%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : DAT055_1 : TPTP v9.0.0. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/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 06:08:01 PM UTC 2025
% Result : Theorem 2.68s 1.64s
% Output : CNFRefutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 22 ( 4 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 14 ( 11 ~; 0 |; 2 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 24 ( 17 atm; 5 fun; 2 num; 0 var)
% Number of types : 2 ( 1 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 : 9 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 3 ( 3 !; 0 ?; 3 :)
% Comments :
%------------------------------------------------------------------------------
%$ #nlpp > min > max > a
%Foreground sorts:
tff(list,type,
list: $tType ).
%Background operators:
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff(l,type,
l: $int ).
tff(k,type,
k: $int ).
%Foreground operators:
tff(min,type,
min: list > $int ).
tff(max,type,
max: list > $int ).
tff(a,type,
a: list ).
tff(f_37,negated_conjecture,
~ ( ( ! [X: list] : $lesseq(min(X),max(X))
& $lesseq(l,min(a))
& $less(0,k) )
=> $less(l,$sum(max(a),k)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boyer_moore_max_min) ).
tff(c_2,plain,
~ $less(l,$sum(max(a),k)),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_20,plain,
~ $less(l,$sum(k,max(a))),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_2]) ).
tff(c_44,plain,
max(a) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_20]) ).
tff(c_24,plain,
~ $less(l,$sum(k,max(a))),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_2]) ).
tff(c_48,plain,
~ $less(l,$sum(k,'#skE_2')),
inference(demodulation,[status(thm),theory(equality)],[c_44,c_24]) ).
tff(c_6,plain,
$lesseq(l,min(a)),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_15,plain,
~ $less(min(a),l),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_6]) ).
tff(c_29,plain,
min(a) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_15]) ).
tff(c_47,plain,
max(a) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_20]) ).
tff(c_9,plain,
! [X_1: list] : $lesseq(min(X_1),max(X_1)),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_11,plain,
! [X_1: list] : ~ $less(max(X_1),min(X_1)),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_9]) ).
tff(c_53,plain,
~ $less('#skE_2',min(a)),
inference(superposition,[status(thm),theory(equality)],[c_47,c_11]) ).
tff(c_59,plain,
~ $less('#skE_2','#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_29,c_53]) ).
tff(c_26,plain,
min(a) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_15]) ).
tff(c_22,plain,
~ $less(min(a),l),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_6]) ).
tff(c_30,plain,
~ $less('#skE_1',l),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_22]) ).
tff(c_16,plain,
$less(0,k),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_62,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_48,c_59,c_30,c_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : DAT055_1 : TPTP v9.0.0. Released v5.0.0.
% 0.02/0.12 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.11/0.33 % Computer : n002.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Apr 7 18:17:01 EDT 2025
% 0.11/0.33 % CPUTime :
% 2.68/1.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.68/1.64
% 2.68/1.64 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------