%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET900+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/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 : 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 08:39:32 PM UTC 2025
% Result : Theorem 2.31s 1.64s
% Output : CNFRefutation 2.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 27 ( 22 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 30 ( 15 ~; 9 |; 6 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 13 ( 13 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > empty > #nlpp > singleton > empty_set > #skF_2 > #skF_3 > #skF_1 > #skF_4 > #skF_5
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(singleton,type,
singleton: $i > $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
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('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff(f_52,negated_conjecture,
~ ! [A,B] :
~ ( ( A != singleton(B) )
& ( A != empty_set )
& ! [C] :
~ ( in(C,A)
& ( C != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_zfmisc_1) ).
tff(f_66,axiom,
! [A,B] :
~ ( ( A != singleton(B) )
& ( A != empty_set )
& ! [C] :
~ ( in(C,A)
& ( C != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l45_zfmisc_1) ).
tff(c_14,plain,
singleton('#skF_4') != '#skF_3',
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_12,plain,
empty_set != '#skF_3',
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_22,plain,
! [A_13,B_14] :
( in('#skF_5'(A_13,B_14),A_13)
| ( empty_set = A_13 )
| ( singleton(B_14) = A_13 ) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_10,plain,
! [C_4] :
( ( C_4 = '#skF_4' )
| ~ in(C_4,'#skF_3') ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_28,plain,
! [B_14] :
( ( '#skF_5'('#skF_3',B_14) = '#skF_4' )
| ( empty_set = '#skF_3' )
| ( singleton(B_14) = '#skF_3' ) ),
inference(resolution,[status(thm)],[c_22,c_10]) ).
tff(c_33,plain,
! [B_15] :
( ( '#skF_5'('#skF_3',B_15) = '#skF_4' )
| ( singleton(B_15) = '#skF_3' ) ),
inference(negUnitSimplification,[status(thm)],[c_12,c_28]) ).
tff(c_44,plain,
'#skF_5'('#skF_3','#skF_4') = '#skF_4',
inference(superposition,[status(thm),theory(equality)],[c_33,c_14]) ).
tff(c_16,plain,
! [A_5,B_6] :
( ( '#skF_5'(A_5,B_6) != B_6 )
| ( empty_set = A_5 )
| ( singleton(B_6) = A_5 ) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_51,plain,
( ( empty_set = '#skF_3' )
| ( singleton('#skF_4') = '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_44,c_16]) ).
tff(c_58,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14,c_12,c_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SET900+1 : TPTP v9.0.0. Released v3.2.0.
% 0.05/0.11 % 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
% 0.10/0.31 % Computer : n006.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue Apr 8 21:49:22 EDT 2025
% 0.16/0.31 % CPUTime :
% 2.31/1.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.31/1.64
% 2.31/1.64 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------