%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET626+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 : n028.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 08:38:55 PM UTC 2025
% Result : Theorem 3.16s 1.81s
% Output : CNFRefutation 3.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 39 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 13 ~; 11 |; 2 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 38 ( 37 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ member > intersect > intersection > #nlpp > #skF_3 > #skF_5 > #skF_6 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(intersect,type,
intersect: ( $i * $i ) > $o ).
tff(intersection,type,
intersection: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': $i ).
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_63,negated_conjecture,
~ ! [B,C,D] :
( intersect(B,intersection(C,D))
=> intersect(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th102) ).
tff(f_44,axiom,
! [B,C] : ( intersection(B,C) = intersection(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
tff(f_49,axiom,
! [B,C] :
( intersect(B,C)
=> intersect(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_intersect) ).
tff(f_41,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,B)
& member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
tff(f_33,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(c_30,plain,
~ intersect('#skF_4','#skF_5'),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_14,plain,
! [C_10,B_9] : ( intersection(C_10,B_9) = intersection(B_9,C_10) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_32,plain,
intersect('#skF_4',intersection('#skF_5','#skF_6')),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_33,plain,
intersect('#skF_4',intersection('#skF_6','#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_32]) ).
tff(c_34,plain,
! [C_18,B_19] :
( intersect(C_18,B_19)
| ~ intersect(B_19,C_18) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_37,plain,
intersect(intersection('#skF_6','#skF_5'),'#skF_4'),
inference(resolution,[status(thm)],[c_33,c_34]) ).
tff(c_88,plain,
! [B_27,C_28] :
( member('#skF_1'(B_27,C_28),B_27)
| ~ intersect(B_27,C_28) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_4,plain,
! [D_3,C_2,B_1] :
( member(D_3,C_2)
| ~ member(D_3,intersection(B_1,C_2)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_312,plain,
! [B_62,C_63,C_64] :
( member('#skF_1'(intersection(B_62,C_63),C_64),C_63)
| ~ intersect(intersection(B_62,C_63),C_64) ),
inference(resolution,[status(thm)],[c_88,c_4]) ).
tff(c_10,plain,
! [B_4,C_5] :
( member('#skF_1'(B_4,C_5),C_5)
| ~ intersect(B_4,C_5) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_111,plain,
! [B_32,C_33,D_34] :
( intersect(B_32,C_33)
| ~ member(D_34,C_33)
| ~ member(D_34,B_32) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_117,plain,
! [B_32,C_5,B_4] :
( intersect(B_32,C_5)
| ~ member('#skF_1'(B_4,C_5),B_32)
| ~ intersect(B_4,C_5) ),
inference(resolution,[status(thm)],[c_10,c_111]) ).
tff(c_402,plain,
! [C_65,C_66,B_67] :
( intersect(C_65,C_66)
| ~ intersect(intersection(B_67,C_65),C_66) ),
inference(resolution,[status(thm)],[c_312,c_117]) ).
tff(c_420,plain,
intersect('#skF_5','#skF_4'),
inference(resolution,[status(thm)],[c_37,c_402]) ).
tff(c_16,plain,
! [C_12,B_11] :
( intersect(C_12,B_11)
| ~ intersect(B_11,C_12) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_426,plain,
intersect('#skF_4','#skF_5'),
inference(resolution,[status(thm)],[c_420,c_16]) ).
tff(c_433,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_30,c_426]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET626+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
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Apr 8 21:20:19 EDT 2025
% 0.12/0.34 % CPUTime :
% 3.16/1.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.16/1.81
% 3.16/1.81 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------