%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET581+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 : n022.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 08:38:46 PM UTC 2025
% Result : Theorem 3.58s 2.49s
% Output : CNFRefutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 13 ~; 6 |; 2 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 21 ( 21 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ not_equal > member > empty > intersection > #nlpp > empty_set > #skF_5 > #skF_6 > #skF_4 > #skF_3 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(intersection,type,
intersection: ( $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(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(not_equal,type,
not_equal: ( $i * $i ) > $o ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_69,negated_conjecture,
~ ! [B,C,D] :
( ( member(B,C)
& member(B,D) )
=> not_equal(intersection(C,D),empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th24) ).
tff(f_37,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
tff(f_51,axiom,
! [B,C] :
( not_equal(B,C)
<=> ( B != C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_equal_defn) ).
tff(f_54,axiom,
! [B,C] : ( intersection(B,C) = intersection(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
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_34,plain,
member('#skF_4','#skF_6'),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_36,plain,
member('#skF_4','#skF_5'),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_8,plain,
! [B_4] : ~ member(B_4,empty_set),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_24,plain,
! [B_10,C_11] :
( not_equal(B_10,C_11)
| ( C_11 = B_10 ) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_26,plain,
! [C_13,B_12] : ( intersection(C_13,B_12) = intersection(B_12,C_13) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_32,plain,
~ not_equal(intersection('#skF_5','#skF_6'),empty_set),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_37,plain,
~ not_equal(intersection('#skF_6','#skF_5'),empty_set),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_32]) ).
tff(c_59,plain,
intersection('#skF_6','#skF_5') = empty_set,
inference(resolution,[status(thm)],[c_24,c_37]) ).
tff(c_138,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_33]) ).
tff(c_156,plain,
! [D_33] :
( member(D_33,empty_set)
| ~ member(D_33,'#skF_5')
| ~ member(D_33,'#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_59,c_138]) ).
tff(c_161,plain,
! [D_36] :
( ~ member(D_36,'#skF_5')
| ~ member(D_36,'#skF_6') ),
inference(negUnitSimplification,[status(thm)],[c_8,c_156]) ).
tff(c_168,plain,
~ member('#skF_4','#skF_6'),
inference(resolution,[status(thm)],[c_36,c_161]) ).
tff(c_175,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_34,c_168]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET581+3 : TPTP v9.0.0. Released v2.2.0.
% 0.06/0.13 % 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 : n022.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Apr 8 21:15:51 EDT 2025
% 0.12/0.34 % CPUTime :
% 3.58/2.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.58/2.50
% 3.58/2.50 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------