%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : FLD019-1 : TPTP v9.0.0. Bugfixed v2.1.0.
% 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 : n012.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 06:10:40 PM UTC 2025
% Result : Unsatisfiable 76.66s 62.40s
% Output : CNFRefutation 76.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 50 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 111 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 124 ( 63 ~; 61 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 67 ( 67 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ less_or_equal > equalish > defined > multiply > add > #nlpp > multiplicative_inverse > additive_inverse > multiplicative_identity > additive_identity > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(less_or_equal,type,
less_or_equal: ( $i * $i ) > $o ).
tff(a,type,
a: $i ).
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(a,additive_identity),
file(unknown,unknown) ).
tff(f_236,axiom,
defined(a),
file(unknown,unknown) ).
tff(f_131,axiom,
! [X] :
( defined(additive_inverse(X))
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_173,axiom,
! [X,Y] :
( less_or_equal(X,Y)
| less_or_equal(Y,X)
| ~ defined(X)
| ~ defined(Y) ),
file(unknown,unknown) ).
tff(f_237,axiom,
equalish(additive_inverse(a),additive_identity),
file(unknown,unknown) ).
tff(f_231,axiom,
! [Y,Z,X] :
( less_or_equal(Y,Z)
| ~ less_or_equal(X,Z)
| ~ equalish(X,Y) ),
file(unknown,unknown) ).
tff(f_199,axiom,
! [X,Y] :
( equalish(X,Y)
| ~ equalish(Y,X) ),
file(unknown,unknown) ).
tff(f_207,axiom,
! [X,Z,Y] :
( equalish(X,Z)
| ~ equalish(X,Y)
| ~ equalish(Y,Z) ),
file(unknown,unknown) ).
tff(f_62,axiom,
! [X] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_215,axiom,
! [X,Z,Y] :
( equalish(add(X,Z),add(Y,Z))
| ~ defined(Z)
| ~ equalish(X,Y) ),
file(unknown,unknown) ).
tff(f_75,axiom,
! [X,Y] :
( equalish(add(X,Y),add(Y,X))
| ~ defined(X)
| ~ defined(Y) ),
file(unknown,unknown) ).
tff(f_67,axiom,
! [X] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(c_60,plain,
~ equalish(a,additive_identity),
inference(cnfTransformation,[status(thm)],[f_239]) ).
tff(c_56,plain,
defined(a),
inference(cnfTransformation,[status(thm)],[f_236]) ).
tff(c_24,plain,
! [X_20] :
( ~ defined(X_20)
| defined(additive_inverse(X_20)) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_36,plain,
! [Y_30,X_29] :
( ~ defined(Y_30)
| ~ defined(X_29)
| less_or_equal(Y_30,X_29)
| less_or_equal(X_29,Y_30) ),
inference(cnfTransformation,[status(thm)],[f_173]) ).
tff(c_270,plain,
! [Y_84] :
( ~ defined(Y_84)
| less_or_equal(Y_84,Y_84) ),
inference(factorization,[status(thm),theory(equality)],[c_36]) ).
tff(c_58,plain,
equalish(additive_inverse(a),additive_identity),
inference(cnfTransformation,[status(thm)],[f_237]) ).
tff(c_183,plain,
! [X_74,Y_75,Z_76] :
( ~ equalish(X_74,Y_75)
| ~ less_or_equal(X_74,Z_76)
| less_or_equal(Y_75,Z_76) ),
inference(cnfTransformation,[status(thm)],[f_231]) ).
tff(c_219,plain,
! [Z_76] :
( ~ less_or_equal(additive_inverse(a),Z_76)
| less_or_equal(additive_identity,Z_76) ),
inference(resolution,[status(thm)],[c_58,c_183]) ).
tff(c_280,plain,
( less_or_equal(additive_identity,additive_inverse(a))
| ~ defined(additive_inverse(a)) ),
inference(resolution,[status(thm)],[c_270,c_219]) ).
tff(c_282,plain,
~ defined(additive_inverse(a)),
inference(splitLeft,[status(thm)],[c_280]) ).
tff(c_285,plain,
~ defined(a),
inference(resolution,[status(thm)],[c_24,c_282]) ).
tff(c_289,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_56,c_285]) ).
tff(c_291,plain,
defined(additive_inverse(a)),
inference(splitRight,[status(thm)],[c_280]) ).
tff(c_63,plain,
! [Y_53,X_54] :
( ~ equalish(Y_53,X_54)
| equalish(X_54,Y_53) ),
inference(cnfTransformation,[status(thm)],[f_199]) ).
tff(c_69,plain,
equalish(additive_identity,additive_inverse(a)),
inference(resolution,[status(thm)],[c_58,c_63]) ).
tff(c_101,plain,
! [Y_66,Z_67,X_68] :
( ~ equalish(Y_66,Z_67)
| ~ equalish(X_68,Y_66)
| equalish(X_68,Z_67) ),
inference(cnfTransformation,[status(thm)],[f_207]) ).
tff(c_129,plain,
! [X_69] :
( ~ equalish(X_69,additive_inverse(a))
| equalish(X_69,additive_identity) ),
inference(resolution,[status(thm)],[c_58,c_101]) ).
tff(c_146,plain,
equalish(additive_identity,additive_identity),
inference(resolution,[status(thm)],[c_69,c_129]) ).
tff(c_70,plain,
! [X_55] :
( ~ defined(X_55)
| equalish(add(additive_identity,X_55),X_55) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_44,plain,
! [Y_38,X_37] :
( ~ equalish(Y_38,X_37)
| equalish(X_37,Y_38) ),
inference(cnfTransformation,[status(thm)],[f_199]) ).
tff(c_73,plain,
! [X_55] :
( equalish(X_55,add(additive_identity,X_55))
| ~ defined(X_55) ),
inference(resolution,[status(thm)],[c_70,c_44]) ).
tff(c_789,plain,
! [X_113,Y_114,Z_115] :
( ~ equalish(X_113,Y_114)
| ~ defined(Z_115)
| equalish(add(X_113,Z_115),add(Y_114,Z_115)) ),
inference(cnfTransformation,[status(thm)],[f_215]) ).
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_207]) ).
tff(c_9087,plain,
! [X_289,X_290,Z_291,Y_292] :
( ~ equalish(X_289,add(X_290,Z_291))
| equalish(X_289,add(Y_292,Z_291))
| ~ equalish(X_290,Y_292)
| ~ defined(Z_291) ),
inference(resolution,[status(thm)],[c_789,c_46]) ).
tff(c_17461,plain,
! [X_421,Y_422] :
( equalish(X_421,add(Y_422,X_421))
| ~ equalish(additive_identity,Y_422)
| ~ defined(X_421) ),
inference(resolution,[status(thm)],[c_73,c_9087]) ).
tff(c_804,plain,
! [X_39,X_113,Z_115,Y_114] :
( ~ equalish(X_39,add(X_113,Z_115))
| equalish(X_39,add(Y_114,Z_115))
| ~ equalish(X_113,Y_114)
| ~ defined(Z_115) ),
inference(resolution,[status(thm)],[c_789,c_46]) ).
tff(c_180592,plain,
! [X_1261,Y_1262,Y_1263] :
( equalish(X_1261,add(Y_1262,X_1261))
| ~ equalish(Y_1263,Y_1262)
| ~ equalish(additive_identity,Y_1263)
| ~ defined(X_1261) ),
inference(resolution,[status(thm)],[c_17461,c_804]) ).
tff(c_181780,plain,
! [X_1261] :
( equalish(X_1261,add(additive_inverse(a),X_1261))
| ~ equalish(additive_identity,additive_identity)
| ~ defined(X_1261) ),
inference(resolution,[status(thm)],[c_69,c_180592]) ).
tff(c_183114,plain,
! [X_1264] :
( equalish(X_1264,add(additive_inverse(a),X_1264))
| ~ defined(X_1264) ),
inference(demodulation,[status(thm),theory(equality)],[c_146,c_181780]) ).
tff(c_333,plain,
! [Y_87,X_88] :
( ~ defined(Y_87)
| ~ defined(X_88)
| equalish(add(X_88,Y_87),add(Y_87,X_88)) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_341,plain,
! [X_39,X_88,Y_87] :
( ~ equalish(X_39,add(X_88,Y_87))
| equalish(X_39,add(Y_87,X_88))
| ~ defined(Y_87)
| ~ defined(X_88) ),
inference(resolution,[status(thm)],[c_333,c_46]) ).
tff(c_183292,plain,
! [X_1264] :
( equalish(X_1264,add(X_1264,additive_inverse(a)))
| ~ defined(additive_inverse(a))
| ~ defined(X_1264) ),
inference(resolution,[status(thm)],[c_183114,c_341]) ).
tff(c_192700,plain,
! [X_1285] :
( equalish(X_1285,add(X_1285,additive_inverse(a)))
| ~ defined(X_1285) ),
inference(demodulation,[status(thm),theory(equality)],[c_291,c_183292]) ).
tff(c_6,plain,
! [X_5] :
( ~ defined(X_5)
| equalish(add(X_5,additive_inverse(X_5)),additive_identity) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_121,plain,
! [X_68,X_5] :
( ~ equalish(X_68,add(X_5,additive_inverse(X_5)))
| equalish(X_68,additive_identity)
| ~ defined(X_5) ),
inference(resolution,[status(thm)],[c_6,c_101]) ).
tff(c_192871,plain,
( equalish(a,additive_identity)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_192700,c_121]) ).
tff(c_193007,plain,
equalish(a,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_56,c_192871]) ).
tff(c_193009,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_60,c_193007]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : FLD019-1 : TPTP v9.0.0. Bugfixed v2.1.0.
% 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
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % 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 : Mon Apr 7 18:42:00 EDT 2025
% 0.12/0.34 % CPUTime :
% 76.66/62.40 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 76.66/62.41
% 76.66/62.41 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------