%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : FLD010-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% 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 : n031.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 06:10:37 PM UTC 2025
% Result : Unsatisfiable 7.80s 2.81s
% Output : CNFRefutation 7.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 14
% Syntax : Number of formulae : 65 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 129 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 129 ( 65 ~; 64 |; 0 &)
% ( 0 <=>; 0 =>; 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 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 50 ( 50 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ less_or_equal > equalish > defined > multiply > add > #nlpp > multiplicative_inverse > additive_inverse > multiplicative_identity > additive_identity
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(less_or_equal,type,
less_or_equal: ( $i * $i ) > $o ).
tff(additive_identity,type,
additive_identity: $i ).
tff(multiplicative_identity,type,
multiplicative_identity: $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(additive_inverse,type,
additive_inverse: $i > $i ).
tff(defined,type,
defined: $i > $o ).
tff(multiplicative_inverse,type,
multiplicative_inverse: $i > $i ).
tff(add,type,
add: ( $i * $i ) > $i ).
tff(equalish,type,
equalish: ( $i * $i ) > $o ).
tff(f_239,axiom,
~ equalish(multiplicative_inverse(multiplicative_identity),multiplicative_identity),
file(unknown,unknown) ).
tff(f_235,axiom,
~ equalish(additive_identity,multiplicative_identity),
file(unknown,unknown) ).
tff(f_142,axiom,
defined(multiplicative_identity),
file(unknown,unknown) ).
tff(f_128,axiom,
defined(additive_identity),
file(unknown,unknown) ).
tff(f_133,axiom,
! [X] :
( defined(additive_inverse(X))
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_69,axiom,
! [X] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_201,axiom,
! [X,Y] :
( equalish(X,Y)
| ~ equalish(Y,X) ),
file(unknown,unknown) ).
tff(f_64,axiom,
! [X] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_209,axiom,
! [X,Z,Y] :
( equalish(X,Z)
| ~ equalish(X,Y)
| ~ equalish(Y,Z) ),
file(unknown,unknown) ).
tff(f_225,axiom,
! [X,Z,Y] :
( equalish(multiply(X,Z),multiply(Y,Z))
| ~ defined(Z)
| ~ equalish(X,Y) ),
file(unknown,unknown) ).
tff(f_108,axiom,
! [X,Y] :
( equalish(multiply(X,Y),multiply(Y,X))
| ~ defined(X)
| ~ defined(Y) ),
file(unknown,unknown) ).
tff(f_93,axiom,
! [X] :
( equalish(multiply(multiplicative_identity,X),X)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_149,axiom,
! [X] :
( defined(multiplicative_inverse(X))
| ~ defined(X)
| equalish(X,additive_identity) ),
file(unknown,unknown) ).
tff(f_100,axiom,
! [X] :
( equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity)
| ~ defined(X)
| equalish(X,additive_identity) ),
file(unknown,unknown) ).
tff(c_56,plain,
~ equalish(multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(cnfTransformation,[status(thm)],[f_239]) ).
tff(c_54,plain,
~ equalish(additive_identity,multiplicative_identity),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_28,plain,
defined(multiplicative_identity),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_22,plain,
defined(additive_identity),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_24,plain,
! [X_20] :
( ~ defined(X_20)
| defined(additive_inverse(X_20)) ),
inference(cnfTransformation,[status(thm)],[f_133]) ).
tff(c_81,plain,
! [X_62] :
( ~ defined(X_62)
| equalish(add(X_62,additive_inverse(X_62)),additive_identity) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_44,plain,
! [Y_38,X_37] :
( ~ equalish(Y_38,X_37)
| equalish(X_37,Y_38) ),
inference(cnfTransformation,[status(thm)],[f_201]) ).
tff(c_84,plain,
! [X_62] :
( equalish(additive_identity,add(X_62,additive_inverse(X_62)))
| ~ defined(X_62) ),
inference(resolution,[status(thm)],[c_81,c_44]) ).
tff(c_4,plain,
! [X_4] :
( ~ defined(X_4)
| equalish(add(additive_identity,X_4),X_4) ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_86,plain,
! [Y_65,Z_66,X_67] :
( ~ equalish(Y_65,Z_66)
| ~ equalish(X_67,Y_65)
| equalish(X_67,Z_66) ),
inference(cnfTransformation,[status(thm)],[f_209]) ).
tff(c_272,plain,
! [X_90,X_91] :
( ~ equalish(X_90,add(additive_identity,X_91))
| equalish(X_90,X_91)
| ~ defined(X_91) ),
inference(resolution,[status(thm)],[c_4,c_86]) ).
tff(c_280,plain,
( equalish(additive_identity,additive_inverse(additive_identity))
| ~ defined(additive_inverse(additive_identity))
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_84,c_272]) ).
tff(c_299,plain,
( equalish(additive_identity,additive_inverse(additive_identity))
| ~ defined(additive_inverse(additive_identity)) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_280]) ).
tff(c_304,plain,
~ defined(additive_inverse(additive_identity)),
inference(splitLeft,[status(thm)],[c_299]) ).
tff(c_307,plain,
~ defined(additive_identity),
inference(resolution,[status(thm)],[c_24,c_304]) ).
tff(c_311,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_22,c_307]) ).
tff(c_312,plain,
equalish(additive_identity,additive_inverse(additive_identity)),
inference(splitRight,[status(thm)],[c_299]) ).
tff(c_46,plain,
! [Y_41,Z_40,X_39] :
( ~ equalish(Y_41,Z_40)
| ~ equalish(X_39,Y_41)
| equalish(X_39,Z_40) ),
inference(cnfTransformation,[status(thm)],[f_209]) ).
tff(c_321,plain,
! [X_39] :
( ~ equalish(X_39,additive_identity)
| equalish(X_39,additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[c_312,c_46]) ).
tff(c_50,plain,
! [X_45,Y_47,Z_46] :
( ~ equalish(X_45,Y_47)
| ~ defined(Z_46)
| equalish(multiply(X_45,Z_46),multiply(Y_47,Z_46)) ),
inference(cnfTransformation,[status(thm)],[f_225]) ).
tff(c_313,plain,
defined(additive_inverse(additive_identity)),
inference(splitRight,[status(thm)],[c_299]) ).
tff(c_206,plain,
! [Y_84,X_85] :
( ~ defined(Y_84)
| ~ defined(X_85)
| equalish(multiply(X_85,Y_84),multiply(Y_84,X_85)) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_12,plain,
! [X_11] :
( ~ defined(X_11)
| equalish(multiply(multiplicative_identity,X_11),X_11) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_102,plain,
! [X_67,X_11] :
( ~ equalish(X_67,multiply(multiplicative_identity,X_11))
| equalish(X_67,X_11)
| ~ defined(X_11) ),
inference(resolution,[status(thm)],[c_12,c_86]) ).
tff(c_210,plain,
! [X_85] :
( equalish(multiply(X_85,multiplicative_identity),X_85)
| ~ defined(multiplicative_identity)
| ~ defined(X_85) ),
inference(resolution,[status(thm)],[c_206,c_102]) ).
tff(c_219,plain,
! [X_85] :
( equalish(multiply(X_85,multiplicative_identity),X_85)
| ~ defined(X_85) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_210]) ).
tff(c_322,plain,
equalish(additive_inverse(additive_identity),additive_identity),
inference(resolution,[status(thm)],[c_312,c_44]) ).
tff(c_424,plain,
! [X_99] :
( ~ equalish(X_99,additive_inverse(additive_identity))
| equalish(X_99,additive_identity) ),
inference(resolution,[status(thm)],[c_322,c_46]) ).
tff(c_438,plain,
( equalish(multiply(additive_inverse(additive_identity),multiplicative_identity),additive_identity)
| ~ defined(additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[c_219,c_424]) ).
tff(c_459,plain,
equalish(multiply(additive_inverse(additive_identity),multiplicative_identity),additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_313,c_438]) ).
tff(c_802,plain,
! [X_122] :
( ~ equalish(X_122,multiply(additive_inverse(additive_identity),multiplicative_identity))
| equalish(X_122,additive_identity) ),
inference(resolution,[status(thm)],[c_459,c_46]) ).
tff(c_813,plain,
! [X_45] :
( equalish(multiply(X_45,multiplicative_identity),additive_identity)
| ~ equalish(X_45,additive_inverse(additive_identity))
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[c_50,c_802]) ).
tff(c_1177,plain,
! [X_134] :
( equalish(multiply(X_134,multiplicative_identity),additive_identity)
| ~ equalish(X_134,additive_inverse(additive_identity)) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_813]) ).
tff(c_2289,plain,
! [X_169] :
( equalish(additive_identity,multiply(X_169,multiplicative_identity))
| ~ equalish(X_169,additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[c_1177,c_44]) ).
tff(c_2457,plain,
! [X_172] :
( equalish(additive_identity,multiply(X_172,multiplicative_identity))
| ~ equalish(X_172,additive_identity) ),
inference(resolution,[status(thm)],[c_321,c_2289]) ).
tff(c_2465,plain,
( equalish(additive_identity,multiplicative_identity)
| ~ defined(multiplicative_identity)
| ~ equalish(multiplicative_identity,additive_identity) ),
inference(resolution,[status(thm)],[c_2457,c_102]) ).
tff(c_2477,plain,
( equalish(additive_identity,multiplicative_identity)
| ~ equalish(multiplicative_identity,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_2465]) ).
tff(c_2478,plain,
~ equalish(multiplicative_identity,additive_identity),
inference(negUnitSimplification,[status(thm)],[c_54,c_2477]) ).
tff(c_30,plain,
! [X_23] :
( equalish(X_23,additive_identity)
| ~ defined(X_23)
| defined(multiplicative_inverse(X_23)) ),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_323,plain,
! [X_92] :
( equalish(X_92,additive_identity)
| ~ defined(X_92)
| equalish(multiply(X_92,multiplicative_inverse(X_92)),multiplicative_identity) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_2400,plain,
! [X_170] :
( equalish(multiplicative_identity,multiply(X_170,multiplicative_inverse(X_170)))
| equalish(X_170,additive_identity)
| ~ defined(X_170) ),
inference(resolution,[status(thm)],[c_323,c_44]) ).
tff(c_2404,plain,
( equalish(multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| ~ defined(multiplicative_inverse(multiplicative_identity))
| equalish(multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[c_2400,c_102]) ).
tff(c_2413,plain,
( equalish(multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| ~ defined(multiplicative_inverse(multiplicative_identity))
| equalish(multiplicative_identity,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_2404]) ).
tff(c_4944,plain,
( equalish(multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| ~ defined(multiplicative_inverse(multiplicative_identity)) ),
inference(negUnitSimplification,[status(thm)],[c_2478,c_2413]) ).
tff(c_4945,plain,
~ defined(multiplicative_inverse(multiplicative_identity)),
inference(splitLeft,[status(thm)],[c_4944]) ).
tff(c_4948,plain,
( equalish(multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[c_30,c_4945]) ).
tff(c_4951,plain,
equalish(multiplicative_identity,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_4948]) ).
tff(c_4953,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2478,c_4951]) ).
tff(c_4954,plain,
equalish(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),
inference(splitRight,[status(thm)],[c_4944]) ).
tff(c_5029,plain,
equalish(multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(resolution,[status(thm)],[c_4954,c_44]) ).
tff(c_5035,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_56,c_5029]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : FLD010-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% 0.12/0.13 % 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 : n031.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 : Mon Apr 7 18:39:07 EDT 2025
% 0.13/0.34 % CPUTime :
% 7.80/2.81 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.80/2.82
% 7.80/2.82 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------