%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET616+3 : TPTP v9.0.0. Released v2.2.0.
% 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 : n015.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 08:38:53 PM UTC 2025
% Result : Theorem 3.05s 1.78s
% Output : CNFRefutation 3.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 46 ( 7 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 39 ( 16 ~; 16 |; 2 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 31 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > difference > #nlpp > #skF_7 > #skF_3 > #skF_6 > #skF_2 > #skF_1 > #skF_5 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(difference,type,
difference: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_75,negated_conjecture,
~ ! [B,C] :
( ( difference(B,C) = difference(C,B) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th90) ).
tff(f_66,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
tff(f_43,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( member(D,B)
& ~ member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
tff(f_50,axiom,
! [B,C] :
( ( B = C )
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
tff(c_42,plain,
'#skF_7' != '#skF_6',
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_38,plain,
! [B_14,C_15] :
( member('#skF_5'(B_14,C_15),B_14)
| subset(B_14,C_15) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_101,plain,
! [D_38,B_39,C_40] :
( member(D_38,difference(B_39,C_40))
| member(D_38,C_40)
| ~ member(D_38,B_39) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_44,plain,
difference('#skF_7','#skF_6') = difference('#skF_6','#skF_7'),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_76,plain,
! [D_30,B_31,C_32] :
( member(D_30,B_31)
| ~ member(D_30,difference(B_31,C_32)) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_83,plain,
! [D_30] :
( member(D_30,'#skF_7')
| ~ member(D_30,difference('#skF_6','#skF_7')) ),
inference(superposition,[status(thm),theory(equality)],[c_44,c_76]) ).
tff(c_131,plain,
! [D_41] :
( member(D_41,'#skF_7')
| ~ member(D_41,'#skF_6') ),
inference(resolution,[status(thm)],[c_101,c_83]) ).
tff(c_36,plain,
! [B_14,C_15] :
( ~ member('#skF_5'(B_14,C_15),C_15)
| subset(B_14,C_15) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_140,plain,
! [B_42] :
( subset(B_42,'#skF_7')
| ~ member('#skF_5'(B_42,'#skF_7'),'#skF_6') ),
inference(resolution,[status(thm)],[c_131,c_36]) ).
tff(c_145,plain,
subset('#skF_6','#skF_7'),
inference(resolution,[status(thm)],[c_38,c_140]) ).
tff(c_16,plain,
! [C_8,B_7] :
( ( C_8 = B_7 )
| ~ subset(C_8,B_7)
| ~ subset(B_7,C_8) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_156,plain,
( ( '#skF_7' = '#skF_6' )
| ~ subset('#skF_7','#skF_6') ),
inference(resolution,[status(thm)],[c_145,c_16]) ).
tff(c_159,plain,
~ subset('#skF_7','#skF_6'),
inference(negUnitSimplification,[status(thm)],[c_42,c_156]) ).
tff(c_165,plain,
! [D_47] :
( member(D_47,difference('#skF_6','#skF_7'))
| member(D_47,'#skF_6')
| ~ member(D_47,'#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_44,c_101]) ).
tff(c_14,plain,
! [D_6,B_4,C_5] :
( member(D_6,B_4)
| ~ member(D_6,difference(B_4,C_5)) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_194,plain,
! [D_48] :
( member(D_48,'#skF_6')
| ~ member(D_48,'#skF_7') ),
inference(resolution,[status(thm)],[c_165,c_14]) ).
tff(c_204,plain,
! [C_49] :
( member('#skF_5'('#skF_7',C_49),'#skF_6')
| subset('#skF_7',C_49) ),
inference(resolution,[status(thm)],[c_38,c_194]) ).
tff(c_214,plain,
subset('#skF_7','#skF_6'),
inference(resolution,[status(thm)],[c_204,c_36]) ).
tff(c_221,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_159,c_159,c_214]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SET616+3 : TPTP v9.0.0. Released v2.2.0.
% 0.09/0.11 % 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 : n015.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 21:19:35 EDT 2025
% 0.10/0.32 % CPUTime :
% 3.05/1.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.05/1.78
% 3.05/1.78 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------