%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ARI601_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 : n011.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 2.84s 1.66s
% Output : CNFRefutation 2.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 31 ( 10 atm; 6 fun; 12 num; 3 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 : 7 ( 3 usr; 5 con; 0-2 aty)
% Number of variables : 3 ( 3 !; 0 ?; 3 :)
% Comments :
%------------------------------------------------------------------------------
%$ #nlpp > f
%Foreground sorts:
%Background operators:
tff('#skE_1',type,
'#skE_1': $int ).
tff(a,type,
a: $int ).
%Foreground operators:
tff(f,type,
f: $int > $int ).
tff(f_34,negated_conjecture,
~ ( ! [Xa: $int] : $greater(f(Xa),Xa)
=> ( $less(3,a)
=> $less(4,f($sum(a,1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fX_gt_X_implies_ineq) ).
tff(c_12,plain,
~ $less(4,f($sum(1,a))),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_26,plain,
f($sum(1,a)) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_12]) ).
tff(c_5,plain,
! [X_1a: $int] : $greater(f(X_1a),X_1a),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_7,plain,
! [X_1a: $int] : $less(X_1a,f(X_1a)),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_5]) ).
tff(c_40,plain,
$less($sum(1,a),'#skE_1'),
inference(superposition,[status(thm),theory(equality)],[c_26,c_7]) ).
tff(c_16,plain,
f($sum(1,a)) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_12]) ).
tff(c_14,plain,
~ $less(4,f($sum(1,a))),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_23,plain,
~ $less(4,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_14]) ).
tff(c_8,plain,
$less(3,a),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_44,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_40,c_23,c_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : ARI601_1 : TPTP v9.0.0. Released v5.1.0.
% 0.11/0.12 % 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
% 0.12/0.32 % Computer : n011.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Apr 7 15:14:03 EDT 2025
% 0.12/0.32 % CPUTime :
% 2.84/1.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.84/1.67
% 2.84/1.67 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------