%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ARI605_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 : n017.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 05:40:40 PM UTC 2025
% Result : Theorem 2.75s 1.77s
% Output : CNFRefutation 2.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 18 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 26 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 6 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 53 ( 21 atm; 20 fun; 2 num; 10 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 : 7 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 10 ( 9 !; 1 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
%$ #nlpp > f
%Foreground sorts:
%Background operators:
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,type,
f: $int > $int ).
tff(f_35,negated_conjecture,
~ ( ! [Xa: $int] : $greater(f(Xa),Xa)
=> ? [Ya: $int] :
( $less($sum(a,b),Ya)
& $less(Ya,$sum(f(a),f(b))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fX_gt_X_implies_f_a_b) ).
tff(c_1,plain,
! [Y_2a: $int] :
( ~ $less(Y_2a,$sum(f(a),f(b)))
| ~ $less($sum(a,b),Y_2a) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_8,plain,
! [Y_2a: $int] :
( ~ $less(Y_2a,$sum(f(b),f(a)))
| ~ $less($sum(a,b),Y_2a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_1]) ).
tff(c_11,plain,
! [Y_2a: $int] :
( ~ $less(Y_2a,$sum(f(a),f(b)))
| ~ $less($sum(a,b),Y_2a) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_8]) ).
tff(c_51,plain,
f(b) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_11]) ).
tff(c_4,plain,
! [X_1a: $int] : $greater(f(X_1a),X_1a),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_6,plain,
! [X_1a: $int] : $less(X_1a,f(X_1a)),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_4]) ).
tff(c_73,plain,
$less(b,'#skE_2'),
inference(superposition,[status(thm),theory(equality)],[c_51,c_6]) ).
tff(c_16,plain,
f(b) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_11]) ).
tff(c_15,plain,
f(a) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_11]) ).
tff(c_13,plain,
! [Y_2a: $int] :
( ~ $less(Y_2a,$sum(f(a),f(b)))
| ~ $less($sum(a,b),Y_2a) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_8]) ).
tff(c_18,plain,
! [Y_2a: $int] :
( ~ $less(Y_2a,$sum('#skE_1','#skE_2'))
| ~ $less($sum(a,b),Y_2a) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_15,c_13]) ).
tff(c_28,plain,
! [Y_2a: $int] :
( ~ $less(Y_2a,$sum('#skE_1','#skE_2'))
| ~ $less($sum(b,a),Y_2a) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_18]) ).
tff(c_79,plain,
$lesseq($sum('#skE_2','#skE_1'),$sum(1,$sum(a,b))),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_28]) ).
tff(c_81,plain,
~ $less($sum(1,$sum(a,b)),$sum('#skE_2','#skE_1')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_79]) ).
tff(c_31,plain,
f(a) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_11]) ).
tff(c_45,plain,
$less(a,'#skE_1'),
inference(superposition,[status(thm),theory(equality)],[c_31,c_6]) ).
tff(c_82,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_73,c_81,c_45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : ARI605_1 : TPTP v9.0.0. Released v5.1.0.
% 0.02/0.13 % 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
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 7 15:14:25 EDT 2025
% 0.12/0.34 % CPUTime :
% 2.75/1.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.75/1.77
% 2.75/1.77 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------