%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ARI599_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 : n003.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 05:40:39 PM UTC 2025
% Result : Theorem 2.71s 1.66s
% Output : CNFRefutation 2.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 18 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 11 ( 8 ~; 1 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 22 ( 6 atm; 8 fun; 8 num; 0 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 : 8 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ f > #nlpp
%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 ) > $int ).
tff(f_33,negated_conjecture,
~ ( ( $lesseq($product(2,a),$product(2,b))
& $lesseq($product(3,b),$product(3,a)) )
=> ( f(a,b) = f(b,a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ineq_imply_f_eq_f) ).
tff(c_12,plain,
f(b,a) != f(a,b),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_16,plain,
f(a,b) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_12]) ).
tff(c_15,plain,
f(b,a) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_12]) ).
tff(c_13,plain,
f(b,a) != f(a,b),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_27,plain,
'#skE_2' != '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_16,c_15,c_13]) ).
tff(c_45,plain,
f(a,b) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_12]) ).
tff(c_23,plain,
f(b,a) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_12]) ).
tff(c_51,plain,
( ( '#skE_2' = '#skE_1' )
| ( b != a ) ),
inference(superposition,[status(thm),theory(equality)],[c_45,c_23]) ).
tff(c_64,plain,
b != a,
inference(negUnitSimplification,[status(thm)],[c_27,c_51]) ).
tff(c_3,plain,
$lesseq($product(3,b),$product(3,a)),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_8,plain,
~ $less(a,b),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_3]) ).
tff(c_5,plain,
$lesseq($product(2,a),$product(2,b)),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_7,plain,
~ $less(b,a),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_5]) ).
tff(c_72,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_64,c_8,c_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ARI599_1 : TPTP v9.0.0. Released v5.1.0.
% 0.12/0.13 % 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 : n003.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 15:14:03 EDT 2025
% 0.12/0.34 % CPUTime :
% 2.71/1.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.71/1.66
% 2.71/1.66 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------