%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET199+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 : n029.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 08:38:14 PM UTC 2025
% Result : Theorem 5.93s 2.56s
% Output : CNFRefutation 6.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 53 ( 2 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 49 ( 21 ~; 22 |; 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 45 !; 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_48,axiom,
! [B] : subset(B,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
tff(f_64,negated_conjecture,
~ ! [B,C,D] :
( ( subset(B,C)
& subset(B,D) )
=> subset(B,intersection(C,D)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersection_of_subsets) ).
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_45,axiom,
! [B,C] : ( intersection(B,C) = intersection(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
tff(c_16,plain,
! [B_11] : subset(B_11,B_11),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_32,plain,
subset('#skF_4','#skF_6'),
inference(cnfTransformation,[status(thm)],[f_64]) ).
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_102,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_129,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_102]) ).
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_382,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_129,c_8]) ).
tff(c_396,plain,
! [B_75,C_76] :
( member('#skF_1'(B_75,C_76),'#skF_6')
| ~ subset(B_75,'#skF_4')
| subset(B_75,C_76) ),
inference(resolution,[status(thm)],[c_32,c_382]) ).
tff(c_34,plain,
subset('#skF_4','#skF_5'),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_397,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_382]) ).
tff(c_106,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_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_1864,plain,
! [B_211,B_212,C_213] :
( subset(B_211,intersection(B_212,C_213))
| ~ member('#skF_1'(B_211,intersection(B_212,C_213)),C_213)
| ~ member('#skF_1'(B_211,intersection(B_212,C_213)),B_212) ),
inference(resolution,[status(thm)],[c_106,c_10]) ).
tff(c_2540,plain,
! [B_229,B_230] :
( ~ member('#skF_1'(B_229,intersection(B_230,'#skF_5')),B_230)
| ~ subset(B_229,'#skF_4')
| subset(B_229,intersection(B_230,'#skF_5')) ),
inference(resolution,[status(thm)],[c_397,c_1864]) ).
tff(c_2630,plain,
! [B_231] :
( ~ subset(B_231,'#skF_4')
| subset(B_231,intersection('#skF_6','#skF_5')) ),
inference(resolution,[status(thm)],[c_396,c_2540]) ).
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_30,plain,
~ subset('#skF_4',intersection('#skF_5','#skF_6')),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_35,plain,
~ subset('#skF_4',intersection('#skF_6','#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_30]) ).
tff(c_2668,plain,
~ subset('#skF_4','#skF_4'),
inference(resolution,[status(thm)],[c_2630,c_35]) ).
tff(c_2686,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_2668]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET199+3 : TPTP v9.0.0. Released v2.2.0.
% 0.11/0.13 % 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 : n029.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 20:19:04 EDT 2025
% 0.12/0.34 % CPUTime :
% 5.93/2.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.93/2.57
% 5.93/2.57 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------