TSTP Solution File: FLD010-5 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : FLD010-5 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n001.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 10:37:27 EDT 2023
% Result : Unsatisfiable 165.67s 142.67s
% Output : CNFRefutation 165.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 30
% Syntax : Number of formulae : 146 ( 38 unt; 10 typ; 0 def)
% Number of atoms : 358 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 441 ( 219 ~; 222 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 8 >; 7 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 209 (; 209 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sum > product > less_or_equal > defined > multiply > add > #nlpp > multiplicative_inverse > additive_inverse > multiplicative_identity > additive_identity
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(sum,type,
sum: ( $i * $i * $i ) > $o ).
tff(less_or_equal,type,
less_or_equal: ( $i * $i ) > $o ).
tff(product,type,
product: ( $i * $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(f_252,axiom,
~ sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
file(unknown,unknown) ).
tff(f_173,axiom,
defined(multiplicative_identity),
file(unknown,unknown) ).
tff(f_73,axiom,
! [X] :
( sum(additive_identity,X,X)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_250,axiom,
~ sum(additive_identity,multiplicative_identity,additive_identity),
file(unknown,unknown) ).
tff(f_180,axiom,
! [X] :
( defined(multiplicative_inverse(X))
| ~ defined(X)
| sum(additive_identity,X,additive_identity) ),
file(unknown,unknown) ).
tff(f_222,axiom,
! [X,Y] :
( less_or_equal(X,Y)
| less_or_equal(Y,X)
| ~ defined(X)
| ~ defined(Y) ),
file(unknown,unknown) ).
tff(f_204,axiom,
! [X,Y] :
( sum(additive_identity,X,Y)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,X) ),
file(unknown,unknown) ).
tff(f_159,axiom,
defined(additive_identity),
file(unknown,unknown) ).
tff(f_164,axiom,
! [X] :
( defined(additive_inverse(X))
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_78,axiom,
! [X] :
( sum(additive_inverse(X),X,additive_identity)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_83,axiom,
! [Y,X,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file(unknown,unknown) ).
tff(f_233,axiom,
! [U,Z,X,Y,V] :
( less_or_equal(U,V)
| ~ less_or_equal(X,Y)
| ~ sum(X,Z,U)
| ~ sum(Y,Z,V) ),
file(unknown,unknown) ).
tff(f_110,axiom,
! [X] :
( product(multiplicative_identity,X,X)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_122,axiom,
! [Y,X,Z] :
( product(Y,X,Z)
| ~ product(X,Y,Z) ),
file(unknown,unknown) ).
tff(f_117,axiom,
! [X] :
( product(multiplicative_inverse(X),X,multiplicative_identity)
| sum(additive_identity,X,additive_identity)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_136,axiom,
! [A,Z,B,C,X,Y,D] :
( sum(C,D,B)
| ~ sum(X,Y,A)
| ~ product(A,Z,B)
| ~ product(X,Z,C)
| ~ product(Y,Z,D) ),
file(unknown,unknown) ).
tff(f_212,axiom,
! [X,Z,Y] :
( less_or_equal(X,Z)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z) ),
file(unknown,unknown) ).
tff(f_57,axiom,
! [W,U,Z,X,Y,V] :
( sum(X,V,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W) ),
file(unknown,unknown) ).
tff(f_68,axiom,
! [W,U,Z,X,Y,V] :
( sum(U,Z,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(X,V,W) ),
file(unknown,unknown) ).
tff(f_105,axiom,
! [W,U,Z,X,Y,V] :
( product(U,Z,W)
| ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W) ),
file(unknown,unknown) ).
tff(c_56,plain,
~ sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_34,plain,
defined(multiplicative_identity),
inference(cnfTransformation,[status(thm)],[f_173]) ).
tff(c_6,plain,
! [X_13] :
( ~ defined(X_13)
| sum(additive_identity,X_13,X_13) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_54,plain,
~ sum(additive_identity,multiplicative_identity,additive_identity),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_36,plain,
! [X_54] :
( sum(additive_identity,X_54,additive_identity)
| ~ defined(X_54)
| defined(multiplicative_inverse(X_54)) ),
inference(cnfTransformation,[status(thm)],[f_180]) ).
tff(c_46,plain,
! [Y_65,X_64] :
( ~ defined(Y_65)
| ~ defined(X_64)
| less_or_equal(Y_65,X_64)
| less_or_equal(X_64,Y_65) ),
inference(cnfTransformation,[status(thm)],[f_222]) ).
tff(c_121,plain,
! [Y_102,X_103] :
( ~ less_or_equal(Y_102,X_103)
| ~ less_or_equal(X_103,Y_102)
| sum(additive_identity,X_103,Y_102) ),
inference(cnfTransformation,[status(thm)],[f_204]) ).
tff(c_134,plain,
( ~ less_or_equal(multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| ~ less_or_equal(multiplicative_inverse(multiplicative_identity),multiplicative_identity) ),
inference(resolution,[status(thm)],[c_121,c_56]) ).
tff(c_186,plain,
~ less_or_equal(multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(splitLeft,[status(thm)],[c_134]) ).
tff(c_28,plain,
defined(additive_identity),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_30,plain,
! [X_51] :
( ~ defined(X_51)
| defined(additive_inverse(X_51)) ),
inference(cnfTransformation,[status(thm)],[f_164]) ).
tff(c_100,plain,
! [Y_65] :
( ~ defined(Y_65)
| less_or_equal(Y_65,Y_65) ),
inference(factorization,[status(thm),theory(equality)],[c_46]) ).
tff(c_8,plain,
! [X_14] :
( ~ defined(X_14)
| sum(additive_inverse(X_14),X_14,additive_identity) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_71,plain,
! [X_86,Y_87,Z_88] :
( ~ sum(X_86,Y_87,Z_88)
| sum(Y_87,X_86,Z_88) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_77,plain,
! [X_13] :
( sum(X_13,additive_identity,X_13)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_6,c_71]) ).
tff(c_215,plain,
! [U_109,Z_111,Y_112,X_110,V_113] :
( ~ sum(Y_112,Z_111,V_113)
| ~ sum(X_110,Z_111,U_109)
| ~ less_or_equal(X_110,Y_112)
| less_or_equal(U_109,V_113) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_532,plain,
! [X_157,U_158,X_159] :
( ~ sum(X_157,additive_identity,U_158)
| ~ less_or_equal(X_157,X_159)
| less_or_equal(U_158,X_159)
| ~ defined(X_159) ),
inference(resolution,[status(thm)],[c_77,c_215]) ).
tff(c_548,plain,
! [X_159] :
( ~ less_or_equal(additive_inverse(additive_identity),X_159)
| less_or_equal(additive_identity,X_159)
| ~ defined(X_159)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_8,c_532]) ).
tff(c_592,plain,
! [X_167] :
( ~ less_or_equal(additive_inverse(additive_identity),X_167)
| less_or_equal(additive_identity,X_167)
| ~ defined(X_167) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_548]) ).
tff(c_626,plain,
( less_or_equal(additive_identity,additive_inverse(additive_identity))
| ~ defined(additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[c_100,c_592]) ).
tff(c_629,plain,
~ defined(additive_inverse(additive_identity)),
inference(splitLeft,[status(thm)],[c_626]) ).
tff(c_632,plain,
~ defined(additive_identity),
inference(resolution,[status(thm)],[c_30,c_629]) ).
tff(c_636,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_632]) ).
tff(c_638,plain,
defined(additive_inverse(additive_identity)),
inference(splitRight,[status(thm)],[c_626]) ).
tff(c_482,plain,
! [X_153,X_154,U_155] :
( ~ sum(X_153,X_154,U_155)
| ~ less_or_equal(X_153,additive_identity)
| less_or_equal(U_155,X_154)
| ~ defined(X_154) ),
inference(resolution,[status(thm)],[c_6,c_215]) ).
tff(c_519,plain,
! [X_156] :
( ~ less_or_equal(additive_inverse(X_156),additive_identity)
| less_or_equal(additive_identity,X_156)
| ~ defined(X_156) ),
inference(resolution,[status(thm)],[c_8,c_482]) ).
tff(c_525,plain,
! [X_156] :
( less_or_equal(additive_identity,X_156)
| ~ defined(X_156)
| ~ defined(additive_identity)
| ~ defined(additive_inverse(X_156))
| less_or_equal(additive_identity,additive_inverse(X_156)) ),
inference(resolution,[status(thm)],[c_46,c_519]) ).
tff(c_531,plain,
! [X_156] :
( less_or_equal(additive_identity,X_156)
| ~ defined(X_156)
| ~ defined(additive_inverse(X_156))
| less_or_equal(additive_identity,additive_inverse(X_156)) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_525]) ).
tff(c_859,plain,
! [X_189,X_190,U_191] :
( ~ sum(X_189,X_190,U_191)
| ~ less_or_equal(X_189,additive_inverse(X_190))
| less_or_equal(U_191,additive_identity)
| ~ defined(X_190) ),
inference(resolution,[status(thm)],[c_8,c_215]) ).
tff(c_871,plain,
! [X_13] :
( ~ less_or_equal(X_13,additive_inverse(additive_identity))
| less_or_equal(X_13,additive_identity)
| ~ defined(additive_identity)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_77,c_859]) ).
tff(c_888,plain,
! [X_192] :
( ~ less_or_equal(X_192,additive_inverse(additive_identity))
| less_or_equal(X_192,additive_identity)
| ~ defined(X_192) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_871]) ).
tff(c_900,plain,
( less_or_equal(additive_identity,additive_identity)
| ~ defined(additive_identity)
| ~ defined(additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[c_531,c_888]) ).
tff(c_942,plain,
less_or_equal(additive_identity,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_638,c_28,c_900]) ).
tff(c_195,plain,
( ~ defined(multiplicative_identity)
| ~ defined(multiplicative_inverse(multiplicative_identity))
| less_or_equal(multiplicative_identity,multiplicative_inverse(multiplicative_identity)) ),
inference(resolution,[status(thm)],[c_46,c_186]) ).
tff(c_202,plain,
( ~ defined(multiplicative_inverse(multiplicative_identity))
| less_or_equal(multiplicative_identity,multiplicative_inverse(multiplicative_identity)) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_195]) ).
tff(c_234,plain,
~ defined(multiplicative_inverse(multiplicative_identity)),
inference(splitLeft,[status(thm)],[c_202]) ).
tff(c_237,plain,
( sum(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[c_36,c_234]) ).
tff(c_240,plain,
sum(additive_identity,multiplicative_identity,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_237]) ).
tff(c_242,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_54,c_240]) ).
tff(c_244,plain,
defined(multiplicative_inverse(multiplicative_identity)),
inference(splitRight,[status(thm)],[c_202]) ).
tff(c_16,plain,
! [X_30] :
( ~ defined(X_30)
| product(multiplicative_identity,X_30,X_30) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_63,plain,
! [X_82,Y_83,Z_84] :
( ~ product(X_82,Y_83,Z_84)
| product(Y_83,X_82,Z_84) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_66,plain,
! [X_30] :
( product(X_30,multiplicative_identity,X_30)
| ~ defined(X_30) ),
inference(resolution,[status(thm)],[c_16,c_63]) ).
tff(c_18,plain,
! [X_31] :
( ~ defined(X_31)
| sum(additive_identity,X_31,additive_identity)
| product(multiplicative_inverse(X_31),X_31,multiplicative_identity) ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_654,plain,
! [Y_169,C_173,Z_170,B_171,X_172,D_174,A_168] :
( ~ product(Y_169,Z_170,D_174)
| ~ product(X_172,Z_170,C_173)
| ~ product(A_168,Z_170,B_171)
| ~ sum(X_172,Y_169,A_168)
| sum(C_173,D_174,B_171) ),
inference(cnfTransformation,[status(thm)],[f_136]) ).
tff(c_13660,plain,
! [C_424,A_426,X_425,B_427,X_428] :
( ~ product(X_425,X_428,C_424)
| ~ product(A_426,X_428,B_427)
| ~ sum(X_425,multiplicative_inverse(X_428),A_426)
| sum(C_424,multiplicative_identity,B_427)
| ~ defined(X_428)
| sum(additive_identity,X_428,additive_identity) ),
inference(resolution,[status(thm)],[c_18,c_654]) ).
tff(c_13766,plain,
! [A_426,B_427,X_30] :
( ~ product(A_426,multiplicative_identity,B_427)
| ~ sum(X_30,multiplicative_inverse(multiplicative_identity),A_426)
| sum(X_30,multiplicative_identity,B_427)
| ~ defined(multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(X_30) ),
inference(resolution,[status(thm)],[c_66,c_13660]) ).
tff(c_13894,plain,
! [A_426,B_427,X_30] :
( ~ product(A_426,multiplicative_identity,B_427)
| ~ sum(X_30,multiplicative_inverse(multiplicative_identity),A_426)
| sum(X_30,multiplicative_identity,B_427)
| sum(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(X_30) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_13766]) ).
tff(c_48600,plain,
! [A_686,B_687,X_688] :
( ~ product(A_686,multiplicative_identity,B_687)
| ~ sum(X_688,multiplicative_inverse(multiplicative_identity),A_686)
| sum(X_688,multiplicative_identity,B_687)
| ~ defined(X_688) ),
inference(negUnitSimplification,[status(thm)],[c_54,c_13894]) ).
tff(c_256344,plain,
! [X_1523,X_1524] :
( ~ sum(X_1523,multiplicative_inverse(multiplicative_identity),X_1524)
| sum(X_1523,multiplicative_identity,X_1524)
| ~ defined(X_1523)
| ~ defined(X_1524) ),
inference(resolution,[status(thm)],[c_66,c_48600]) ).
tff(c_256552,plain,
( sum(additive_identity,multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| ~ defined(additive_identity)
| ~ defined(multiplicative_inverse(multiplicative_identity)) ),
inference(resolution,[status(thm)],[c_6,c_256344]) ).
tff(c_256710,plain,
sum(additive_identity,multiplicative_identity,multiplicative_inverse(multiplicative_identity)),
inference(demodulation,[status(thm),theory(equality)],[c_244,c_28,c_256552]) ).
tff(c_233,plain,
! [X_110,X_13,U_109] :
( ~ sum(X_110,X_13,U_109)
| ~ less_or_equal(X_110,additive_identity)
| less_or_equal(U_109,X_13)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_6,c_215]) ).
tff(c_256776,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[c_256710,c_233]) ).
tff(c_256863,plain,
less_or_equal(multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_942,c_256776]) ).
tff(c_256865,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_186,c_256863]) ).
tff(c_256867,plain,
less_or_equal(multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(splitRight,[status(thm)],[c_134]) ).
tff(c_44,plain,
! [Y_63,Z_62,X_61] :
( ~ less_or_equal(Y_63,Z_62)
| ~ less_or_equal(X_61,Y_63)
| less_or_equal(X_61,Z_62) ),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_256892,plain,
! [X_1530] :
( ~ less_or_equal(X_1530,multiplicative_inverse(multiplicative_identity))
| less_or_equal(X_1530,multiplicative_identity) ),
inference(resolution,[status(thm)],[c_256867,c_44]) ).
tff(c_256908,plain,
! [X_64] :
( less_or_equal(X_64,multiplicative_identity)
| ~ defined(multiplicative_inverse(multiplicative_identity))
| ~ defined(X_64)
| less_or_equal(multiplicative_inverse(multiplicative_identity),X_64) ),
inference(resolution,[status(thm)],[c_46,c_256892]) ).
tff(c_257263,plain,
~ defined(multiplicative_inverse(multiplicative_identity)),
inference(splitLeft,[status(thm)],[c_256908]) ).
tff(c_257266,plain,
( sum(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[c_36,c_257263]) ).
tff(c_257269,plain,
sum(additive_identity,multiplicative_identity,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_257266]) ).
tff(c_257271,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_54,c_257269]) ).
tff(c_257273,plain,
defined(multiplicative_inverse(multiplicative_identity)),
inference(splitRight,[status(thm)],[c_256908]) ).
tff(c_256873,plain,
! [U_1525,Y_1528,Z_1527,V_1529,X_1526] :
( ~ sum(Y_1528,Z_1527,V_1529)
| ~ sum(X_1526,Z_1527,U_1525)
| ~ less_or_equal(X_1526,Y_1528)
| less_or_equal(U_1525,V_1529) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_257055,plain,
! [X_1556,U_1557,X_1558] :
( ~ sum(X_1556,additive_identity,U_1557)
| ~ less_or_equal(X_1556,X_1558)
| less_or_equal(U_1557,X_1558)
| ~ defined(X_1558) ),
inference(resolution,[status(thm)],[c_77,c_256873]) ).
tff(c_257071,plain,
! [X_1558] :
( ~ less_or_equal(additive_inverse(additive_identity),X_1558)
| less_or_equal(additive_identity,X_1558)
| ~ defined(X_1558)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_8,c_257055]) ).
tff(c_257090,plain,
! [X_1559] :
( ~ less_or_equal(additive_inverse(additive_identity),X_1559)
| less_or_equal(additive_identity,X_1559)
| ~ defined(X_1559) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_257071]) ).
tff(c_257110,plain,
( less_or_equal(additive_identity,additive_inverse(additive_identity))
| ~ defined(additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[c_100,c_257090]) ).
tff(c_257113,plain,
~ defined(additive_inverse(additive_identity)),
inference(splitLeft,[status(thm)],[c_257110]) ).
tff(c_257116,plain,
~ defined(additive_identity),
inference(resolution,[status(thm)],[c_30,c_257113]) ).
tff(c_257120,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_257116]) ).
tff(c_257122,plain,
defined(additive_inverse(additive_identity)),
inference(splitRight,[status(thm)],[c_257110]) ).
tff(c_257196,plain,
! [U_1572,V_1571,W_1574,Y_1570,X_1573,Z_1569] :
( ~ sum(U_1572,Z_1569,W_1574)
| ~ sum(Y_1570,Z_1569,V_1571)
| ~ sum(X_1573,Y_1570,U_1572)
| sum(X_1573,V_1571,W_1574) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_258414,plain,
! [Y_1622,X_1623,V_1624,X_1625] :
( ~ sum(Y_1622,X_1623,V_1624)
| ~ sum(X_1625,Y_1622,additive_identity)
| sum(X_1625,V_1624,X_1623)
| ~ defined(X_1623) ),
inference(resolution,[status(thm)],[c_6,c_257196]) ).
tff(c_258443,plain,
! [X_1626,X_1627] :
( ~ sum(X_1626,additive_identity,additive_identity)
| sum(X_1626,X_1627,X_1627)
| ~ defined(X_1627) ),
inference(resolution,[status(thm)],[c_6,c_258414]) ).
tff(c_258455,plain,
! [X_1627] :
( sum(additive_inverse(additive_identity),X_1627,X_1627)
| ~ defined(X_1627)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_8,c_258443]) ).
tff(c_258472,plain,
! [X_1628] :
( sum(additive_inverse(additive_identity),X_1628,X_1628)
| ~ defined(X_1628) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_258455]) ).
tff(c_10,plain,
! [X_16,Y_15,Z_17] :
( ~ sum(X_16,Y_15,Z_17)
| sum(Y_15,X_16,Z_17) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_258511,plain,
! [X_1628] :
( sum(X_1628,additive_inverse(additive_identity),X_1628)
| ~ defined(X_1628) ),
inference(resolution,[status(thm)],[c_258472,c_10]) ).
tff(c_257123,plain,
! [X_1564,W_1561,Y_1565,V_1563,Z_1560,U_1562] :
( ~ sum(X_1564,V_1563,W_1561)
| ~ sum(Y_1565,Z_1560,V_1563)
| ~ sum(X_1564,Y_1565,U_1562)
| sum(U_1562,Z_1560,W_1561) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_289815,plain,
! [Y_1986,Z_1987,X_1988,U_1989] :
( ~ sum(Y_1986,Z_1987,additive_identity)
| ~ sum(X_1988,Y_1986,U_1989)
| sum(U_1989,Z_1987,X_1988)
| ~ defined(X_1988) ),
inference(resolution,[status(thm)],[c_77,c_257123]) ).
tff(c_290050,plain,
! [X_1988,U_1989] :
( ~ sum(X_1988,additive_identity,U_1989)
| sum(U_1989,additive_inverse(additive_identity),X_1988)
| ~ defined(X_1988)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_258511,c_289815]) ).
tff(c_293265,plain,
! [X_2020,U_2021] :
( ~ sum(X_2020,additive_identity,U_2021)
| sum(U_2021,additive_inverse(additive_identity),X_2020)
| ~ defined(X_2020) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_290050]) ).
tff(c_293454,plain,
! [U_2021,X_2020] :
( sum(additive_inverse(additive_identity),U_2021,X_2020)
| ~ sum(X_2020,additive_identity,U_2021)
| ~ defined(X_2020) ),
inference(resolution,[status(thm)],[c_293265,c_10]) ).
tff(c_257274,plain,
! [B_1583,D_1586,A_1580,Y_1581,X_1584,C_1585,Z_1582] :
( ~ product(Y_1581,Z_1582,D_1586)
| ~ product(X_1584,Z_1582,C_1585)
| ~ product(A_1580,Z_1582,B_1583)
| ~ sum(X_1584,Y_1581,A_1580)
| sum(C_1585,D_1586,B_1583) ),
inference(cnfTransformation,[status(thm)],[f_136]) ).
tff(c_263532,plain,
! [X_1728,X_1730,B_1729,A_1731,C_1732] :
( ~ product(X_1728,X_1730,C_1732)
| ~ product(A_1731,X_1730,B_1729)
| ~ sum(X_1728,multiplicative_identity,A_1731)
| sum(C_1732,X_1730,B_1729)
| ~ defined(X_1730) ),
inference(resolution,[status(thm)],[c_16,c_257274]) ).
tff(c_263570,plain,
! [A_1731,B_1729,X_30] :
( ~ product(A_1731,multiplicative_identity,B_1729)
| ~ sum(X_30,multiplicative_identity,A_1731)
| sum(X_30,multiplicative_identity,B_1729)
| ~ defined(multiplicative_identity)
| ~ defined(X_30) ),
inference(resolution,[status(thm)],[c_66,c_263532]) ).
tff(c_343148,plain,
! [A_2294,B_2295,X_2296] :
( ~ product(A_2294,multiplicative_identity,B_2295)
| ~ sum(X_2296,multiplicative_identity,A_2294)
| sum(X_2296,multiplicative_identity,B_2295)
| ~ defined(X_2296) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_263570]) ).
tff(c_343287,plain,
! [X_2296] :
( ~ sum(X_2296,multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| sum(X_2296,multiplicative_identity,multiplicative_identity)
| ~ defined(X_2296)
| ~ defined(multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity) ),
inference(resolution,[status(thm)],[c_18,c_343148]) ).
tff(c_343400,plain,
! [X_2296] :
( ~ sum(X_2296,multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| sum(X_2296,multiplicative_identity,multiplicative_identity)
| ~ defined(X_2296)
| sum(additive_identity,multiplicative_identity,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_343287]) ).
tff(c_343470,plain,
! [X_2298] :
( ~ sum(X_2298,multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| sum(X_2298,multiplicative_identity,multiplicative_identity)
| ~ defined(X_2298) ),
inference(negUnitSimplification,[status(thm)],[c_54,c_343400]) ).
tff(c_343474,plain,
( sum(additive_inverse(additive_identity),multiplicative_identity,multiplicative_identity)
| ~ defined(additive_inverse(additive_identity))
| ~ sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_identity)
| ~ defined(multiplicative_inverse(multiplicative_identity)) ),
inference(resolution,[status(thm)],[c_293454,c_343470]) ).
tff(c_343485,plain,
( sum(additive_inverse(additive_identity),multiplicative_identity,multiplicative_identity)
| ~ sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_257273,c_257122,c_343474]) ).
tff(c_343492,plain,
~ sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_identity),
inference(splitLeft,[status(thm)],[c_343485]) ).
tff(c_138,plain,
! [X_104] :
( ~ defined(X_104)
| sum(additive_identity,X_104,additive_identity)
| product(multiplicative_inverse(X_104),X_104,multiplicative_identity) ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_20,plain,
! [X_33,Y_32,Z_34] :
( ~ product(X_33,Y_32,Z_34)
| product(Y_32,X_33,Z_34) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_141,plain,
! [X_104] :
( product(X_104,multiplicative_inverse(X_104),multiplicative_identity)
| ~ defined(X_104)
| sum(additive_identity,X_104,additive_identity) ),
inference(resolution,[status(thm)],[c_138,c_20]) ).
tff(c_257036,plain,
! [X_1553,Y_1550,Z_1551,W_1554,U_1552,V_1555] :
( ~ product(X_1553,V_1555,W_1554)
| ~ product(Y_1550,Z_1551,V_1555)
| ~ product(X_1553,Y_1550,U_1552)
| product(U_1552,Z_1551,W_1554) ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_259075,plain,
! [Y_1640,Z_1641,X_1642,U_1643] :
( ~ product(Y_1640,Z_1641,X_1642)
| ~ product(multiplicative_identity,Y_1640,U_1643)
| product(U_1643,Z_1641,X_1642)
| ~ defined(X_1642) ),
inference(resolution,[status(thm)],[c_16,c_257036]) ).
tff(c_262859,plain,
! [X_1713,U_1714] :
( ~ product(multiplicative_identity,X_1713,U_1714)
| product(U_1714,multiplicative_identity,X_1713)
| ~ defined(X_1713) ),
inference(resolution,[status(thm)],[c_66,c_259075]) ).
tff(c_262865,plain,
( product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| ~ defined(multiplicative_inverse(multiplicative_identity))
| ~ defined(multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity) ),
inference(resolution,[status(thm)],[c_141,c_262859]) ).
tff(c_262882,plain,
( product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| sum(additive_identity,multiplicative_identity,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_257273,c_262865]) ).
tff(c_262883,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(multiplicative_identity)),
inference(negUnitSimplification,[status(thm)],[c_54,c_262882]) ).
tff(c_343920,plain,
! [X_2301] :
( ~ sum(X_2301,multiplicative_identity,multiplicative_identity)
| sum(X_2301,multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| ~ defined(X_2301) ),
inference(resolution,[status(thm)],[c_262883,c_343148]) ).
tff(c_258745,plain,
! [Y_1634,Z_1635,X_1636,U_1637] :
( ~ sum(Y_1634,Z_1635,X_1636)
| ~ sum(additive_identity,Y_1634,U_1637)
| sum(U_1637,Z_1635,X_1636)
| ~ defined(X_1636) ),
inference(resolution,[status(thm)],[c_6,c_257123]) ).
tff(c_258780,plain,
! [X_13,U_1637] :
( ~ sum(additive_identity,X_13,U_1637)
| sum(U_1637,additive_identity,X_13)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_77,c_258745]) ).
tff(c_343956,plain,
( sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_identity)
| ~ defined(multiplicative_identity)
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_343920,c_258780]) ).
tff(c_344009,plain,
( sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_identity)
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_34,c_343956]) ).
tff(c_344010,plain,
~ sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference(negUnitSimplification,[status(thm)],[c_343492,c_344009]) ).
tff(c_344034,plain,
~ defined(multiplicative_identity),
inference(resolution,[status(thm)],[c_6,c_344010]) ).
tff(c_344039,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_34,c_344034]) ).
tff(c_344041,plain,
sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_identity),
inference(splitRight,[status(thm)],[c_343485]) ).
tff(c_344369,plain,
sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(resolution,[status(thm)],[c_344041,c_10]) ).
tff(c_344417,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_56,c_344369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : FLD010-5 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.15 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.20/0.36 % Computer : n001.cluster.edu
% 0.20/0.36 % Model : x86_64 x86_64
% 0.20/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.36 % Memory : 8042.1875MB
% 0.20/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.36 % CPULimit : 300
% 0.20/0.36 % WCLimit : 300
% 0.20/0.36 % DateTime : Thu Aug 3 20:22:10 EDT 2023
% 0.20/0.36 % CPUTime :
% 165.67/142.67 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 165.67/142.69
% 165.67/142.69 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 165.67/142.75
% 165.67/142.75 Inference rules
% 165.67/142.75 ----------------------
% 165.67/142.75 #Ref : 0
% 165.67/142.75 #Sup : 74439
% 165.67/142.75 #Fact : 22
% 165.67/142.75 #Define : 0
% 165.67/142.75 #Split : 44
% 165.67/142.75 #Chain : 0
% 165.67/142.75 #Close : 0
% 165.67/142.75
% 165.67/142.75 Ordering : KBO
% 165.67/142.75
% 165.67/142.75 Simplification rules
% 165.67/142.75 ----------------------
% 165.67/142.75 #Subsume : 5479
% 165.67/142.75 #Demod : 59322
% 165.67/142.75 #Tautology : 12274
% 165.67/142.75 #SimpNegUnit : 4505
% 165.67/142.75 #BackRed : 0
% 165.67/142.75
% 165.67/142.75 #Partial instantiations: 0
% 165.67/142.75 #Strategies tried : 1
% 165.67/142.75
% 165.67/142.75 Timing (in seconds)
% 165.67/142.75 ----------------------
% 165.67/142.75 Preprocessing : 0.49
% 165.67/142.75 Parsing : 0.27
% 165.67/142.75 CNF conversion : 0.03
% 165.67/142.75 Main loop : 141.06
% 165.67/142.75 Inferencing : 8.77
% 165.67/142.75 Reduction : 69.10
% 165.67/142.75 Demodulation : 59.80
% 165.67/142.75 BG Simplification : 0.41
% 165.67/142.75 Subsumption : 49.91
% 165.67/142.75 Abstraction : 0.62
% 165.67/142.75 MUC search : 0.00
% 165.67/142.75 Cooper : 0.00
% 165.67/142.75 Total : 141.64
% 165.67/142.75 Index Insertion : 0.00
% 165.67/142.75 Index Deletion : 0.00
% 165.67/142.75 Index Matching : 0.00
% 165.67/142.75 BG Taut test : 0.00
%------------------------------------------------------------------------------