%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SYO524_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/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 : n006.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 10:37:48 PM UTC 2025
% Result : Theorem 2.98s 1.70s
% Output : CNFRefutation 2.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 33 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 23 ~; 3 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 100 ( 26 atm; 17 fun; 50 num; 7 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 : 14 ( 6 usr; 12 con; 0-2 aty)
% Number of variables : 7 ( 7 !; 0 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
%$ #nlpp > f
%Foreground sorts:
%Background operators:
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skE_5',type,
'#skE_5': $int ).
tff('#skE_4',type,
'#skE_4': $int ).
tff('#skE_3',type,
'#skE_3': $int ).
%Foreground operators:
tff(f,type,
f: $int > $int ).
tff(f_35,negated_conjecture,
~ ( ( ! [Ua: $int] : $lesseq(f($sum(Ua,1)),f($sum(Ua,2)))
& $lesseq(f(7),3) )
=> $lesseq(f(4),3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(c_2,plain,
~ $lesseq(f(4),3),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_15,plain,
$less(3,f(4)),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_2]) ).
tff(c_32,plain,
f(4) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_15]) ).
tff(c_5,plain,
$lesseq(f(7),3),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_14,plain,
~ $less(3,f(7)),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_5]) ).
tff(c_21,plain,
f(7) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_14]) ).
tff(c_8,plain,
! [U_1a: $int] : $lesseq(f($sum(1,U_1a)),f($sum(2,U_1a))),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_40,plain,
! [U_8a: $int] : ~ $less(f($sum(2,U_8a)),f($sum(1,U_8a))),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_8]) ).
tff(c_69,plain,
! [U_8a: $int] :
( ~ $less('#skE_1',f($sum(1,U_8a)))
| ( $sum(2,U_8a) != 7 ) ),
inference(superposition,[status(thm),theory(equality)],[c_21,c_40]) ).
tff(c_71,plain,
~ $less('#skE_1',f($sum(1,5))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_69]) ).
tff(c_74,plain,
~ $less('#skE_1',f(6)),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_71]) ).
tff(c_122,plain,
f(6) = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_74]) ).
tff(c_13,plain,
! [U_1a: $int] : ~ $less(f($sum(2,U_1a)),f($sum(1,U_1a))),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_8]) ).
tff(c_136,plain,
! [U_1a: $int] :
( ~ $less('#skE_4',f($sum(1,U_1a)))
| ( $sum(2,U_1a) != 6 ) ),
inference(superposition,[status(thm),theory(equality)],[c_122,c_13]) ).
tff(c_138,plain,
~ $less('#skE_4',f($sum(1,4))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_136]) ).
tff(c_141,plain,
~ $less('#skE_4',f(5)),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_138]) ).
tff(c_157,plain,
f(5) = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_141]) ).
tff(c_171,plain,
! [U_1a: $int] :
( ~ $less('#skE_5',f($sum(1,U_1a)))
| ( $sum(2,U_1a) != 5 ) ),
inference(superposition,[status(thm),theory(equality)],[c_157,c_13]) ).
tff(c_173,plain,
~ $less('#skE_5',f($sum(1,3))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_171]) ).
tff(c_176,plain,
~ $less('#skE_5',f(4)),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_173]) ).
tff(c_189,plain,
~ $less('#skE_5','#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_176]) ).
tff(c_154,plain,
f(5) = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_141]) ).
tff(c_153,plain,
~ $less('#skE_4',f(5)),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_138]) ).
tff(c_158,plain,
~ $less('#skE_4','#skE_5'),
inference(demodulation,[status(thm),theory(equality)],[c_154,c_153]) ).
tff(c_119,plain,
f(6) = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_74]) ).
tff(c_118,plain,
~ $less('#skE_1',f(6)),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_71]) ).
tff(c_123,plain,
~ $less('#skE_1','#skE_4'),
inference(demodulation,[status(thm),theory(equality)],[c_119,c_118]) ).
tff(c_29,plain,
f(4) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_15]) ).
tff(c_33,plain,
$less(3,'#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_29,c_15]) ).
tff(c_18,plain,
f(7) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_14]) ).
tff(c_22,plain,
~ $less(3,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_14]) ).
tff(c_190,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_189,c_158,c_123,c_33,c_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO524_1 : TPTP v9.0.0. Released v5.0.0.
% 0.07/0.13 % 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
% 0.12/0.32 % Computer : n006.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 : Wed Apr 9 09:18:52 EDT 2025
% 0.12/0.32 % CPUTime :
% 2.98/1.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.98/1.70
% 2.98/1.70 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------