseq(Xa,Ya)
=> $lesseq(f(Xa),f(Ya)) )
& $less(f(b),f(a)) )
=> $lesseq(f(0),f($sum(a,$uminus(b)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_mon_implies_f_a_b_2) ).
tff(c_2,plain,
~ $lesseq(f(0),f($sum($uminus(b),a))),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_14,plain,
$less(f($sum(a,$uminus(b))),f(0)),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_2]) ).
tff(c_17,plain,
$less(f($sum($uminus(b),a)),f(0)),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_14]) ).
tff(c_105,plain,
f(0) = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_17]) ).
tff(c_104,plain,
f($sum($uminus(b),a)) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_17]) ).
tff(c_21,plain,
$less(f($sum($uminus(b),a)),f(0)),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_14]) ).
tff(c_114,plain,
$less('#skE_3','#skE_4'),
inference(demodulation,[status(thm),theory(equality)],[c_105,c_104,c_21]) ).
tff(c_109,plain,
f($sum($uminus(b),a)) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_17]) ).
tff(c_112,plain,
f($sum(a,$uminus(b))) = '#skE_3',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_109]) ).
tff(c_113,plain,
f(0) = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_17]) ).
tff(c_6,plain,
! [X_1a: $int,Y_2a: $int] :
( $lesseq(f(X_1a),f(Y_2a))
| ~ $lesseq(X_1a,Y_2a) ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_8,plain,
! [Y_2a: $int,X_1a: $int] :
( ~ $less(f(Y_2a),f(X_1a))
| $less(Y_2a,X_1a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_6]) ).
tff(c_286,plain,
! [Y_40a: $int] :
( ~ $less(f(Y_40a),'#skE_4')
| $less(Y_40a,0) ),
inference(superposition,[status(thm),theory(equality)],[c_113,c_8]) ).
tff(c_289,plain,
( ~ $less('#skE_3','#skE_4')
| $less($sum(a,$uminus(b)),0) ),
inference(superposition,[status(thm),theory(equality)],[c_112,c_286]) ).
tff(c_301,plain,
$less($sum(a,$uminus(b)),0),
inference(demodulation,[status(thm),theory(equality)],[c_114,c_289]) ).
tff(c_303,plain,
$less(a,b),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_301]) ).
tff(c_12,plain,
$less(f(b),f(a)),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_24,plain,
f(a) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_12]) ).
tff(c_23,plain,
f(b) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_12]) ).
tff(c_19,plain,
$less(f(b),f(a)),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_35,plain,
$less('#skE_1','#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_23,c_19]) ).
tff(c_31,plain,
f(b) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_12]) ).
tff(c_67,plain,
f(a) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_12]) ).
tff(c_226,plain,
! [Y_36a: $int] :
( ~ $less(f(Y_36a),'#skE_2')
| $less(Y_36a,a) ),
inference(superposition,[status(thm),theory(equality)],[c_67,c_8]) ).
tff(c_238,plain,
( ~ $less('#skE_1','#skE_2')
| $less(b,a) ),
inference(superposition,[status(thm),theory(equality)],[c_31,c_226]) ).
tff(c_250,plain,
$less(b,a),
inference(demodulation,[status(thm),theory(equality)],[c_35,c_238]) ).
tff(c_311,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_303,c_250]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ARI610_1 : TPTP v9.0.0. Released v5.1.0.
% 0.11/0.13 % 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 : n028.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 15:14:20 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.17/1.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.23/1.80
% 3.23/1.80 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------