%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ARI618_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/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 : n032.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 05:40:42 PM UTC 2025
% Result : Theorem 2.63s 1.75s
% Output : CNFRefutation 2.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 28 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 12 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 28 ( 20 ~; 5 |; 2 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 48 ( 22 atm; 11 fun; 7 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 : 7 ( 4 usr; 4 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('#skF_1',type,
'#skF_1': $int ).
%Foreground operators:
tff(f,type,
f: $int > $int ).
tff(f_39,negated_conjecture,
~ ( ! [Xa: $int] :
( $lesseq(Xa,f(Xa))
& $lesseq($uminus(Xa),f(Xa))
& ( $lesseq(f(Xa),Xa)
| $lesseq(f(Xa),$uminus(Xa)) ) )
=> ! [Xa: $int] : ( f(f(Xa)) = f(Xa) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absolute_value_idempotent) ).
tff(c_18,plain,
f(f('#skF_1')) != f('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_23,plain,
f('#skF_1') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_18]) ).
tff(c_20,plain,
f(f('#skF_1')) != f('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_33,plain,
f('#skE_1') != '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_23,c_23,c_20]) ).
tff(c_71,plain,
f('#skE_1') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_33]) ).
tff(c_68,plain,
f('#skE_1') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_33]) ).
tff(c_10,plain,
! [X_1a: $int] :
( $lesseq(f(X_1a),$uminus(X_1a))
| $lesseq(f(X_1a),X_1a) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_110,plain,
! [X_16a: $int] :
( ~ $less(0,$sum(X_16a,f(X_16a)))
| ~ $less(X_16a,f(X_16a)) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_10]) ).
tff(c_113,plain,
( ~ $less(0,$sum('#skE_1','#skE_2'))
| ~ $less('#skE_1',f('#skE_1')) ),
inference(superposition,[status(thm),theory(equality)],[c_68,c_110]) ).
tff(c_119,plain,
( ~ $less(0,$sum('#skE_1','#skE_2'))
| ~ $less('#skE_1','#skE_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_71,c_113]) ).
tff(c_131,plain,
~ $less('#skE_1','#skE_2'),
inference(splitLeft,[status(thm)],[c_119]) ).
tff(c_72,plain,
f('#skE_1') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_33]) ).
tff(c_4,plain,
! [X_1a: $int] : $lesseq(X_1a,f(X_1a)),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_14,plain,
! [X_1a: $int] : ~ $less(f(X_1a),X_1a),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_4]) ).
tff(c_102,plain,
~ $less('#skE_2','#skE_1'),
inference(superposition,[status(thm),theory(equality)],[c_72,c_14]) ).
tff(c_62,plain,
f('#skE_1') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_33]) ).
tff(c_61,plain,
f('#skE_1') != '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_23,c_23,c_20]) ).
tff(c_69,plain,
'#skE_2' != '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_62,c_61]) ).
tff(c_132,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_131,c_102,c_69]) ).
tff(c_135,plain,
~ $less(0,$sum('#skE_1','#skE_2')),
inference(splitRight,[status(thm)],[c_119]) ).
tff(c_36,plain,
f('#skF_1') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_18]) ).
tff(c_7,plain,
! [X_1a: $int] : $lesseq($uminus(X_1a),f(X_1a)),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_13,plain,
! [X_1a: $int] : ~ $less($sum(X_1a,f(X_1a)),0),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_7]) ).
tff(c_52,plain,
~ $less($sum('#skF_1','#skE_1'),0),
inference(superposition,[status(thm),theory(equality)],[c_36,c_13]) ).
tff(c_54,plain,
~ $less($sum('#skE_1','#skF_1'),0),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_52]) ).
tff(c_56,plain,
~ $less('#skE_1','#skF_1'),
inference(superposition,[status(thm),theory(equality)],[c_36,c_14]) ).
tff(c_137,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_135,c_54,c_102,c_69,c_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08 % Problem : ARI618_1 : TPTP v9.0.0. Released v5.1.0.
% 0.02/0.08 % 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
% 0.09/0.27 % Computer : n032.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8042.1875MB
% 0.09/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.27 % CPULimit : 300
% 0.09/0.27 % WCLimit : 300
% 0.09/0.27 % DateTime : Mon Apr 7 15:14:46 EDT 2025
% 0.09/0.27 % CPUTime :
% 2.63/1.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.63/1.75
% 2.63/1.75 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------