%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET201+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 : n009.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 08:38:15 PM UTC 2025
% Result : Theorem 6.20s 2.54s
% Output : CNFRefutation 6.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 62 ( 2 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 59 ( 25 ~; 28 |; 2 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 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; 4 con; 0-2 aty)
% Number of variables : 57 ( 57 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > intersection > #nlpp > #skF_7 > #skF_3 > #skF_5 > #skF_6 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
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('#skF_4',type,
'#skF_4': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_43,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
tff(f_35,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
tff(f_46,axiom,
! [B,C] : ( intersection(B,C) = intersection(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
tff(f_65,negated_conjecture,
~ ! [B,C,D,E] :
( ( subset(B,C)
& subset(D,E) )
=> subset(intersection(B,D),intersection(C,E)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th41) ).
tff(c_12,plain,
! [B_4,C_5] :
( member('#skF_1'(B_4,C_5),B_4)
| subset(B_4,C_5) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_89,plain,
! [D_27,C_28,B_29] :
( member(D_27,C_28)
| ~ member(D_27,intersection(B_29,C_28)) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_212,plain,
! [B_47,C_48,C_49] :
( member('#skF_1'(intersection(B_47,C_48),C_49),C_48)
| subset(intersection(B_47,C_48),C_49) ),
inference(resolution,[status(thm)],[c_12,c_89]) ).
tff(c_10,plain,
! [B_4,C_5] :
( ~ member('#skF_1'(B_4,C_5),C_5)
| subset(B_4,C_5) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_235,plain,
! [B_47,C_48] : subset(intersection(B_47,C_48),C_48),
inference(resolution,[status(thm)],[c_212,c_10]) ).
tff(c_14,plain,
! [C_10,B_9] : ( intersection(C_10,B_9) = intersection(B_9,C_10) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_237,plain,
! [B_50,C_51] : subset(intersection(B_50,C_51),C_51),
inference(resolution,[status(thm)],[c_212,c_10]) ).
tff(c_240,plain,
! [C_10,B_9] : subset(intersection(C_10,B_9),C_10),
inference(superposition,[status(thm),theory(equality)],[c_14,c_237]) ).
tff(c_32,plain,
subset('#skF_6','#skF_7'),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_101,plain,
! [D_30,C_31,B_32] :
( member(D_30,C_31)
| ~ member(D_30,B_32)
| ~ subset(B_32,C_31) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_128,plain,
! [B_36,C_37,C_38] :
( member('#skF_1'(B_36,C_37),C_38)
| ~ subset(B_36,C_38)
| subset(B_36,C_37) ),
inference(resolution,[status(thm)],[c_12,c_101]) ).
tff(c_8,plain,
! [D_8,C_5,B_4] :
( member(D_8,C_5)
| ~ member(D_8,B_4)
| ~ subset(B_4,C_5) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_381,plain,
! [B_75,C_76,C_77,C_78] :
( member('#skF_1'(B_75,C_76),C_77)
| ~ subset(C_78,C_77)
| ~ subset(B_75,C_78)
| subset(B_75,C_76) ),
inference(resolution,[status(thm)],[c_128,c_8]) ).
tff(c_395,plain,
! [B_75,C_76] :
( member('#skF_1'(B_75,C_76),'#skF_7')
| ~ subset(B_75,'#skF_6')
| subset(B_75,C_76) ),
inference(resolution,[status(thm)],[c_32,c_381]) ).
tff(c_34,plain,
subset('#skF_4','#skF_5'),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_396,plain,
! [B_75,C_76] :
( member('#skF_1'(B_75,C_76),'#skF_5')
| ~ subset(B_75,'#skF_4')
| subset(B_75,C_76) ),
inference(resolution,[status(thm)],[c_34,c_381]) ).
tff(c_105,plain,
! [D_33,B_34,C_35] :
( member(D_33,intersection(B_34,C_35))
| ~ member(D_33,C_35)
| ~ member(D_33,B_34) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_2064,plain,
! [B_207,B_208,C_209] :
( subset(B_207,intersection(B_208,C_209))
| ~ member('#skF_1'(B_207,intersection(B_208,C_209)),C_209)
| ~ member('#skF_1'(B_207,intersection(B_208,C_209)),B_208) ),
inference(resolution,[status(thm)],[c_105,c_10]) ).
tff(c_2617,plain,
! [B_225,B_226] :
( ~ member('#skF_1'(B_225,intersection(B_226,'#skF_5')),B_226)
| ~ subset(B_225,'#skF_4')
| subset(B_225,intersection(B_226,'#skF_5')) ),
inference(resolution,[status(thm)],[c_396,c_2064]) ).
tff(c_2653,plain,
! [B_75] :
( ~ subset(B_75,'#skF_4')
| ~ subset(B_75,'#skF_6')
| subset(B_75,intersection('#skF_7','#skF_5')) ),
inference(resolution,[status(thm)],[c_395,c_2617]) ).
tff(c_3197,plain,
! [B_248] :
( ~ subset(B_248,'#skF_4')
| ~ subset(B_248,'#skF_6')
| subset(B_248,intersection('#skF_5','#skF_7')) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_2653]) ).
tff(c_30,plain,
~ subset(intersection('#skF_4','#skF_6'),intersection('#skF_5','#skF_7')),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_3229,plain,
( ~ subset(intersection('#skF_4','#skF_6'),'#skF_4')
| ~ subset(intersection('#skF_4','#skF_6'),'#skF_6') ),
inference(resolution,[status(thm)],[c_3197,c_30]) ).
tff(c_3249,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_235,c_240,c_3229]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET201+3 : TPTP v9.0.0. Released v2.2.0.
% 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
% 0.13/0.35 % Computer : n009.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Apr 8 20:19:26 EDT 2025
% 0.13/0.35 % CPUTime :
% 6.20/2.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.20/2.55
% 6.20/2.55 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------