%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SYO523_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 : n024.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 3.21s 1.86s
% Output : CNFRefutation 3.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 32 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 24 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 25 ( 12 ~; 7 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 75 ( 20 atm; 0 fun; 49 num; 6 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 : 9 ( 4 usr; 8 con; 0-1 aty)
% Number of variables : 6 ( 6 !; 0 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
%$ #nlpp > f
%Foreground sorts:
%Background operators:
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skE_3',type,
'#skE_3': $int ).
%Foreground operators:
tff(f,type,
f: $int > $int ).
tff(f_44,negated_conjecture,
~ ( ( ! [Xa: $int,Ya: $int] :
( ( f(Xa) = f(Ya) )
=> ( Xa = Ya ) )
& $less(6,f(3))
& $less(f(3),9)
& $less(6,f(4))
& $less(f(4),9) )
=> ( $lesseq(f(5),6)
| $lesseq(9,f(5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',injective_f_pigeonhole) ).
tff(c_17,plain,
$less(6,f(3)),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_26,plain,
f(3) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_17]) ).
tff(c_5,plain,
~ $lesseq(f(5),6),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_21,plain,
$less(6,f(5)),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_5]) ).
tff(c_39,plain,
f(5) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_21]) ).
tff(c_71,plain,
! [Y_3a: $int,X_4a: $int] :
( ( f(Y_3a) != f(X_4a) )
| ( Y_3a = X_4a ) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_113,plain,
! [Y_6a: $int] :
( ( f(Y_6a) != '#skE_2' )
| ( Y_6a = 5 ) ),
inference(superposition,[status(thm),theory(equality)],[c_39,c_71]) ).
tff(c_122,plain,
( ( '#skE_2' != '#skE_1' )
| ( 5 = 3 ) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_113]) ).
tff(c_127,plain,
'#skE_2' != '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_122]) ).
tff(c_19,plain,
$less(6,f(4)),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_52,plain,
f(4) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_19]) ).
tff(c_96,plain,
! [X_5a: $int] :
( ( f(X_5a) != '#skE_3' )
| ( X_5a = 4 ) ),
inference(superposition,[status(thm),theory(equality)],[c_52,c_71]) ).
tff(c_105,plain,
( ( '#skE_3' != '#skE_1' )
| ( 4 = 3 ) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_96]) ).
tff(c_112,plain,
'#skE_3' != '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_105]) ).
tff(c_102,plain,
( ( '#skE_3' != '#skE_2' )
| ( 5 = 4 ) ),
inference(superposition,[status(thm),theory(equality)],[c_39,c_96]) ).
tff(c_110,plain,
'#skE_3' != '#skE_2',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_102]) ).
tff(c_49,plain,
f(4) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_19]) ).
tff(c_53,plain,
$less(6,'#skE_3'),
inference(demodulation,[status(thm),theory(equality)],[c_49,c_19]) ).
tff(c_20,plain,
$less(f(4),9),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_54,plain,
f(4) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_20]) ).
tff(c_58,plain,
$less('#skE_3',9),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_20]) ).
tff(c_2,plain,
~ $lesseq(9,f(5)),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_22,plain,
$less(f(5),9),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_2]) ).
tff(c_48,plain,
$less('#skE_2',9),
inference(demodulation,[status(thm),theory(equality)],[c_39,c_22]) ).
tff(c_36,plain,
f(5) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_21]) ).
tff(c_40,plain,
$less(6,'#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_21]) ).
tff(c_18,plain,
$less(f(3),9),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_35,plain,
$less('#skE_1',9),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_18]) ).
tff(c_23,plain,
f(3) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_17]) ).
tff(c_27,plain,
$less(6,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_23,c_17]) ).
tff(c_128,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_127,c_112,c_110,c_53,c_58,c_48,c_40,c_35,c_27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYO523_1 : TPTP v9.0.0. Released v5.0.0.
% 0.10/0.13 % 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
% 0.12/0.34 % Computer : n024.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 : Wed Apr 9 09:19:06 EDT 2025
% 0.12/0.34 % CPUTime :
% 3.21/1.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.21/1.86
% 3.21/1.86 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------