%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET903+1 : TPTP v9.0.0. Released v3.2.0.
% 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 : n028.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 08:39:33 PM UTC 2025
% Result : Theorem 2.90s 1.73s
% Output : CNFRefutation 2.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 35 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 37 ( 18 ~; 10 |; 9 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 16 ( 16 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ empty > set_union2 > #nlpp > singleton > empty_set > #skF_5 > #skF_2 > #skF_3 > #skF_1 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff(f_79,negated_conjecture,
~ ! [A,B,C] :
~ ( ( singleton(A) = set_union2(B,C) )
& ( B != C )
& ( B != empty_set )
& ( C != empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_zfmisc_1) ).
tff(f_66,axiom,
! [A,B,C] :
~ ( ( singleton(A) = set_union2(B,C) )
& ~ ( ( B = singleton(A) )
& ( C = singleton(A) ) )
& ~ ( ( B = empty_set )
& ( C = singleton(A) ) )
& ~ ( ( B = singleton(A) )
& ( C = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_zfmisc_1) ).
tff(c_36,plain,
'#skF_5' != '#skF_4',
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_34,plain,
empty_set != '#skF_4',
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_38,plain,
set_union2('#skF_4','#skF_5') = singleton('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_112,plain,
! [B_19,A_20,C_21] :
( ( empty_set = B_19 )
| ( singleton(A_20) = B_19 )
| ( singleton(A_20) != set_union2(B_19,C_21) ) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_121,plain,
! [A_20] :
( ( empty_set = '#skF_4' )
| ( singleton(A_20) = '#skF_4' )
| ( singleton(A_20) != singleton('#skF_3') ) ),
inference(superposition,[status(thm),theory(equality)],[c_38,c_112]) ).
tff(c_125,plain,
! [A_20] :
( ( singleton(A_20) = '#skF_4' )
| ( singleton(A_20) != singleton('#skF_3') ) ),
inference(negUnitSimplification,[status(thm)],[c_34,c_121]) ).
tff(c_128,plain,
singleton('#skF_3') = '#skF_4',
inference(reflexivity,[status(thm),theory(equality)],[c_125]) ).
tff(c_32,plain,
empty_set != '#skF_5',
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_132,plain,
set_union2('#skF_4','#skF_5') = '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_128,c_38]) ).
tff(c_152,plain,
! [A_23,C_24,B_25] :
( ( singleton(A_23) = C_24 )
| ( empty_set = C_24 )
| ( singleton(A_23) != set_union2(B_25,C_24) ) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_155,plain,
! [A_23] :
( ( singleton(A_23) = '#skF_5' )
| ( empty_set = '#skF_5' )
| ( singleton(A_23) != '#skF_4' ) ),
inference(superposition,[status(thm),theory(equality)],[c_132,c_152]) ).
tff(c_166,plain,
! [A_26] :
( ( singleton(A_26) = '#skF_5' )
| ( singleton(A_26) != '#skF_4' ) ),
inference(negUnitSimplification,[status(thm)],[c_32,c_155]) ).
tff(c_169,plain,
singleton('#skF_3') = '#skF_5',
inference(superposition,[status(thm),theory(equality)],[c_128,c_166]) ).
tff(c_171,plain,
'#skF_5' = '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_128,c_169]) ).
tff(c_173,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_36,c_171]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET903+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % 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 : n028.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 : Tue Apr 8 21:49:49 EDT 2025
% 0.12/0.34 % CPUTime :
% 2.90/1.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.90/1.74
% 2.90/1.74 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------