%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET592+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/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 : n011.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 08:38:48 PM UTC 2025
% Result : Theorem 3.42s 1.82s
% Output : CNFRefutation 3.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 42 ( 10 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 38 ( 16 ~; 13 |; 4 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 24 ( 24 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > empty > intersection > #nlpp > empty_set > #skF_2 > #skF_7 > #skF_3 > #skF_5 > #skF_6 > #skF_1 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff(intersection,type,
intersection: ( $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_97,negated_conjecture,
~ ! [B,C,D] :
( ( subset(B,C)
& subset(B,D)
& ( intersection(C,D) = empty_set ) )
=> ( B = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th51) ).
tff(f_59,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
tff(f_44,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
tff(f_40,axiom,
! [B,C,D] :
( ( subset(B,C)
& subset(B,D) )
=> subset(B,intersection(C,D)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_of_subsets) ).
tff(f_66,axiom,
! [B,C] :
( ( B = C )
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
tff(c_46,plain,
empty_set != '#skF_5',
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_52,plain,
subset('#skF_5','#skF_6'),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_50,plain,
subset('#skF_5','#skF_7'),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_158,plain,
! [B_46,C_47] :
( member('#skF_1'(B_46,C_47),B_46)
| subset(B_46,C_47) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_6,plain,
! [B_5] : ~ member(B_5,empty_set),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_183,plain,
! [C_47] : subset(empty_set,C_47),
inference(resolution,[status(thm)],[c_158,c_6]) ).
tff(c_48,plain,
intersection('#skF_6','#skF_7') = empty_set,
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_329,plain,
! [B_66,C_67,D_68] :
( subset(B_66,intersection(C_67,D_68))
| ~ subset(B_66,D_68)
| ~ subset(B_66,C_67) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_394,plain,
! [B_72] :
( subset(B_72,empty_set)
| ~ subset(B_72,'#skF_7')
| ~ subset(B_72,'#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_48,c_329]) ).
tff(c_20,plain,
! [C_15,B_14] :
( ( C_15 = B_14 )
| ~ subset(C_15,B_14)
| ~ subset(B_14,C_15) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_405,plain,
! [B_72] :
( ( empty_set = B_72 )
| ~ subset(empty_set,B_72)
| ~ subset(B_72,'#skF_7')
| ~ subset(B_72,'#skF_6') ),
inference(resolution,[status(thm)],[c_394,c_20]) ).
tff(c_420,plain,
! [B_73] :
( ( empty_set = B_73 )
| ~ subset(B_73,'#skF_7')
| ~ subset(B_73,'#skF_6') ),
inference(demodulation,[status(thm),theory(equality)],[c_183,c_405]) ).
tff(c_435,plain,
( ( empty_set = '#skF_5' )
| ~ subset('#skF_5','#skF_6') ),
inference(resolution,[status(thm)],[c_50,c_420]) ).
tff(c_444,plain,
empty_set = '#skF_5',
inference(demodulation,[status(thm),theory(equality)],[c_52,c_435]) ).
tff(c_446,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_444]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET592+3 : TPTP v9.0.0. Released v2.2.0.
% 0.12/0.13 % 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 : n011.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 21:16:33 EDT 2025
% 0.12/0.34 % CPUTime :
% 3.42/1.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.42/1.83
% 3.42/1.83 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------