%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ARI632_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 : n031.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 05:40:44 PM UTC 2025
% Result : Theorem 3.28s 1.93s
% Output : CNFRefutation 3.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 4 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 15 ~; 4 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 37 ( 22 atm; 8 fun; 0 num; 7 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 : 8 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 7 ( 7 !; 0 ?; 7 :)
% 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(y,type,
y: $real ).
tff(v,type,
v: $real ).
%Foreground operators:
tff(f,type,
f: $real > $real ).
tff(f_37,negated_conjecture,
~ $less($sum(u,f(x)),$sum(v,f(y))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conclusion) ).
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_35,hypothesis,
$lesseq(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_01) ).
tff(f_34,hypothesis,
$less(u,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis) ).
tff(c_11,plain,
~ $less($sum(u,f(x)),$sum(v,f(y))),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_22,plain,
f(x) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_11]) ).
tff(c_52,plain,
f(y) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_11]) ).
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_99,plain,
! [Y_30a: $real] :
( ~ $less('#skE_2',f(Y_30a))
| ~ $lesseq(Y_30a,y) ),
inference(superposition,[status(thm),theory(equality)],[c_52,c_2]) ).
tff(c_108,plain,
( ~ $less('#skE_2','#skE_1')
| ~ $lesseq(x,y) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_99]) ).
tff(c_109,plain,
~ $lesseq(x,y),
inference(splitLeft,[status(thm)],[c_108]) ).
tff(c_5,plain,
$lesseq(x,y),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_6,plain,
~ $less(y,x),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_5]) ).
tff(c_122,plain,
$false,
inference(close,[status(thm),theory('LFA')],[c_109,c_6]) ).
tff(c_123,plain,
~ $less('#skE_2','#skE_1'),
inference(splitRight,[status(thm)],[c_108]) ).
tff(c_16,plain,
f(y) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_11]) ).
tff(c_15,plain,
f(x) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_11]) ).
tff(c_12,plain,
~ $less($sum(u,f(x)),$sum(v,f(y))),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_18,plain,
~ $less($sum(u,'#skE_1'),$sum(v,'#skE_2')),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_15,c_12]) ).
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_126,plain,
$false,
inference(close,[status(thm),theory('LFA')],[c_123,c_18,c_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ARI632_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 : n031.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 15:15:22 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.28/1.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.28/1.93
% 3.28/1.93 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------