%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET018-1 : TPTP v9.0.0. Released v1.0.0.
% 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 : n023.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 08:37:31 PM UTC 2025
% Result : Unsatisfiable 3.56s 1.97s
% Output : CNFRefutation 3.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 57 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 75 ( 47 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 13 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 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 : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 38 ( 38 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ member > unordered_pair > ordered_pair > #nlpp > singleton_set > r2 > r1 > m2 > m1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(m2,type,
m2: $i ).
tff(r1,type,
r1: $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff(r2,type,
r2: $i ).
tff(singleton_set,type,
singleton_set: $i > $i ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff(m1,type,
m1: $i ).
tff(f_45,axiom,
r1 != r2,
file(unknown,unknown) ).
tff(f_43,axiom,
ordered_pair(m1,r1) = ordered_pair(m2,r2),
file(unknown,unknown) ).
tff(f_42,axiom,
! [X,Y] : ( ordered_pair(X,Y) = unordered_pair(singleton_set(X),unordered_pair(X,Y)) ),
file(unknown,unknown) ).
tff(f_31,axiom,
! [X,Y] : member(X,unordered_pair(X,Y)),
file(unknown,unknown) ).
tff(f_40,axiom,
! [X,Y,Z] :
( ~ member(X,unordered_pair(Y,Z))
| ( X = Y )
| ( X = Z ) ),
file(unknown,unknown) ).
tff(f_24,axiom,
! [X] : member(X,singleton_set(X)),
file(unknown,unknown) ).
tff(f_29,axiom,
! [X,Y] :
( ~ member(X,singleton_set(Y))
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_33,axiom,
! [Y,X] : member(Y,unordered_pair(X,Y)),
file(unknown,unknown) ).
tff(c_16,plain,
r2 != r1,
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_14,plain,
ordered_pair(m2,r2) = ordered_pair(m1,r1),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_41,plain,
! [X_23,Y_24] : ( unordered_pair(singleton_set(X_23),unordered_pair(X_23,Y_24)) = ordered_pair(X_23,Y_24) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_6,plain,
! [X_4,Y_5] : member(X_4,unordered_pair(X_4,Y_5)),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_65,plain,
! [X_25,Y_26] : member(singleton_set(X_25),ordered_pair(X_25,Y_26)),
inference(superposition,[status(thm),theory(equality)],[c_41,c_6]) ).
tff(c_68,plain,
member(singleton_set(m2),ordered_pair(m1,r1)),
inference(superposition,[status(thm),theory(equality)],[c_14,c_65]) ).
tff(c_10,plain,
! [Z_10,X_8,Y_9] :
( ( Z_10 = X_8 )
| ( Y_9 = X_8 )
| ~ member(X_8,unordered_pair(Y_9,Z_10)) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_83,plain,
! [X_31,Y_32,X_33] :
( ( unordered_pair(X_31,Y_32) = X_33 )
| ( singleton_set(X_31) = X_33 )
| ~ member(X_33,ordered_pair(X_31,Y_32)) ),
inference(superposition,[status(thm),theory(equality)],[c_41,c_10]) ).
tff(c_112,plain,
( ( unordered_pair(m1,r1) = singleton_set(m2) )
| ( singleton_set(m2) = singleton_set(m1) ) ),
inference(resolution,[status(thm)],[c_68,c_83]) ).
tff(c_147,plain,
singleton_set(m2) = singleton_set(m1),
inference(splitLeft,[status(thm)],[c_112]) ).
tff(c_2,plain,
! [X_1] : member(X_1,singleton_set(X_1)),
inference(cnfTransformation,[status(thm)],[f_24]) ).
tff(c_169,plain,
member(m2,singleton_set(m1)),
inference(superposition,[status(thm),theory(equality)],[c_147,c_2]) ).
tff(c_4,plain,
! [Y_3,X_2] :
( ( Y_3 = X_2 )
| ~ member(X_2,singleton_set(Y_3)) ),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_177,plain,
m2 = m1,
inference(resolution,[status(thm)],[c_169,c_4]) ).
tff(c_8,plain,
! [Y_6,X_7] : member(Y_6,unordered_pair(X_7,Y_6)),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_69,plain,
! [X_27,Y_28] : member(unordered_pair(X_27,Y_28),ordered_pair(X_27,Y_28)),
inference(superposition,[status(thm),theory(equality)],[c_41,c_8]) ).
tff(c_75,plain,
member(unordered_pair(m2,r2),ordered_pair(m1,r1)),
inference(superposition,[status(thm),theory(equality)],[c_14,c_69]) ).
tff(c_109,plain,
( ( unordered_pair(m2,r2) = unordered_pair(m1,r1) )
| ( unordered_pair(m2,r2) = singleton_set(m1) ) ),
inference(resolution,[status(thm)],[c_75,c_83]) ).
tff(c_243,plain,
( ( unordered_pair(m1,r2) = unordered_pair(m1,r1) )
| ( unordered_pair(m1,r2) = singleton_set(m1) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_177,c_177,c_109]) ).
tff(c_244,plain,
unordered_pair(m1,r2) = singleton_set(m1),
inference(splitLeft,[status(thm)],[c_243]) ).
tff(c_267,plain,
member(r2,singleton_set(m1)),
inference(superposition,[status(thm),theory(equality)],[c_244,c_8]) ).
tff(c_278,plain,
r2 = m1,
inference(resolution,[status(thm)],[c_267,c_4]) ).
tff(c_282,plain,
r1 != m1,
inference(demodulation,[status(thm),theory(equality)],[c_278,c_16]) ).
tff(c_181,plain,
ordered_pair(m1,r2) = ordered_pair(m1,r1),
inference(demodulation,[status(thm),theory(equality)],[c_177,c_14]) ).
tff(c_281,plain,
ordered_pair(m1,r1) = ordered_pair(m1,m1),
inference(demodulation,[status(thm),theory(equality)],[c_278,c_181]) ).
tff(c_56,plain,
! [X_23,Y_24] : member(unordered_pair(X_23,Y_24),ordered_pair(X_23,Y_24)),
inference(superposition,[status(thm),theory(equality)],[c_41,c_8]) ).
tff(c_354,plain,
member(unordered_pair(m1,r1),ordered_pair(m1,m1)),
inference(superposition,[status(thm),theory(equality)],[c_281,c_56]) ).
tff(c_280,plain,
unordered_pair(m1,m1) = singleton_set(m1),
inference(demodulation,[status(thm),theory(equality)],[c_278,c_244]) ).
tff(c_12,plain,
! [X_11,Y_12] : ( unordered_pair(singleton_set(X_11),unordered_pair(X_11,Y_12)) = ordered_pair(X_11,Y_12) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_326,plain,
unordered_pair(singleton_set(m1),singleton_set(m1)) = ordered_pair(m1,m1),
inference(superposition,[status(thm),theory(equality)],[c_280,c_12]) ).
tff(c_425,plain,
! [X_39] :
( ( singleton_set(m1) = X_39 )
| ( singleton_set(m1) = X_39 )
| ~ member(X_39,ordered_pair(m1,m1)) ),
inference(superposition,[status(thm),theory(equality)],[c_326,c_10]) ).
tff(c_437,plain,
unordered_pair(m1,r1) = singleton_set(m1),
inference(resolution,[status(thm)],[c_354,c_425]) ).
tff(c_465,plain,
member(r1,singleton_set(m1)),
inference(superposition,[status(thm),theory(equality)],[c_437,c_8]) ).
tff(c_476,plain,
r1 = m1,
inference(resolution,[status(thm)],[c_465,c_4]) ).
tff(c_480,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_282,c_476]) ).
tff(c_481,plain,
unordered_pair(m1,r2) = unordered_pair(m1,r1),
inference(splitRight,[status(thm)],[c_243]) ).
tff(c_507,plain,
member(r2,unordered_pair(m1,r1)),
inference(superposition,[status(thm),theory(equality)],[c_481,c_8]) ).
tff(c_518,plain,
( ( r2 = r1 )
| ( r2 = m1 ) ),
inference(resolution,[status(thm)],[c_507,c_10]) ).
tff(c_521,plain,
r2 = m1,
inference(negUnitSimplification,[status(thm)],[c_16,c_518]) ).
tff(c_525,plain,
r1 != m1,
inference(demodulation,[status(thm),theory(equality)],[c_521,c_16]) ).
tff(c_501,plain,
! [X_8] :
( ( r2 = X_8 )
| ( m1 = X_8 )
| ~ member(X_8,unordered_pair(m1,r1)) ),
inference(superposition,[status(thm),theory(equality)],[c_481,c_10]) ).
tff(c_532,plain,
! [X_40] :
( ( m1 = X_40 )
| ( m1 = X_40 )
| ~ member(X_40,unordered_pair(m1,r1)) ),
inference(demodulation,[status(thm),theory(equality)],[c_521,c_501]) ).
tff(c_540,plain,
r1 = m1,
inference(resolution,[status(thm)],[c_8,c_532]) ).
tff(c_546,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_525,c_525,c_540]) ).
tff(c_547,plain,
unordered_pair(m1,r1) = singleton_set(m2),
inference(splitRight,[status(thm)],[c_112]) ).
tff(c_564,plain,
member(m1,singleton_set(m2)),
inference(superposition,[status(thm),theory(equality)],[c_547,c_6]) ).
tff(c_575,plain,
m2 = m1,
inference(resolution,[status(thm)],[c_564,c_4]) ).
tff(c_548,plain,
singleton_set(m2) != singleton_set(m1),
inference(splitRight,[status(thm)],[c_112]) ).
tff(c_585,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_575,c_548]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : SET018-1 : TPTP v9.0.0. Released v1.0.0.
% 0.05/0.13 % 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
% 0.13/0.34 % Computer : n023.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 19:42:24 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.56/1.97 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.56/1.98
% 3.56/1.98 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------