TSTP Solution File: FLD064-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : FLD064-1 : TPTP v8.1.2. 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 : n011.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 : Tue Aug 22 10:37:40 EDT 2023
% Result : Unsatisfiable 141.95s 127.14s
% Output : CNFRefutation 142.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 31
% Syntax : Number of formulae : 166 ( 48 unt; 10 typ; 0 def)
% Number of atoms : 332 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 354 ( 178 ~; 176 |; 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 : 11 ( 7 >; 4 *; 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 : 147 (; 147 !; 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,
~ less_or_equal(additive_inverse(a),additive_identity),
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_237,axiom,
less_or_equal(additive_identity,a),
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_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_236,axiom,
defined(a),
file(unknown,unknown) ).
tff(f_140,axiom,
defined(multiplicative_identity),
file(unknown,unknown) ).
tff(f_233,axiom,
~ equalish(additive_identity,multiplicative_identity),
file(unknown,unknown) ).
tff(f_223,axiom,
! [X,Z,Y] :
( equalish(multiply(X,Z),multiply(Y,Z))
| ~ defined(Z)
| ~ equalish(X,Y) ),
file(unknown,unknown) ).
tff(f_106,axiom,
! [X,Y] :
( equalish(multiply(X,Y),multiply(Y,X))
| ~ defined(X)
| ~ defined(Y) ),
file(unknown,unknown) ).
tff(f_91,axiom,
! [X] :
( equalish(multiply(multiplicative_identity,X),X)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_147,axiom,
! [X] :
( defined(multiplicative_inverse(X))
| ~ defined(X)
| equalish(X,additive_identity) ),
file(unknown,unknown) ).
tff(f_98,axiom,
! [X] :
( equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity)
| ~ defined(X)
| equalish(X,additive_identity) ),
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_60,plain,
~ less_or_equal(additive_inverse(a),additive_identity),
inference(cnfTransformation,[status(thm)],[f_239]) ).
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_84,plain,
! [X_61] :
( ~ defined(X_61)
| equalish(add(X_61,additive_inverse(X_61)),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_87,plain,
! [X_61] :
( equalish(additive_identity,add(X_61,additive_inverse(X_61)))
| ~ defined(X_61) ),
inference(resolution,[status(thm)],[c_84,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_94,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_282,plain,
! [X_85,X_86] :
( ~ equalish(X_85,add(additive_identity,X_86))
| equalish(X_85,X_86)
| ~ defined(X_86) ),
inference(resolution,[status(thm)],[c_4,c_94]) ).
tff(c_286,plain,
( equalish(additive_identity,additive_inverse(additive_identity))
| ~ defined(additive_inverse(additive_identity))
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_87,c_282]) ).
tff(c_304,plain,
( equalish(additive_identity,additive_inverse(additive_identity))
| ~ defined(additive_inverse(additive_identity)) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_286]) ).
tff(c_319,plain,
~ defined(additive_inverse(additive_identity)),
inference(splitLeft,[status(thm)],[c_304]) ).
tff(c_322,plain,
~ defined(additive_identity),
inference(resolution,[status(thm)],[c_24,c_319]) ).
tff(c_326,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_22,c_322]) ).
tff(c_328,plain,
defined(additive_inverse(additive_identity)),
inference(splitRight,[status(thm)],[c_304]) ).
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_160,plain,
! [Y_30] :
( ~ defined(Y_30)
| less_or_equal(Y_30,Y_30) ),
inference(factorization,[status(thm),theory(equality)],[c_36]) ).
tff(c_327,plain,
equalish(additive_identity,additive_inverse(additive_identity)),
inference(splitRight,[status(thm)],[c_304]) ).
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_355,plain,
! [Z_91] :
( ~ less_or_equal(additive_identity,Z_91)
| less_or_equal(additive_inverse(additive_identity),Z_91) ),
inference(resolution,[status(thm)],[c_327,c_52]) ).
tff(c_58,plain,
less_or_equal(additive_identity,a),
inference(cnfTransformation,[status(thm)],[f_237]) ).
tff(c_116,plain,
! [Y_69,Z_70,X_71] :
( ~ less_or_equal(Y_69,Z_70)
| ~ less_or_equal(X_71,Y_69)
| less_or_equal(X_71,Z_70) ),
inference(cnfTransformation,[status(thm)],[f_163]) ).
tff(c_119,plain,
! [X_71] :
( ~ less_or_equal(X_71,additive_identity)
| less_or_equal(X_71,a) ),
inference(resolution,[status(thm)],[c_58,c_116]) ).
tff(c_365,plain,
( less_or_equal(additive_inverse(additive_identity),a)
| ~ less_or_equal(additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[c_355,c_119]) ).
tff(c_626,plain,
~ less_or_equal(additive_identity,additive_identity),
inference(splitLeft,[status(thm)],[c_365]) ).
tff(c_642,plain,
~ defined(additive_identity),
inference(resolution,[status(thm)],[c_160,c_626]) ).
tff(c_651,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_22,c_642]) ).
tff(c_653,plain,
less_or_equal(additive_identity,additive_identity),
inference(splitRight,[status(thm)],[c_365]) ).
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_126,plain,
! [X_75,Y_76,Z_77] :
( ~ equalish(X_75,Y_76)
| ~ less_or_equal(X_75,Z_77)
| less_or_equal(Y_76,Z_77) ),
inference(cnfTransformation,[status(thm)],[f_231]) ).
tff(c_1245,plain,
! [X_134,Z_135] :
( ~ less_or_equal(add(additive_identity,X_134),Z_135)
| less_or_equal(X_134,Z_135)
| ~ defined(X_134) ),
inference(resolution,[status(thm)],[c_4,c_126]) ).
tff(c_16722,plain,
! [Z_405,Y_406] :
( less_or_equal(Z_405,add(Y_406,Z_405))
| ~ less_or_equal(additive_identity,Y_406)
| ~ defined(Z_405) ),
inference(resolution,[status(thm)],[c_38,c_1245]) ).
tff(c_534,plain,
! [X_100,Y_101,Z_102] :
( ~ less_or_equal(X_100,Y_101)
| ~ defined(Z_102)
| less_or_equal(add(X_100,Z_102),add(Y_101,Z_102)) ),
inference(cnfTransformation,[status(thm)],[f_181]) ).
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_540,plain,
! [X_26,X_100,Z_102,Y_101] :
( ~ less_or_equal(X_26,add(X_100,Z_102))
| less_or_equal(X_26,add(Y_101,Z_102))
| ~ less_or_equal(X_100,Y_101)
| ~ defined(Z_102) ),
inference(resolution,[status(thm)],[c_534,c_34]) ).
tff(c_208910,plain,
! [Z_1351,Y_1352,Y_1353] :
( less_or_equal(Z_1351,add(Y_1352,Z_1351))
| ~ less_or_equal(Y_1353,Y_1352)
| ~ less_or_equal(additive_identity,Y_1353)
| ~ defined(Z_1351) ),
inference(resolution,[status(thm)],[c_16722,c_540]) ).
tff(c_209690,plain,
! [Z_1351] :
( less_or_equal(Z_1351,add(additive_identity,Z_1351))
| ~ less_or_equal(additive_identity,additive_identity)
| ~ defined(Z_1351) ),
inference(resolution,[status(thm)],[c_653,c_208910]) ).
tff(c_210489,plain,
! [Z_1354] :
( less_or_equal(Z_1354,add(additive_identity,Z_1354))
| ~ defined(Z_1354) ),
inference(demodulation,[status(thm),theory(equality)],[c_653,c_209690]) ).
tff(c_337,plain,
equalish(additive_inverse(additive_identity),additive_identity),
inference(resolution,[status(thm)],[c_327,c_44]) ).
tff(c_344,plain,
! [Z_49] :
( ~ less_or_equal(additive_inverse(additive_identity),Z_49)
| less_or_equal(additive_identity,Z_49) ),
inference(resolution,[status(thm)],[c_337,c_52]) ).
tff(c_210830,plain,
( less_or_equal(additive_identity,add(additive_identity,additive_inverse(additive_identity)))
| ~ defined(additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[c_210489,c_344]) ).
tff(c_211020,plain,
less_or_equal(additive_identity,add(additive_identity,additive_inverse(additive_identity))),
inference(demodulation,[status(thm),theory(equality)],[c_328,c_210830]) ).
tff(c_56,plain,
defined(a),
inference(cnfTransformation,[status(thm)],[f_236]) ).
tff(c_162,plain,
! [Y_78,X_79] :
( ~ defined(Y_78)
| ~ defined(X_79)
| less_or_equal(Y_78,X_79)
| less_or_equal(X_79,Y_78) ),
inference(cnfTransformation,[status(thm)],[f_173]) ).
tff(c_174,plain,
( ~ defined(additive_inverse(a))
| ~ defined(additive_identity)
| less_or_equal(additive_identity,additive_inverse(a)) ),
inference(resolution,[status(thm)],[c_162,c_60]) ).
tff(c_194,plain,
( ~ defined(additive_inverse(a))
| less_or_equal(additive_identity,additive_inverse(a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_174]) ).
tff(c_217,plain,
~ defined(additive_inverse(a)),
inference(splitLeft,[status(thm)],[c_194]) ).
tff(c_230,plain,
~ defined(a),
inference(resolution,[status(thm)],[c_24,c_217]) ).
tff(c_234,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_56,c_230]) ).
tff(c_236,plain,
defined(additive_inverse(a)),
inference(splitRight,[status(thm)],[c_194]) ).
tff(c_7234,plain,
! [X_252,X_253,Z_254,Y_255] :
( ~ less_or_equal(X_252,add(X_253,Z_254))
| less_or_equal(X_252,add(Y_255,Z_254))
| ~ less_or_equal(X_253,Y_255)
| ~ defined(Z_254) ),
inference(resolution,[status(thm)],[c_534,c_34]) ).
tff(c_55264,plain,
! [X_676,Z_677,Y_678,Y_679] :
( less_or_equal(add(X_676,Z_677),add(Y_678,Z_677))
| ~ less_or_equal(Y_679,Y_678)
| ~ less_or_equal(X_676,Y_679)
| ~ defined(Z_677) ),
inference(resolution,[status(thm)],[c_38,c_7234]) ).
tff(c_183663,plain,
! [X_1298,Z_1299] :
( less_or_equal(add(X_1298,Z_1299),add(a,Z_1299))
| ~ less_or_equal(X_1298,additive_identity)
| ~ defined(Z_1299) ),
inference(resolution,[status(thm)],[c_58,c_55264]) ).
tff(c_146,plain,
! [X_4,Z_77] :
( ~ less_or_equal(add(additive_identity,X_4),Z_77)
| less_or_equal(X_4,Z_77)
| ~ defined(X_4) ),
inference(resolution,[status(thm)],[c_4,c_126]) ).
tff(c_183780,plain,
! [Z_1299] :
( less_or_equal(Z_1299,add(a,Z_1299))
| ~ less_or_equal(additive_identity,additive_identity)
| ~ defined(Z_1299) ),
inference(resolution,[status(thm)],[c_183663,c_146]) ).
tff(c_183856,plain,
! [Z_1299] :
( less_or_equal(Z_1299,add(a,Z_1299))
| ~ defined(Z_1299) ),
inference(demodulation,[status(thm),theory(equality)],[c_653,c_183780]) ).
tff(c_22180,plain,
! [Z_458,X_459] :
( ~ less_or_equal(additive_identity,Z_458)
| less_or_equal(add(X_459,additive_inverse(X_459)),Z_458)
| ~ defined(X_459) ),
inference(resolution,[status(thm)],[c_87,c_126]) ).
tff(c_318878,plain,
! [X_1577,X_1578,Z_1579] :
( ~ less_or_equal(X_1577,add(X_1578,additive_inverse(X_1578)))
| less_or_equal(X_1577,Z_1579)
| ~ less_or_equal(additive_identity,Z_1579)
| ~ defined(X_1578) ),
inference(resolution,[status(thm)],[c_22180,c_34]) ).
tff(c_318969,plain,
! [Z_1579] :
( less_or_equal(additive_inverse(a),Z_1579)
| ~ less_or_equal(additive_identity,Z_1579)
| ~ defined(a)
| ~ defined(additive_inverse(a)) ),
inference(resolution,[status(thm)],[c_183856,c_318878]) ).
tff(c_319315,plain,
! [Z_1580] :
( less_or_equal(additive_inverse(a),Z_1580)
| ~ less_or_equal(additive_identity,Z_1580) ),
inference(demodulation,[status(thm),theory(equality)],[c_236,c_56,c_318969]) ).
tff(c_558,plain,
! [Z_104] :
( ~ less_or_equal(additive_inverse(additive_identity),Z_104)
| less_or_equal(additive_identity,Z_104) ),
inference(resolution,[status(thm)],[c_337,c_52]) ).
tff(c_573,plain,
( less_or_equal(additive_identity,additive_inverse(additive_identity))
| ~ defined(additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[c_160,c_558]) ).
tff(c_590,plain,
less_or_equal(additive_identity,additive_inverse(additive_identity)),
inference(demodulation,[status(thm),theory(equality)],[c_328,c_573]) ).
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_377,plain,
! [X_93] :
( ~ equalish(X_93,additive_inverse(additive_identity))
| equalish(X_93,additive_identity) ),
inference(resolution,[status(thm)],[c_337,c_46]) ).
tff(c_391,plain,
( equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity)
| ~ defined(additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[c_4,c_377]) ).
tff(c_403,plain,
equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_328,c_391]) ).
tff(c_442,plain,
equalish(additive_identity,add(additive_identity,additive_inverse(additive_identity))),
inference(resolution,[status(thm)],[c_403,c_44]) ).
tff(c_464,plain,
! [Z_49] :
( ~ less_or_equal(additive_identity,Z_49)
| less_or_equal(add(additive_identity,additive_inverse(additive_identity)),Z_49) ),
inference(resolution,[status(thm)],[c_442,c_52]) ).
tff(c_335,plain,
! [Z_49] :
( ~ less_or_equal(additive_identity,Z_49)
| less_or_equal(additive_inverse(additive_identity),Z_49) ),
inference(resolution,[status(thm)],[c_327,c_52]) ).
tff(c_28,plain,
defined(multiplicative_identity),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_3815,plain,
! [X_199,Y_200,X_201] :
( ~ less_or_equal(X_199,Y_200)
| less_or_equal(X_199,X_201)
| ~ defined(Y_200)
| ~ defined(X_201)
| less_or_equal(X_201,Y_200) ),
inference(resolution,[status(thm)],[c_162,c_34]) ).
tff(c_3863,plain,
! [X_201] :
( less_or_equal(additive_identity,X_201)
| ~ defined(additive_identity)
| ~ defined(X_201)
| less_or_equal(X_201,additive_identity) ),
inference(resolution,[status(thm)],[c_653,c_3815]) ).
tff(c_3933,plain,
! [X_201] :
( less_or_equal(additive_identity,X_201)
| ~ defined(X_201)
| less_or_equal(X_201,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_3863]) ).
tff(c_54,plain,
~ equalish(additive_identity,multiplicative_identity),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_336,plain,
! [X_39] :
( ~ equalish(X_39,additive_identity)
| equalish(X_39,additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[c_327,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_223]) ).
tff(c_16,plain,
! [Y_14,X_13] :
( ~ defined(Y_14)
| ~ defined(X_13)
| equalish(multiply(X_13,Y_14),multiply(Y_14,X_13)) ),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_12,plain,
! [X_11] :
( ~ defined(X_11)
| equalish(multiply(multiplicative_identity,X_11),X_11) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_387,plain,
( equalish(multiply(multiplicative_identity,additive_inverse(additive_identity)),additive_identity)
| ~ defined(additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[c_12,c_377]) ).
tff(c_400,plain,
equalish(multiply(multiplicative_identity,additive_inverse(additive_identity)),additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_328,c_387]) ).
tff(c_829,plain,
! [X_119] :
( ~ equalish(X_119,multiply(multiplicative_identity,additive_inverse(additive_identity)))
| equalish(X_119,additive_identity) ),
inference(resolution,[status(thm)],[c_400,c_46]) ).
tff(c_848,plain,
( equalish(multiply(additive_inverse(additive_identity),multiplicative_identity),additive_identity)
| ~ defined(multiplicative_identity)
| ~ defined(additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[c_16,c_829]) ).
tff(c_876,plain,
equalish(multiply(additive_inverse(additive_identity),multiplicative_identity),additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_328,c_28,c_848]) ).
tff(c_1814,plain,
! [X_155] :
( ~ equalish(X_155,multiply(additive_inverse(additive_identity),multiplicative_identity))
| equalish(X_155,additive_identity) ),
inference(resolution,[status(thm)],[c_876,c_46]) ).
tff(c_1833,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_1814]) ).
tff(c_2959,plain,
! [X_179] :
( equalish(multiply(X_179,multiplicative_identity),additive_identity)
| ~ equalish(X_179,additive_inverse(additive_identity)) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_1833]) ).
tff(c_3126,plain,
! [X_183] :
( equalish(additive_identity,multiply(X_183,multiplicative_identity))
| ~ equalish(X_183,additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[c_2959,c_44]) ).
tff(c_3414,plain,
! [X_189] :
( equalish(additive_identity,multiply(X_189,multiplicative_identity))
| ~ equalish(X_189,additive_identity) ),
inference(resolution,[status(thm)],[c_336,c_3126]) ).
tff(c_113,plain,
! [X_68,X_11] :
( ~ equalish(X_68,multiply(multiplicative_identity,X_11))
| equalish(X_68,X_11)
| ~ defined(X_11) ),
inference(resolution,[status(thm)],[c_12,c_94]) ).
tff(c_3422,plain,
( equalish(additive_identity,multiplicative_identity)
| ~ defined(multiplicative_identity)
| ~ equalish(multiplicative_identity,additive_identity) ),
inference(resolution,[status(thm)],[c_3414,c_113]) ).
tff(c_3434,plain,
( equalish(additive_identity,multiplicative_identity)
| ~ equalish(multiplicative_identity,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_3422]) ).
tff(c_3435,plain,
~ equalish(multiplicative_identity,additive_identity),
inference(negUnitSimplification,[status(thm)],[c_54,c_3434]) ).
tff(c_30,plain,
! [X_23] :
( equalish(X_23,additive_identity)
| ~ defined(X_23)
| defined(multiplicative_inverse(X_23)) ),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_71,plain,
! [X_56] :
( ~ defined(X_56)
| equalish(multiply(multiplicative_identity,X_56),X_56) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_74,plain,
! [X_56] :
( equalish(X_56,multiply(multiplicative_identity,X_56))
| ~ defined(X_56) ),
inference(resolution,[status(thm)],[c_71,c_44]) ).
tff(c_252,plain,
! [X_83] :
( equalish(X_83,additive_identity)
| ~ defined(X_83)
| equalish(multiply(X_83,multiplicative_inverse(X_83)),multiplicative_identity) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_5045,plain,
! [X_222,X_223] :
( ~ equalish(X_222,multiply(X_223,multiplicative_inverse(X_223)))
| equalish(X_222,multiplicative_identity)
| equalish(X_223,additive_identity)
| ~ defined(X_223) ),
inference(resolution,[status(thm)],[c_252,c_46]) ).
tff(c_5108,plain,
( equalish(multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| equalish(multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity)
| ~ defined(multiplicative_inverse(multiplicative_identity)) ),
inference(resolution,[status(thm)],[c_74,c_5045]) ).
tff(c_5139,plain,
( equalish(multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| equalish(multiplicative_identity,additive_identity)
| ~ defined(multiplicative_inverse(multiplicative_identity)) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_5108]) ).
tff(c_5140,plain,
( equalish(multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ defined(multiplicative_inverse(multiplicative_identity)) ),
inference(negUnitSimplification,[status(thm)],[c_3435,c_5139]) ).
tff(c_5144,plain,
~ defined(multiplicative_inverse(multiplicative_identity)),
inference(splitLeft,[status(thm)],[c_5140]) ).
tff(c_5147,plain,
( equalish(multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[c_30,c_5144]) ).
tff(c_5150,plain,
equalish(multiplicative_identity,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_5147]) ).
tff(c_5152,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3435,c_5150]) ).
tff(c_5153,plain,
equalish(multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(splitRight,[status(thm)],[c_5140]) ).
tff(c_5262,plain,
equalish(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),
inference(resolution,[status(thm)],[c_5153,c_44]) ).
tff(c_5806,plain,
! [Z_234] :
( ~ less_or_equal(multiplicative_identity,Z_234)
| less_or_equal(multiplicative_inverse(multiplicative_identity),Z_234) ),
inference(resolution,[status(thm)],[c_5262,c_52]) ).
tff(c_5858,plain,
( less_or_equal(multiplicative_inverse(multiplicative_identity),a)
| ~ less_or_equal(multiplicative_identity,additive_identity) ),
inference(resolution,[status(thm)],[c_5806,c_119]) ).
tff(c_5954,plain,
~ less_or_equal(multiplicative_identity,additive_identity),
inference(splitLeft,[status(thm)],[c_5858]) ).
tff(c_5957,plain,
( less_or_equal(additive_identity,multiplicative_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[c_3933,c_5954]) ).
tff(c_5966,plain,
less_or_equal(additive_identity,multiplicative_identity),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_5957]) ).
tff(c_6056,plain,
! [X_238] :
( ~ less_or_equal(X_238,additive_identity)
| less_or_equal(X_238,multiplicative_identity) ),
inference(resolution,[status(thm)],[c_5966,c_34]) ).
tff(c_407,plain,
! [Y_94,X_95] :
( ~ defined(Y_94)
| ~ defined(X_95)
| equalish(add(X_95,Y_94),add(Y_94,X_95)) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_114,plain,
! [X_68,X_4] :
( ~ equalish(X_68,add(additive_identity,X_4))
| equalish(X_68,X_4)
| ~ defined(X_4) ),
inference(resolution,[status(thm)],[c_4,c_94]) ).
tff(c_411,plain,
! [X_95] :
( equalish(add(X_95,additive_identity),X_95)
| ~ defined(additive_identity)
| ~ defined(X_95) ),
inference(resolution,[status(thm)],[c_407,c_114]) ).
tff(c_493,plain,
! [X_99] :
( equalish(add(X_99,additive_identity),X_99)
| ~ defined(X_99) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_411]) ).
tff(c_345,plain,
! [X_39] :
( ~ equalish(X_39,additive_inverse(additive_identity))
| equalish(X_39,additive_identity) ),
inference(resolution,[status(thm)],[c_337,c_46]) ).
tff(c_497,plain,
( equalish(add(additive_inverse(additive_identity),additive_identity),additive_identity)
| ~ defined(additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[c_493,c_345]) ).
tff(c_510,plain,
equalish(add(additive_inverse(additive_identity),additive_identity),additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_328,c_497]) ).
tff(c_968,plain,
! [Z_124] :
( ~ less_or_equal(add(additive_inverse(additive_identity),additive_identity),Z_124)
| less_or_equal(additive_identity,Z_124) ),
inference(resolution,[status(thm)],[c_510,c_52]) ).
tff(c_980,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_968]) ).
tff(c_1007,plain,
! [Y_33] :
( less_or_equal(additive_identity,add(Y_33,additive_identity))
| ~ less_or_equal(additive_inverse(additive_identity),Y_33) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_980]) ).
tff(c_6138,plain,
( less_or_equal(additive_identity,add(multiplicative_identity,additive_identity))
| ~ less_or_equal(additive_inverse(additive_identity),additive_identity) ),
inference(resolution,[status(thm)],[c_6056,c_1007]) ).
tff(c_15312,plain,
~ less_or_equal(additive_inverse(additive_identity),additive_identity),
inference(splitLeft,[status(thm)],[c_6138]) ).
tff(c_15492,plain,
~ less_or_equal(additive_identity,additive_identity),
inference(resolution,[status(thm)],[c_335,c_15312]) ).
tff(c_15508,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_653,c_15492]) ).
tff(c_15510,plain,
less_or_equal(additive_inverse(additive_identity),additive_identity),
inference(splitRight,[status(thm)],[c_6138]) ).
tff(c_15568,plain,
! [X_400] :
( ~ less_or_equal(X_400,additive_inverse(additive_identity))
| less_or_equal(X_400,additive_identity) ),
inference(resolution,[status(thm)],[c_15510,c_34]) ).
tff(c_15644,plain,
( less_or_equal(add(additive_identity,additive_inverse(additive_identity)),additive_identity)
| ~ less_or_equal(additive_identity,additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[c_464,c_15568]) ).
tff(c_15717,plain,
less_or_equal(add(additive_identity,additive_inverse(additive_identity)),additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_590,c_15644]) ).
tff(c_16310,plain,
! [X_26] :
( ~ less_or_equal(X_26,add(additive_identity,additive_inverse(additive_identity)))
| less_or_equal(X_26,additive_identity) ),
inference(resolution,[status(thm)],[c_15717,c_34]) ).
tff(c_319551,plain,
( less_or_equal(additive_inverse(a),additive_identity)
| ~ less_or_equal(additive_identity,add(additive_identity,additive_inverse(additive_identity))) ),
inference(resolution,[status(thm)],[c_319315,c_16310]) ).
tff(c_319799,plain,
less_or_equal(additive_inverse(a),additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_211020,c_319551]) ).
tff(c_319801,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_60,c_319799]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : FLD064-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.15 % 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
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 19:55:21 EDT 2023
% 0.14/0.36 % CPUTime :
% 141.95/127.14 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 141.95/127.16
% 141.95/127.16 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 142.31/127.21
% 142.31/127.21 Inference rules
% 142.31/127.21 ----------------------
% 142.31/127.21 #Ref : 0
% 142.31/127.21 #Sup : 69395
% 142.31/127.21 #Fact : 22
% 142.31/127.21 #Define : 0
% 142.31/127.21 #Split : 23
% 142.31/127.21 #Chain : 0
% 142.31/127.21 #Close : 0
% 142.31/127.21
% 142.31/127.21 Ordering : KBO
% 142.31/127.21
% 142.31/127.21 Simplification rules
% 142.31/127.21 ----------------------
% 142.31/127.21 #Subsume : 19599
% 142.31/127.21 #Demod : 40913
% 142.31/127.21 #Tautology : 11824
% 142.31/127.21 #SimpNegUnit : 2021
% 142.31/127.21 #BackRed : 0
% 142.31/127.21
% 142.31/127.22 #Partial instantiations: 0
% 142.31/127.22 #Strategies tried : 1
% 142.31/127.22
% 142.31/127.22 Timing (in seconds)
% 142.31/127.22 ----------------------
% 142.31/127.22 Preprocessing : 0.51
% 142.31/127.22 Parsing : 0.28
% 142.31/127.22 CNF conversion : 0.03
% 142.31/127.22 Main loop : 125.59
% 142.31/127.22 Inferencing : 8.33
% 142.31/127.22 Reduction : 58.89
% 142.31/127.22 Demodulation : 48.13
% 142.31/127.22 BG Simplification : 0.28
% 142.31/127.22 Subsumption : 47.83
% 142.31/127.22 Abstraction : 0.50
% 142.31/127.22 MUC search : 0.00
% 142.31/127.22 Cooper : 0.00
% 142.31/127.22 Total : 126.18
% 142.31/127.22 Index Insertion : 0.00
% 142.31/127.22 Index Deletion : 0.00
% 142.31/127.22 Index Matching : 0.00
% 142.31/127.22 BG Taut test : 0.00
%------------------------------------------------------------------------------