%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET366+4 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n008.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 08:38:28 PM UTC 2025
% Result : Theorem 3.16s 1.74s
% Output : CNFRefutation 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 11 ( 6 ~; 2 |; 0 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 2 con; 0-2 aty)
% Number of variables : 13 ( 13 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > equal_set > unordered_pair > union > intersection > difference > #nlpp > sum > singleton > product > power_set > empty_set > #skF_3 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(equal_set,type,
equal_set: ( $i * $i ) > $o ).
tff(power_set,type,
power_set: $i > $i ).
tff(product,type,
product: $i > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(sum,type,
sum: $i > $i ).
tff(intersection,type,
intersection: ( $i * $i ) > $i ).
tff(union,type,
union: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(difference,type,
difference: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_56,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
tff(f_81,axiom,
! [X] : ~ member(X,empty_set),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',empty_set) ).
tff(f_66,axiom,
! [X,A] :
( member(X,power_set(A))
<=> subset(X,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',power_set) ).
tff(f_117,negated_conjecture,
~ ! [A] : member(empty_set,power_set(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI47) ).
tff(c_111,plain,
! [A_65,B_66] :
( member('#skF_1'(A_65,B_66),A_65)
| subset(A_65,B_66) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_30,plain,
! [X_16] : ~ member(X_16,empty_set),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_141,plain,
! [B_66] : subset(empty_set,B_66),
inference(resolution,[status(thm)],[c_111,c_30]) ).
tff(c_74,plain,
! [X_49,A_50] :
( member(X_49,power_set(A_50))
| ~ subset(X_49,A_50) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_60,plain,
~ member(empty_set,power_set('#skF_4')),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_82,plain,
~ subset(empty_set,'#skF_4'),
inference(resolution,[status(thm)],[c_74,c_60]) ).
tff(c_151,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_141,c_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET366+4 : TPTP v9.0.0. Released v2.2.0.
% 0.13/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 8 20:44:18 EDT 2025
% 0.13/0.35 % CPUTime :
% 3.16/1.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.16/1.74
% 3.16/1.74 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------