%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET766+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 : n027.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 08:39:12 PM UTC 2025
% Result : Theorem 7.09s 2.75s
% Output : CNFRefutation 7.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 33 ( 11 ~; 6 |; 8 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 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 : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 33 ( 33 usr; 4 con; 0-3 aty)
% Number of variables : 23 ( 23 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ apply > subset > pre_order > partition > member > equivalence > equal_set > disjoint > equivalence_class > unordered_pair > union > intersection > difference > #nlpp > sum > singleton > product > power_set > empty_set > #skF_11 > #skF_6 > #skF_17 > #skF_20 > #skF_3 > #skF_13 > #skF_14 > #skF_12 > #skF_18 > #skF_19 > #skF_8 > #skF_21 > #skF_22 > #skF_2 > #skF_23 > #skF_7 > #skF_1 > #skF_16 > #skF_9 > #skF_5 > #skF_15 > #skF_4 > #skF_10
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_11',type,
'#skF_11': ( $i * $i ) > $i ).
tff(equal_set,type,
equal_set: ( $i * $i ) > $o ).
tff(power_set,type,
power_set: $i > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i ) > $i ).
tff(product,type,
product: $i > $i ).
tff(apply,type,
apply: ( $i * $i * $i ) > $o ).
tff(singleton,type,
singleton: $i > $i ).
tff(partition,type,
partition: ( $i * $i ) > $o ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_17',type,
'#skF_17': ( $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': ( $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('#skF_13',type,
'#skF_13': ( $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i ) > $i ).
tff('#skF_18',type,
'#skF_18': ( $i * $i ) > $i ).
tff('#skF_19',type,
'#skF_19': ( $i * $i ) > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff(equivalence,type,
equivalence: ( $i * $i ) > $o ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff(disjoint,type,
disjoint: ( $i * $i ) > $o ).
tff('#skF_21',type,
'#skF_21': $i ).
tff(empty_set,type,
empty_set: $i ).
tff(pre_order,type,
pre_order: ( $i * $i ) > $o ).
tff('#skF_22',type,
'#skF_22': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(difference,type,
difference: ( $i * $i ) > $i ).
tff('#skF_23',type,
'#skF_23': $i ).
tff(equivalence_class,type,
equivalence_class: ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i ) > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i * $i ) > $i ).
tff(f_237,negated_conjecture,
~ ! [E,R,A] :
( ( equivalence(R,E)
& member(A,E) )
=> member(A,equivalence_class(A,E,R)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIII02) ).
tff(f_202,axiom,
! [A,R] :
( equivalence(R,A)
<=> ( ! [X] :
( member(X,A)
=> apply(R,X,X) )
& ! [X,Y] :
( ( member(X,A)
& member(Y,A) )
=> ( apply(R,X,Y)
=> apply(R,Y,X) ) )
& ! [X,Y,Z] :
( ( member(X,A)
& member(Y,A)
& member(Z,A) )
=> ( ( apply(R,X,Y)
& apply(R,Y,Z) )
=> apply(R,X,Z) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+2.ax',equivalence) ).
tff(f_208,axiom,
! [R,E,A,X] :
( member(X,equivalence_class(A,E,R))
<=> ( member(X,E)
& apply(R,A,X) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+2.ax',equivalence_class) ).
tff(c_254,plain,
equivalence('#skF_22','#skF_21'),
inference(cnfTransformation,[status(thm)],[f_237]) ).
tff(c_252,plain,
member('#skF_23','#skF_21'),
inference(cnfTransformation,[status(thm)],[f_237]) ).
tff(c_1536,plain,
! [R_289,X_290,A_291] :
( apply(R_289,X_290,X_290)
| ~ member(X_290,A_291)
| ~ equivalence(R_289,A_291) ),
inference(cnfTransformation,[status(thm)],[f_202]) ).
tff(c_1587,plain,
! [R_289] :
( apply(R_289,'#skF_23','#skF_23')
| ~ equivalence(R_289,'#skF_21') ),
inference(resolution,[status(thm)],[c_252,c_1536]) ).
tff(c_3553,plain,
! [X_393,A_394,E_395,R_396] :
( member(X_393,equivalence_class(A_394,E_395,R_396))
| ~ apply(R_396,A_394,X_393)
| ~ member(X_393,E_395) ),
inference(cnfTransformation,[status(thm)],[f_208]) ).
tff(c_250,plain,
~ member('#skF_23',equivalence_class('#skF_23','#skF_21','#skF_22')),
inference(cnfTransformation,[status(thm)],[f_237]) ).
tff(c_3595,plain,
( ~ apply('#skF_22','#skF_23','#skF_23')
| ~ member('#skF_23','#skF_21') ),
inference(resolution,[status(thm)],[c_3553,c_250]) ).
tff(c_3613,plain,
~ apply('#skF_22','#skF_23','#skF_23'),
inference(demodulation,[status(thm),theory(equality)],[c_252,c_3595]) ).
tff(c_3619,plain,
~ equivalence('#skF_22','#skF_21'),
inference(resolution,[status(thm)],[c_1587,c_3613]) ).
tff(c_3624,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_254,c_3619]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET766+4 : TPTP v9.0.0. Released v2.2.0.
% 0.03/0.13 % 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 : n027.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 21:35:35 EDT 2025
% 0.13/0.34 % CPUTime :
% 7.09/2.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.09/2.75
% 7.09/2.75 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------