%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : FLD069-1 : 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 : 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 06:10:54 PM UTC 2025
% Result : Unsatisfiable 10.75s 3.87s
% Output : CNFRefutation 11.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 17
% Syntax : Number of formulae : 88 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 169 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 169 ( 88 ~; 81 |; 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 79 ( 79 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ less_or_equal > equalish > defined > multiply > add > #nlpp > multiplicative_inverse > additive_inverse > multiplicative_identity > b > 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(b,type,
b: $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_241,axiom,
~ equalish(b,additive_identity),
file(unknown,unknown) ).
tff(f_239,axiom,
less_or_equal(additive_identity,b),
file(unknown,unknown) ).
tff(f_155,axiom,
! [X,Y] :
( equalish(X,Y)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,X) ),
file(unknown,unknown) ).
tff(f_238,axiom,
less_or_equal(additive_identity,a),
file(unknown,unknown) ).
tff(f_237,axiom,
defined(b),
file(unknown,unknown) ).
tff(f_181,axiom,
! [X,Z,Y] :
( less_or_equal(add(X,Z),add(Y,Z))
| ~ defined(Z)
| ~ less_or_equal(X,Y) ),
file(unknown,unknown) ).
tff(f_126,axiom,
defined(additive_identity),
file(unknown,unknown) ).
tff(f_131,axiom,
! [X] :
( defined(additive_inverse(X))
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_67,axiom,
! [X] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_199,axiom,
! [X,Y] :
( equalish(X,Y)
| ~ equalish(Y,X) ),
file(unknown,unknown) ).
tff(f_62,axiom,
! [X] :
( equalish(add(additive_identity,X),X)
| ~ defined(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_173,axiom,
! [X,Y] :
( less_or_equal(X,Y)
| less_or_equal(Y,X)
| ~ defined(X)
| ~ defined(Y) ),
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_242,axiom,
equalish(add(a,b),additive_identity),
file(unknown,unknown) ).
tff(f_163,axiom,
! [X,Z,Y] :
( less_or_equal(X,Z)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z) ),
file(unknown,unknown) ).
tff(f_75,axiom,
! [X,Y] :
( equalish(add(X,Y),add(Y,X))
| ~ defined(X)
| ~ defined(Y) ),
file(unknown,unknown) ).
tff(c_64,plain,
~ equalish(b,additive_identity),
inference(cnfTransformation,[status(thm)],[f_241]) ).
tff(c_62,plain,
less_or_equal(additive_identity,b),
inference(cnfTransformation,[status(thm)],[f_239]) ).
tff(c_387,plain,
! [Y_88,X_89] :
( ~ less_or_equal(Y_88,X_89)
| ~ less_or_equal(X_89,Y_88)
| equalish(X_89,Y_88) ),
inference(cnfTransformation,[status(thm)],[f_155]) ).
tff(c_397,plain,
( ~ less_or_equal(b,additive_identity)
| equalish(b,additive_identity) ),
inference(resolution,[status(thm)],[c_62,c_387]) ).
tff(c_408,plain,
~ less_or_equal(b,additive_identity),
inference(negUnitSimplification,[status(thm)],[c_64,c_397]) ).
tff(c_60,plain,
less_or_equal(additive_identity,a),
inference(cnfTransformation,[status(thm)],[f_238]) ).
tff(c_58,plain,
defined(b),
inference(cnfTransformation,[status(thm)],[f_237]) ).
tff(c_38,plain,
! [X_31,Y_33,Z_32] :
( ~ less_or_equal(X_31,Y_33)
| ~ defined(Z_32)
| less_or_equal(add(X_31,Z_32),add(Y_33,Z_32)) ),
inference(cnfTransformation,[status(thm)],[f_181]) ).
tff(c_22,plain,
defined(additive_identity),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_24,plain,
! [X_20] :
( ~ defined(X_20)
| defined(additive_inverse(X_20)) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_99,plain,
! [X_64] :
( ~ defined(X_64)
| equalish(add(X_64,additive_inverse(X_64)),additive_identity) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
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_102,plain,
! [X_64] :
( equalish(additive_identity,add(X_64,additive_inverse(X_64)))
| ~ defined(X_64) ),
inference(resolution,[status(thm)],[c_99,c_44]) ).
tff(c_4,plain,
! [X_4] :
( ~ defined(X_4)
| equalish(add(additive_identity,X_4),X_4) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_107,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_1507,plain,
! [X_153,X_154] :
( ~ equalish(X_153,add(additive_identity,X_154))
| equalish(X_153,X_154)
| ~ defined(X_154) ),
inference(resolution,[status(thm)],[c_4,c_107]) ).
tff(c_1539,plain,
( equalish(additive_identity,additive_inverse(additive_identity))
| ~ defined(additive_inverse(additive_identity))
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_102,c_1507]) ).
tff(c_1570,plain,
( equalish(additive_identity,additive_inverse(additive_identity))
| ~ defined(additive_inverse(additive_identity)) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_1539]) ).
tff(c_1634,plain,
~ defined(additive_inverse(additive_identity)),
inference(splitLeft,[status(thm)],[c_1570]) ).
tff(c_1637,plain,
~ defined(additive_identity),
inference(resolution,[status(thm)],[c_24,c_1634]) ).
tff(c_1641,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_22,c_1637]) ).
tff(c_1643,plain,
defined(additive_inverse(additive_identity)),
inference(splitRight,[status(thm)],[c_1570]) ).
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_422,plain,
! [Y_30] :
( ~ defined(Y_30)
| less_or_equal(Y_30,Y_30) ),
inference(factorization,[status(thm),theory(equality)],[c_36]) ).
tff(c_1642,plain,
equalish(additive_identity,additive_inverse(additive_identity)),
inference(splitRight,[status(thm)],[c_1570]) ).
tff(c_1669,plain,
equalish(additive_inverse(additive_identity),additive_identity),
inference(resolution,[status(thm)],[c_1642,c_44]) ).
tff(c_52,plain,
! [X_50,Y_48,Z_49] :
( ~ equalish(X_50,Y_48)
| ~ less_or_equal(X_50,Z_49)
| less_or_equal(Y_48,Z_49) ),
inference(cnfTransformation,[status(thm)],[f_231]) ).
tff(c_1766,plain,
! [Z_162] :
( ~ less_or_equal(additive_inverse(additive_identity),Z_162)
| less_or_equal(additive_identity,Z_162) ),
inference(resolution,[status(thm)],[c_1669,c_52]) ).
tff(c_1788,plain,
( less_or_equal(additive_identity,additive_inverse(additive_identity))
| ~ defined(additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[c_422,c_1766]) ).
tff(c_1813,plain,
less_or_equal(additive_identity,additive_inverse(additive_identity)),
inference(demodulation,[status(thm),theory(equality)],[c_1643,c_1788]) ).
tff(c_66,plain,
equalish(add(a,b),additive_identity),
inference(cnfTransformation,[status(thm)],[f_242]) ).
tff(c_69,plain,
! [Y_53,X_54] :
( ~ equalish(Y_53,X_54)
| equalish(X_54,Y_53) ),
inference(cnfTransformation,[status(thm)],[f_199]) ).
tff(c_74,plain,
equalish(additive_identity,add(a,b)),
inference(resolution,[status(thm)],[c_66,c_69]) ).
tff(c_163,plain,
! [X_70,Y_71,Z_72] :
( ~ equalish(X_70,Y_71)
| ~ less_or_equal(X_70,Z_72)
| less_or_equal(Y_71,Z_72) ),
inference(cnfTransformation,[status(thm)],[f_231]) ).
tff(c_191,plain,
! [Z_72] :
( ~ less_or_equal(additive_identity,Z_72)
| less_or_equal(add(a,b),Z_72) ),
inference(resolution,[status(thm)],[c_74,c_163]) ).
tff(c_341,plain,
! [Y_86] :
( ~ defined(Y_86)
| less_or_equal(Y_86,Y_86) ),
inference(factorization,[status(thm),theory(equality)],[c_36]) ).
tff(c_214,plain,
! [Y_76,Z_77,X_78] :
( ~ less_or_equal(Y_76,Z_77)
| ~ less_or_equal(X_78,Y_76)
| less_or_equal(X_78,Z_77) ),
inference(cnfTransformation,[status(thm)],[f_163]) ).
tff(c_234,plain,
! [X_80] :
( ~ less_or_equal(X_80,additive_identity)
| less_or_equal(X_80,a) ),
inference(resolution,[status(thm)],[c_60,c_214]) ).
tff(c_239,plain,
( less_or_equal(add(a,b),a)
| ~ less_or_equal(additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[c_191,c_234]) ).
tff(c_257,plain,
~ less_or_equal(additive_identity,additive_identity),
inference(splitLeft,[status(thm)],[c_239]) ).
tff(c_346,plain,
~ defined(additive_identity),
inference(resolution,[status(thm)],[c_341,c_257]) ).
tff(c_361,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_22,c_346]) ).
tff(c_363,plain,
less_or_equal(additive_identity,additive_identity),
inference(splitRight,[status(thm)],[c_239]) ).
tff(c_1667,plain,
! [Z_49] :
( ~ less_or_equal(additive_identity,Z_49)
| less_or_equal(additive_inverse(additive_identity),Z_49) ),
inference(resolution,[status(thm)],[c_1642,c_52]) ).
tff(c_222,plain,
! [X_78] :
( ~ less_or_equal(X_78,additive_identity)
| less_or_equal(X_78,b) ),
inference(resolution,[status(thm)],[c_62,c_214]) ).
tff(c_8,plain,
! [Y_7,X_6] :
( ~ defined(Y_7)
| ~ defined(X_6)
| equalish(add(X_6,Y_7),add(Y_7,X_6)) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_1531,plain,
! [X_6] :
( equalish(add(X_6,additive_identity),X_6)
| ~ defined(additive_identity)
| ~ defined(X_6) ),
inference(resolution,[status(thm)],[c_8,c_1507]) ).
tff(c_1566,plain,
! [X_6] :
( equalish(add(X_6,additive_identity),X_6)
| ~ defined(X_6) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_1531]) ).
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_1833,plain,
! [X_163] :
( ~ equalish(X_163,additive_inverse(additive_identity))
| equalish(X_163,additive_identity) ),
inference(resolution,[status(thm)],[c_1669,c_46]) ).
tff(c_1843,plain,
( equalish(add(additive_inverse(additive_identity),additive_identity),additive_identity)
| ~ defined(additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[c_1566,c_1833]) ).
tff(c_1873,plain,
equalish(add(additive_inverse(additive_identity),additive_identity),additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_1643,c_1843]) ).
tff(c_2510,plain,
! [Z_176] :
( ~ less_or_equal(add(additive_inverse(additive_identity),additive_identity),Z_176)
| less_or_equal(additive_identity,Z_176) ),
inference(resolution,[status(thm)],[c_1873,c_52]) ).
tff(c_2526,plain,
! [Y_33] :
( less_or_equal(additive_identity,add(Y_33,additive_identity))
| ~ less_or_equal(additive_inverse(additive_identity),Y_33)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_38,c_2510]) ).
tff(c_3196,plain,
! [Y_193] :
( less_or_equal(additive_identity,add(Y_193,additive_identity))
| ~ less_or_equal(additive_inverse(additive_identity),Y_193) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_2526]) ).
tff(c_3270,plain,
( less_or_equal(additive_identity,add(b,additive_identity))
| ~ less_or_equal(additive_inverse(additive_identity),additive_identity) ),
inference(resolution,[status(thm)],[c_222,c_3196]) ).
tff(c_9351,plain,
~ less_or_equal(additive_inverse(additive_identity),additive_identity),
inference(splitLeft,[status(thm)],[c_3270]) ).
tff(c_9360,plain,
~ less_or_equal(additive_identity,additive_identity),
inference(resolution,[status(thm)],[c_1667,c_9351]) ).
tff(c_9376,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_363,c_9360]) ).
tff(c_9378,plain,
less_or_equal(additive_inverse(additive_identity),additive_identity),
inference(splitRight,[status(thm)],[c_3270]) ).
tff(c_34,plain,
! [Y_28,Z_27,X_26] :
( ~ less_or_equal(Y_28,Z_27)
| ~ less_or_equal(X_26,Y_28)
| less_or_equal(X_26,Z_27) ),
inference(cnfTransformation,[status(thm)],[f_163]) ).
tff(c_9506,plain,
! [X_314] :
( ~ less_or_equal(X_314,additive_inverse(additive_identity))
| less_or_equal(X_314,additive_identity) ),
inference(resolution,[status(thm)],[c_9378,c_34]) ).
tff(c_9581,plain,
( less_or_equal(add(a,b),additive_identity)
| ~ less_or_equal(additive_identity,additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[c_191,c_9506]) ).
tff(c_9627,plain,
less_or_equal(add(a,b),additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_1813,c_9581]) ).
tff(c_11339,plain,
! [X_339] :
( ~ less_or_equal(X_339,add(a,b))
| less_or_equal(X_339,additive_identity) ),
inference(resolution,[status(thm)],[c_9627,c_34]) ).
tff(c_11399,plain,
! [X_31] :
( less_or_equal(add(X_31,b),additive_identity)
| ~ less_or_equal(X_31,a)
| ~ defined(b) ),
inference(resolution,[status(thm)],[c_38,c_11339]) ).
tff(c_11718,plain,
! [X_343] :
( less_or_equal(add(X_343,b),additive_identity)
| ~ less_or_equal(X_343,a) ),
inference(demodulation,[status(thm),theory(equality)],[c_58,c_11399]) ).
tff(c_190,plain,
! [X_4,Z_72] :
( ~ less_or_equal(add(additive_identity,X_4),Z_72)
| less_or_equal(X_4,Z_72)
| ~ defined(X_4) ),
inference(resolution,[status(thm)],[c_4,c_163]) ).
tff(c_11728,plain,
( less_or_equal(b,additive_identity)
| ~ defined(b)
| ~ less_or_equal(additive_identity,a) ),
inference(resolution,[status(thm)],[c_11718,c_190]) ).
tff(c_11753,plain,
less_or_equal(b,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_58,c_11728]) ).
tff(c_11755,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_408,c_11753]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : FLD069-1 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.08/0.13 % 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
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 7 18:57:17 EDT 2025
% 0.13/0.35 % CPUTime :
% 10.75/3.87 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.02/3.89
% 11.02/3.89 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------