%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET586+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 : n007.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 08:38:47 PM UTC 2025
% Result : Theorem 6.78s 2.87s
% Output : CNFRefutation 7.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 58 ( 2 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 55 ( 24 ~; 26 |; 1 &)
% ( 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 57 ( 57 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > intersection > #nlpp > #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_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_45,axiom,
! [B,C] : ( intersection(B,C) = intersection(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
tff(f_42,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
tff(f_34,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_62,negated_conjecture,
~ ! [B,C,D] :
( subset(B,C)
=> subset(intersection(B,D),intersection(C,D)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersection_of_subset) ).
tff(c_14,plain,
! [C_10,B_9] : ( intersection(C_10,B_9) = intersection(B_9,C_10) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
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_42]) ).
tff(c_88,plain,
! [D_27,B_28,C_29] :
( member(D_27,B_28)
| ~ member(D_27,intersection(B_28,C_29)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_211,plain,
! [B_47,C_48,C_49] :
( member('#skF_1'(intersection(B_47,C_48),C_49),B_47)
| subset(intersection(B_47,C_48),C_49) ),
inference(resolution,[status(thm)],[c_12,c_88]) ).
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_42]) ).
tff(c_236,plain,
! [B_50,C_51] : subset(intersection(B_50,C_51),B_50),
inference(resolution,[status(thm)],[c_211,c_10]) ).
tff(c_239,plain,
! [C_10,B_9] : subset(intersection(C_10,B_9),B_9),
inference(superposition,[status(thm),theory(equality)],[c_14,c_236]) ).
tff(c_235,plain,
! [B_47,C_48] : subset(intersection(B_47,C_48),B_47),
inference(resolution,[status(thm)],[c_211,c_10]) ).
tff(c_100,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_42]) ).
tff(c_103,plain,
! [B_4,C_5,C_31] :
( member('#skF_1'(B_4,C_5),C_31)
| ~ subset(B_4,C_31)
| subset(B_4,C_5) ),
inference(resolution,[status(thm)],[c_12,c_100]) ).
tff(c_32,plain,
subset('#skF_4','#skF_5'),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_127,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_100]) ).
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_42]) ).
tff(c_380,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_127,c_8]) ).
tff(c_392,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_32,c_380]) ).
tff(c_104,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_34]) ).
tff(c_1761,plain,
! [B_205,B_206,C_207] :
( subset(B_205,intersection(B_206,C_207))
| ~ member('#skF_1'(B_205,intersection(B_206,C_207)),C_207)
| ~ member('#skF_1'(B_205,intersection(B_206,C_207)),B_206) ),
inference(resolution,[status(thm)],[c_104,c_10]) ).
tff(c_2309,plain,
! [B_223,B_224] :
( ~ member('#skF_1'(B_223,intersection(B_224,'#skF_5')),B_224)
| ~ subset(B_223,'#skF_4')
| subset(B_223,intersection(B_224,'#skF_5')) ),
inference(resolution,[status(thm)],[c_392,c_1761]) ).
tff(c_2605,plain,
! [B_234,C_235] :
( ~ subset(B_234,'#skF_4')
| ~ subset(B_234,C_235)
| subset(B_234,intersection(C_235,'#skF_5')) ),
inference(resolution,[status(thm)],[c_103,c_2309]) ).
tff(c_30,plain,
~ subset(intersection('#skF_4','#skF_6'),intersection('#skF_5','#skF_6')),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_33,plain,
~ subset(intersection('#skF_4','#skF_6'),intersection('#skF_6','#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_30]) ).
tff(c_2640,plain,
( ~ subset(intersection('#skF_4','#skF_6'),'#skF_4')
| ~ subset(intersection('#skF_4','#skF_6'),'#skF_6') ),
inference(resolution,[status(thm)],[c_2605,c_33]) ).
tff(c_2669,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_239,c_235,c_2640]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SET586+3 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.15 % 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
% 0.15/0.37 % Computer : n007.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Tue Apr 8 21:16:24 EDT 2025
% 0.15/0.37 % CPUTime :
% 6.78/2.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.78/2.87
% 6.78/2.87 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------