TSTP Solution File: FLD040-5 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : FLD040-5 : 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/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 : n023.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 10:37:34 EDT 2023
% Result : Unsatisfiable 94.77s 80.53s
% Output : CNFRefutation 94.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 36
% Syntax : Number of formulae : 253 ( 79 unt; 11 typ; 0 def)
% Number of atoms : 581 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 666 ( 327 ~; 339 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 307 (; 307 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sum > product > less_or_equal > defined > multiply > add > #nlpp > multiplicative_inverse > additive_inverse > multiplicative_identity > additive_identity > a
%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(a,type,
a: $i ).
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_251,axiom,
~ sum(additive_identity,a,additive_identity),
file(unknown,unknown) ).
tff(f_249,axiom,
defined(a),
file(unknown,unknown) ).
tff(f_78,axiom,
! [X] :
( sum(additive_inverse(X),X,additive_identity)
| ~ defined(X) ),
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_122,axiom,
! [Y,X,Z] :
( product(Y,X,Z)
| ~ product(X,Y,Z) ),
file(unknown,unknown) ).
tff(f_173,axiom,
defined(multiplicative_identity),
file(unknown,unknown) ).
tff(f_159,axiom,
defined(additive_identity),
file(unknown,unknown) ).
tff(f_110,axiom,
! [X] :
( product(multiplicative_identity,X,X)
| ~ defined(X) ),
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_73,axiom,
! [X] :
( sum(additive_identity,X,X)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_252,axiom,
sum(additive_identity,multiplicative_inverse(a),additive_identity),
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_150,axiom,
! [A,Z,B,C,X,Y,D] :
( product(A,Z,B)
| ~ sum(X,Y,A)
| ~ product(X,Z,C)
| ~ product(Y,Z,D)
| ~ sum(C,D,B) ),
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(f_94,axiom,
! [W,U,Z,X,Y,V] :
( product(X,V,W)
| ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W) ),
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_246,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file(unknown,unknown) ).
tff(f_83,axiom,
! [Y,X,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
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_196,axiom,
! [X,Y] :
( product(X,Y,multiply(X,Y))
| ~ defined(X)
| ~ defined(Y) ),
file(unknown,unknown) ).
tff(f_164,axiom,
! [X] :
( defined(additive_inverse(X))
| ~ defined(X) ),
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_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_188,axiom,
! [X,Y] :
( sum(X,Y,add(X,Y))
| ~ defined(X)
| ~ defined(Y) ),
file(unknown,unknown) ).
tff(f_158,axiom,
! [X,Y] :
( defined(add(X,Y))
| ~ defined(X)
| ~ defined(Y) ),
file(unknown,unknown) ).
tff(c_56,plain,
~ sum(additive_identity,a,additive_identity),
inference(cnfTransformation,[status(thm)],[f_251]) ).
tff(c_54,plain,
defined(a),
inference(cnfTransformation,[status(thm)],[f_249]) ).
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_833,plain,
! [X_186] :
( ~ defined(X_186)
| sum(additive_identity,X_186,additive_identity)
| product(multiplicative_inverse(X_186),X_186,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_836,plain,
! [X_186] :
( product(X_186,multiplicative_inverse(X_186),multiplicative_identity)
| ~ defined(X_186)
| sum(additive_identity,X_186,additive_identity) ),
inference(resolution,[status(thm)],[c_833,c_20]) ).
tff(c_34,plain,
defined(multiplicative_identity),
inference(cnfTransformation,[status(thm)],[f_173]) ).
tff(c_28,plain,
defined(additive_identity),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_16,plain,
! [X_30] :
( ~ defined(X_30)
| product(multiplicative_identity,X_30,X_30) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_64,plain,
! [X_80,Y_81,Z_82] :
( ~ product(X_80,Y_81,Z_82)
| product(Y_81,X_80,Z_82) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_67,plain,
! [X_30] :
( product(X_30,multiplicative_identity,X_30)
| ~ defined(X_30) ),
inference(resolution,[status(thm)],[c_16,c_64]) ).
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_6,plain,
! [X_13] :
( ~ defined(X_13)
| sum(additive_identity,X_13,X_13) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_58,plain,
sum(additive_identity,multiplicative_inverse(a),additive_identity),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_934,plain,
! [V_201,X_198,Z_199,Y_200,U_197] :
( ~ sum(Y_200,Z_199,V_201)
| ~ sum(X_198,Z_199,U_197)
| ~ less_or_equal(X_198,Y_200)
| less_or_equal(U_197,V_201) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_965,plain,
! [X_202,U_203] :
( ~ sum(X_202,multiplicative_inverse(a),U_203)
| ~ less_or_equal(X_202,additive_identity)
| less_or_equal(U_203,additive_identity) ),
inference(resolution,[status(thm)],[c_58,c_934]) ).
tff(c_993,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(multiplicative_inverse(a),additive_identity)
| ~ defined(multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[c_6,c_965]) ).
tff(c_995,plain,
~ defined(multiplicative_inverse(a)),
inference(splitLeft,[status(thm)],[c_993]) ).
tff(c_998,plain,
( sum(additive_identity,a,additive_identity)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_36,c_995]) ).
tff(c_1001,plain,
sum(additive_identity,a,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_998]) ).
tff(c_1003,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_56,c_1001]) ).
tff(c_1005,plain,
defined(multiplicative_inverse(a)),
inference(splitRight,[status(thm)],[c_993]) ).
tff(c_1424,plain,
! [A_246,B_249,C_245,X_250,D_248,Z_247,Y_244] :
( ~ sum(C_245,D_248,B_249)
| ~ product(Y_244,Z_247,D_248)
| ~ product(X_250,Z_247,C_245)
| ~ sum(X_250,Y_244,A_246)
| product(A_246,Z_247,B_249) ),
inference(cnfTransformation,[status(thm)],[f_150]) ).
tff(c_9916,plain,
! [Z_420,A_419,Y_417,X_416,X_418] :
( ~ product(Y_417,Z_420,X_418)
| ~ product(X_416,Z_420,additive_identity)
| ~ sum(X_416,Y_417,A_419)
| product(A_419,Z_420,X_418)
| ~ defined(X_418) ),
inference(resolution,[status(thm)],[c_6,c_1424]) ).
tff(c_42062,plain,
! [X_629,X_630,A_631] :
( ~ product(X_629,multiplicative_identity,additive_identity)
| ~ sum(X_629,X_630,A_631)
| product(A_631,multiplicative_identity,X_630)
| ~ defined(X_630) ),
inference(resolution,[status(thm)],[c_67,c_9916]) ).
tff(c_42881,plain,
( ~ product(additive_identity,multiplicative_identity,additive_identity)
| product(additive_identity,multiplicative_identity,multiplicative_inverse(a))
| ~ defined(multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[c_58,c_42062]) ).
tff(c_43484,plain,
( ~ product(additive_identity,multiplicative_identity,additive_identity)
| product(additive_identity,multiplicative_identity,multiplicative_inverse(a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_1005,c_42881]) ).
tff(c_44507,plain,
~ product(additive_identity,multiplicative_identity,additive_identity),
inference(splitLeft,[status(thm)],[c_43484]) ).
tff(c_44659,plain,
~ defined(additive_identity),
inference(resolution,[status(thm)],[c_67,c_44507]) ).
tff(c_44663,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_44659]) ).
tff(c_44664,plain,
product(additive_identity,multiplicative_identity,multiplicative_inverse(a)),
inference(splitRight,[status(thm)],[c_43484]) ).
tff(c_44981,plain,
product(multiplicative_identity,additive_identity,multiplicative_inverse(a)),
inference(resolution,[status(thm)],[c_44664,c_20]) ).
tff(c_1311,plain,
! [V_232,Y_227,U_229,W_231,Z_228,X_230] :
( ~ product(X_230,V_232,W_231)
| ~ product(Y_227,Z_228,V_232)
| ~ product(X_230,Y_227,U_229)
| product(U_229,Z_228,W_231) ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_4092,plain,
! [Y_318,Z_319,X_320,U_321] :
( ~ product(Y_318,Z_319,X_320)
| ~ product(multiplicative_identity,Y_318,U_321)
| product(U_321,Z_319,X_320)
| ~ defined(X_320) ),
inference(resolution,[status(thm)],[c_16,c_1311]) ).
tff(c_4113,plain,
! [X_30,U_321] :
( ~ product(multiplicative_identity,X_30,U_321)
| product(U_321,multiplicative_identity,X_30)
| ~ defined(X_30) ),
inference(resolution,[status(thm)],[c_67,c_4092]) ).
tff(c_44995,plain,
( product(multiplicative_inverse(a),multiplicative_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_44981,c_4113]) ).
tff(c_45041,plain,
product(multiplicative_inverse(a),multiplicative_identity,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_44995]) ).
tff(c_1006,plain,
! [Y_209,V_208,U_204,Z_205,W_206,X_207] :
( ~ product(U_204,Z_205,W_206)
| ~ product(Y_209,Z_205,V_208)
| ~ product(X_207,Y_209,U_204)
| product(X_207,V_208,W_206) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_1024,plain,
! [Y_209,X_30,V_208,X_207] :
( ~ product(Y_209,X_30,V_208)
| ~ product(X_207,Y_209,multiplicative_identity)
| product(X_207,V_208,X_30)
| ~ defined(X_30) ),
inference(resolution,[status(thm)],[c_16,c_1006]) ).
tff(c_45097,plain,
! [X_207] :
( ~ product(X_207,multiplicative_inverse(a),multiplicative_identity)
| product(X_207,additive_identity,multiplicative_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[c_45041,c_1024]) ).
tff(c_50125,plain,
! [X_680] :
( ~ product(X_680,multiplicative_inverse(a),multiplicative_identity)
| product(X_680,additive_identity,multiplicative_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_45097]) ).
tff(c_50136,plain,
( product(a,additive_identity,multiplicative_identity)
| ~ defined(a)
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[status(thm)],[c_836,c_50125]) ).
tff(c_50145,plain,
( product(a,additive_identity,multiplicative_identity)
| sum(additive_identity,a,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_50136]) ).
tff(c_50146,plain,
product(a,additive_identity,multiplicative_identity),
inference(negUnitSimplification,[status(thm)],[c_56,c_50145]) ).
tff(c_50233,plain,
product(additive_identity,a,multiplicative_identity),
inference(resolution,[status(thm)],[c_50146,c_20]) ).
tff(c_50261,plain,
! [X_207] :
( ~ product(X_207,additive_identity,multiplicative_identity)
| product(X_207,multiplicative_identity,a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_50233,c_1024]) ).
tff(c_50858,plain,
! [X_686] :
( ~ product(X_686,additive_identity,multiplicative_identity)
| product(X_686,multiplicative_identity,a) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_50261]) ).
tff(c_52087,plain,
! [X_695] :
( product(multiplicative_identity,X_695,a)
| ~ product(X_695,additive_identity,multiplicative_identity) ),
inference(resolution,[status(thm)],[c_50858,c_20]) ).
tff(c_52102,plain,
product(multiplicative_identity,a,a),
inference(resolution,[status(thm)],[c_50146,c_52087]) ).
tff(c_1330,plain,
! [C_238,D_239,Z_235,X_237,A_233,Y_234,B_236] :
( ~ product(Y_234,Z_235,D_239)
| ~ product(X_237,Z_235,C_238)
| ~ product(A_233,Z_235,B_236)
| ~ sum(X_237,Y_234,A_233)
| sum(C_238,D_239,B_236) ),
inference(cnfTransformation,[status(thm)],[f_136]) ).
tff(c_7741,plain,
! [X_382,B_386,A_383,X_384,C_385] :
( ~ product(X_384,X_382,C_385)
| ~ product(A_383,X_382,B_386)
| ~ sum(X_384,multiplicative_identity,A_383)
| sum(C_385,X_382,B_386)
| ~ defined(X_382) ),
inference(resolution,[status(thm)],[c_16,c_1330]) ).
tff(c_54029,plain,
! [A_706,X_707,B_708] :
( ~ product(A_706,X_707,B_708)
| ~ sum(multiplicative_identity,multiplicative_identity,A_706)
| sum(X_707,X_707,B_708)
| ~ defined(X_707) ),
inference(resolution,[status(thm)],[c_16,c_7741]) ).
tff(c_54045,plain,
( ~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| sum(a,a,a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_52102,c_54029]) ).
tff(c_54207,plain,
( ~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| sum(a,a,a) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_54045]) ).
tff(c_55807,plain,
~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(splitLeft,[status(thm)],[c_54207]) ).
tff(c_52,plain,
~ sum(additive_identity,additive_identity,multiplicative_identity),
inference(cnfTransformation,[status(thm)],[f_246]) ).
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_44665,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(splitRight,[status(thm)],[c_43484]) ).
tff(c_44746,plain,
product(multiplicative_identity,additive_identity,additive_identity),
inference(resolution,[status(thm)],[c_44665,c_20]) ).
tff(c_44774,plain,
! [X_207] :
( ~ product(X_207,multiplicative_identity,multiplicative_identity)
| product(X_207,additive_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_44746,c_1024]) ).
tff(c_45653,plain,
! [X_648] :
( ~ product(X_648,multiplicative_identity,multiplicative_identity)
| product(X_648,additive_identity,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_44774]) ).
tff(c_45675,plain,
( product(multiplicative_inverse(multiplicative_identity),additive_identity,additive_identity)
| ~ defined(multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity) ),
inference(resolution,[status(thm)],[c_18,c_45653]) ).
tff(c_45698,plain,
( product(multiplicative_inverse(multiplicative_identity),additive_identity,additive_identity)
| sum(additive_identity,multiplicative_identity,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_45675]) ).
tff(c_70039,plain,
sum(additive_identity,multiplicative_identity,additive_identity),
inference(splitLeft,[status(thm)],[c_45698]) ).
tff(c_72,plain,
! [X_84,Y_85,Z_86] :
( ~ sum(X_84,Y_85,Z_86)
| sum(Y_85,X_84,Z_86) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_80,plain,
! [X_13] :
( sum(X_13,additive_identity,X_13)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_6,c_72]) ).
tff(c_1070,plain,
! [V_213,W_211,U_212,Y_215,Z_210,X_214] :
( ~ sum(X_214,V_213,W_211)
| ~ sum(Y_215,Z_210,V_213)
| ~ sum(X_214,Y_215,U_212)
| sum(U_212,Z_210,W_211) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_3158,plain,
! [Y_292,Z_293,X_294,U_295] :
( ~ sum(Y_292,Z_293,X_294)
| ~ sum(additive_identity,Y_292,U_295)
| sum(U_295,Z_293,X_294)
| ~ defined(X_294) ),
inference(resolution,[status(thm)],[c_6,c_1070]) ).
tff(c_3251,plain,
! [X_13,U_295] :
( ~ sum(additive_identity,X_13,U_295)
| sum(U_295,additive_identity,X_13)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_80,c_3158]) ).
tff(c_70061,plain,
( sum(additive_identity,additive_identity,multiplicative_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[c_70039,c_3251]) ).
tff(c_70106,plain,
sum(additive_identity,additive_identity,multiplicative_identity),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_70061]) ).
tff(c_70108,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_70106]) ).
tff(c_70110,plain,
~ sum(additive_identity,multiplicative_identity,additive_identity),
inference(splitRight,[status(thm)],[c_45698]) ).
tff(c_13269,plain,
! [Y_467,Z_468,X_469,U_470] :
( ~ product(Y_467,Z_468,X_469)
| ~ product(multiplicative_inverse(X_469),Y_467,U_470)
| product(U_470,Z_468,multiplicative_identity)
| ~ defined(X_469)
| sum(additive_identity,X_469,additive_identity) ),
inference(resolution,[status(thm)],[c_18,c_1311]) ).
tff(c_71423,plain,
! [X_791,U_792] :
( ~ product(multiplicative_inverse(X_791),X_791,U_792)
| product(U_792,multiplicative_identity,multiplicative_identity)
| sum(additive_identity,X_791,additive_identity)
| ~ defined(X_791) ),
inference(resolution,[status(thm)],[c_67,c_13269]) ).
tff(c_71517,plain,
( product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity)
| ~ defined(multiplicative_inverse(multiplicative_identity)) ),
inference(resolution,[status(thm)],[c_67,c_71423]) ).
tff(c_71577,plain,
( product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(multiplicative_inverse(multiplicative_identity)) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_71517]) ).
tff(c_71578,plain,
( product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| ~ defined(multiplicative_inverse(multiplicative_identity)) ),
inference(negUnitSimplification,[status(thm)],[c_70110,c_71577]) ).
tff(c_71579,plain,
~ defined(multiplicative_inverse(multiplicative_identity)),
inference(splitLeft,[status(thm)],[c_71578]) ).
tff(c_71582,plain,
( sum(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[c_36,c_71579]) ).
tff(c_71585,plain,
sum(additive_identity,multiplicative_identity,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_71582]) ).
tff(c_71587,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_70110,c_71585]) ).
tff(c_71588,plain,
product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity),
inference(splitRight,[status(thm)],[c_71578]) ).
tff(c_7767,plain,
! [A_383,X_30,B_386] :
( ~ product(A_383,X_30,B_386)
| ~ sum(multiplicative_identity,multiplicative_identity,A_383)
| sum(X_30,X_30,B_386)
| ~ defined(X_30) ),
inference(resolution,[status(thm)],[c_16,c_7741]) ).
tff(c_71600,plain,
( ~ sum(multiplicative_identity,multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[c_71588,c_7767]) ).
tff(c_71661,plain,
( ~ sum(multiplicative_identity,multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| sum(multiplicative_identity,multiplicative_identity,multiplicative_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_71600]) ).
tff(c_71662,plain,
~ sum(multiplicative_identity,multiplicative_identity,multiplicative_inverse(multiplicative_identity)),
inference(negUnitSimplification,[status(thm)],[c_55807,c_71661]) ).
tff(c_71589,plain,
defined(multiplicative_inverse(multiplicative_identity)),
inference(splitRight,[status(thm)],[c_71578]) ).
tff(c_3520,plain,
! [Y_302,X_303,V_304,X_305] :
( ~ product(Y_302,X_303,V_304)
| ~ product(X_305,Y_302,multiplicative_identity)
| product(X_305,V_304,X_303)
| ~ defined(X_303) ),
inference(resolution,[status(thm)],[c_16,c_1006]) ).
tff(c_3540,plain,
! [X_305,X_30] :
( ~ product(X_305,multiplicative_identity,multiplicative_identity)
| product(X_305,X_30,X_30)
| ~ defined(X_30) ),
inference(resolution,[status(thm)],[c_16,c_3520]) ).
tff(c_71705,plain,
! [X_30] :
( product(multiplicative_inverse(multiplicative_identity),X_30,X_30)
| ~ defined(X_30) ),
inference(resolution,[status(thm)],[c_71588,c_3540]) ).
tff(c_12246,plain,
! [Y_449,X_450,V_451,X_452] :
( ~ product(Y_449,X_450,V_451)
| ~ product(X_452,Y_449,multiplicative_inverse(X_450))
| product(X_452,V_451,multiplicative_identity)
| ~ defined(X_450)
| sum(additive_identity,X_450,additive_identity) ),
inference(resolution,[status(thm)],[c_18,c_1006]) ).
tff(c_12260,plain,
! [X_452,X_30] :
( ~ product(X_452,X_30,multiplicative_inverse(multiplicative_identity))
| product(X_452,X_30,multiplicative_identity)
| ~ defined(multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(X_30) ),
inference(resolution,[status(thm)],[c_67,c_12246]) ).
tff(c_12271,plain,
! [X_452,X_30] :
( ~ product(X_452,X_30,multiplicative_inverse(multiplicative_identity))
| product(X_452,X_30,multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(X_30) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_12260]) ).
tff(c_77079,plain,
! [X_830,X_831] :
( ~ product(X_830,X_831,multiplicative_inverse(multiplicative_identity))
| product(X_830,X_831,multiplicative_identity)
| ~ defined(X_831) ),
inference(negUnitSimplification,[status(thm)],[c_70110,c_12271]) ).
tff(c_77123,plain,
( product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ defined(multiplicative_inverse(multiplicative_identity)) ),
inference(resolution,[status(thm)],[c_71705,c_77079]) ).
tff(c_77214,plain,
product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(demodulation,[status(thm),theory(equality)],[c_71589,c_77123]) ).
tff(c_40,plain,
! [Y_58,X_57] :
( ~ defined(Y_58)
| ~ defined(X_57)
| product(X_57,Y_58,multiply(X_57,Y_58)) ),
inference(cnfTransformation,[status(thm)],[f_196]) ).
tff(c_10511,plain,
! [X_425,Y_428,X_426,Y_427,V_429] :
( ~ product(Y_427,Y_428,V_429)
| ~ product(X_426,Y_427,X_425)
| product(X_426,V_429,multiply(X_425,Y_428))
| ~ defined(Y_428)
| ~ defined(X_425) ),
inference(resolution,[status(thm)],[c_40,c_1006]) ).
tff(c_159595,plain,
! [X_1137,X_1138,X_1139] :
( ~ product(X_1137,multiplicative_inverse(X_1138),X_1139)
| product(X_1137,multiplicative_identity,multiply(X_1139,X_1138))
| ~ defined(X_1139)
| ~ defined(X_1138)
| sum(additive_identity,X_1138,additive_identity) ),
inference(resolution,[status(thm)],[c_18,c_10511]) ).
tff(c_159721,plain,
( product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiply(multiplicative_identity,multiplicative_identity))
| ~ defined(multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity) ),
inference(resolution,[status(thm)],[c_77214,c_159595]) ).
tff(c_159966,plain,
( product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiply(multiplicative_identity,multiplicative_identity))
| sum(additive_identity,multiplicative_identity,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_159721]) ).
tff(c_159967,plain,
product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiply(multiplicative_identity,multiplicative_identity)),
inference(negUnitSimplification,[status(thm)],[c_70110,c_159966]) ).
tff(c_167041,plain,
product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiply(multiplicative_identity,multiplicative_identity)),
inference(resolution,[status(thm)],[c_159967,c_20]) ).
tff(c_167336,plain,
( product(multiply(multiplicative_identity,multiplicative_identity),multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| ~ defined(multiplicative_inverse(multiplicative_identity)) ),
inference(resolution,[status(thm)],[c_167041,c_4113]) ).
tff(c_167429,plain,
product(multiply(multiplicative_identity,multiplicative_identity),multiplicative_identity,multiplicative_inverse(multiplicative_identity)),
inference(demodulation,[status(thm),theory(equality)],[c_71589,c_167336]) ).
tff(c_167494,plain,
( ~ sum(multiplicative_identity,multiplicative_identity,multiply(multiplicative_identity,multiplicative_identity))
| sum(multiplicative_identity,multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[c_167429,c_7767]) ).
tff(c_167580,plain,
( ~ sum(multiplicative_identity,multiplicative_identity,multiply(multiplicative_identity,multiplicative_identity))
| sum(multiplicative_identity,multiplicative_identity,multiplicative_inverse(multiplicative_identity)) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_167494]) ).
tff(c_167581,plain,
~ sum(multiplicative_identity,multiplicative_identity,multiply(multiplicative_identity,multiplicative_identity)),
inference(negUnitSimplification,[status(thm)],[c_71662,c_167580]) ).
tff(c_30,plain,
! [X_51] :
( ~ defined(X_51)
| defined(additive_inverse(X_51)) ),
inference(cnfTransformation,[status(thm)],[f_164]) ).
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_775,plain,
! [Y_65] :
( ~ defined(Y_65)
| less_or_equal(Y_65,Y_65) ),
inference(factorization,[status(thm),theory(equality)],[c_46]) ).
tff(c_1889,plain,
! [X_265,X_266,U_267] :
( ~ sum(X_265,X_266,U_267)
| ~ less_or_equal(X_265,additive_inverse(X_266))
| less_or_equal(U_267,additive_identity)
| ~ defined(X_266) ),
inference(resolution,[status(thm)],[c_8,c_934]) ).
tff(c_1901,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_80,c_1889]) ).
tff(c_1968,plain,
! [X_268] :
( ~ less_or_equal(X_268,additive_inverse(additive_identity))
| less_or_equal(X_268,additive_identity)
| ~ defined(X_268) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_1901]) ).
tff(c_1999,plain,
( less_or_equal(additive_inverse(additive_identity),additive_identity)
| ~ defined(additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[c_775,c_1968]) ).
tff(c_2002,plain,
~ defined(additive_inverse(additive_identity)),
inference(splitLeft,[status(thm)],[c_1999]) ).
tff(c_2010,plain,
~ defined(additive_identity),
inference(resolution,[status(thm)],[c_30,c_2002]) ).
tff(c_2014,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_2010]) ).
tff(c_2016,plain,
defined(additive_inverse(additive_identity)),
inference(splitRight,[status(thm)],[c_1999]) ).
tff(c_81,plain,
sum(multiplicative_inverse(a),additive_identity,additive_identity),
inference(resolution,[status(thm)],[c_58,c_72]) ).
tff(c_1161,plain,
! [X_222,V_220,U_221,Y_219,Z_218,W_223] :
( ~ sum(U_221,Z_218,W_223)
| ~ sum(Y_219,Z_218,V_220)
| ~ sum(X_222,Y_219,U_221)
| sum(X_222,V_220,W_223) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_2120,plain,
! [Y_270,V_271,X_272] :
( ~ sum(Y_270,multiplicative_inverse(a),V_271)
| ~ sum(X_272,Y_270,additive_identity)
| sum(X_272,V_271,additive_identity) ),
inference(resolution,[status(thm)],[c_58,c_1161]) ).
tff(c_2135,plain,
! [X_272] :
( ~ sum(X_272,additive_identity,additive_identity)
| sum(X_272,multiplicative_inverse(a),additive_identity)
| ~ defined(multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[c_6,c_2120]) ).
tff(c_2274,plain,
! [X_277] :
( ~ sum(X_277,additive_identity,additive_identity)
| sum(X_277,multiplicative_inverse(a),additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_1005,c_2135]) ).
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_2309,plain,
! [X_278] :
( sum(multiplicative_inverse(a),X_278,additive_identity)
| ~ sum(X_278,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[c_2274,c_10]) ).
tff(c_1191,plain,
! [Y_219,V_220,X_222] :
( ~ sum(Y_219,multiplicative_inverse(a),V_220)
| ~ sum(X_222,Y_219,additive_identity)
| sum(X_222,V_220,additive_identity) ),
inference(resolution,[status(thm)],[c_58,c_1161]) ).
tff(c_2312,plain,
! [X_222] :
( ~ sum(X_222,multiplicative_inverse(a),additive_identity)
| sum(X_222,additive_identity,additive_identity)
| ~ sum(multiplicative_inverse(a),additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[c_2309,c_1191]) ).
tff(c_2424,plain,
! [X_280] :
( ~ sum(X_280,multiplicative_inverse(a),additive_identity)
| sum(X_280,additive_identity,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_81,c_2312]) ).
tff(c_2439,plain,
( sum(additive_inverse(multiplicative_inverse(a)),additive_identity,additive_identity)
| ~ defined(multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[c_8,c_2424]) ).
tff(c_2452,plain,
sum(additive_inverse(multiplicative_inverse(a)),additive_identity,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_1005,c_2439]) ).
tff(c_3615,plain,
! [Y_309,X_310,V_311,X_312] :
( ~ sum(Y_309,X_310,V_311)
| ~ sum(X_312,Y_309,additive_identity)
| sum(X_312,V_311,X_310)
| ~ defined(X_310) ),
inference(resolution,[status(thm)],[c_6,c_1161]) ).
tff(c_4147,plain,
! [X_323,X_324] :
( ~ sum(X_323,additive_identity,additive_identity)
| sum(X_323,X_324,X_324)
| ~ defined(X_324) ),
inference(resolution,[status(thm)],[c_6,c_3615]) ).
tff(c_4199,plain,
! [X_324] :
( sum(additive_inverse(multiplicative_inverse(a)),X_324,X_324)
| ~ defined(X_324) ),
inference(resolution,[status(thm)],[c_2452,c_4147]) ).
tff(c_5423,plain,
! [Y_346,X_347,V_348,X_349] :
( ~ sum(Y_346,X_347,V_348)
| ~ sum(X_349,Y_346,additive_inverse(X_347))
| sum(X_349,V_348,additive_identity)
| ~ defined(X_347) ),
inference(resolution,[status(thm)],[c_8,c_1161]) ).
tff(c_5505,plain,
! [X_349,X_13] :
( ~ sum(X_349,X_13,additive_inverse(additive_identity))
| sum(X_349,X_13,additive_identity)
| ~ defined(additive_identity)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_80,c_5423]) ).
tff(c_19595,plain,
! [X_523,X_524] :
( ~ sum(X_523,X_524,additive_inverse(additive_identity))
| sum(X_523,X_524,additive_identity)
| ~ defined(X_524) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_5505]) ).
tff(c_19728,plain,
( sum(additive_inverse(multiplicative_inverse(a)),additive_inverse(additive_identity),additive_identity)
| ~ defined(additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[c_4199,c_19595]) ).
tff(c_19872,plain,
sum(additive_inverse(multiplicative_inverse(a)),additive_inverse(additive_identity),additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_2016,c_19728]) ).
tff(c_4524,plain,
! [Y_330,Z_331,X_332,U_333] :
( ~ sum(Y_330,Z_331,X_332)
| ~ sum(additive_inverse(X_332),Y_330,U_333)
| sum(U_333,Z_331,additive_identity)
| ~ defined(X_332) ),
inference(resolution,[status(thm)],[c_8,c_1070]) ).
tff(c_4592,plain,
! [U_333] :
( ~ sum(additive_inverse(additive_identity),additive_identity,U_333)
| sum(U_333,multiplicative_inverse(a),additive_identity)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_58,c_4524]) ).
tff(c_11995,plain,
! [U_448] :
( ~ sum(additive_inverse(additive_identity),additive_identity,U_448)
| sum(U_448,multiplicative_inverse(a),additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_4592]) ).
tff(c_12030,plain,
( sum(additive_inverse(additive_identity),multiplicative_inverse(a),additive_identity)
| ~ defined(additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[c_80,c_11995]) ).
tff(c_12066,plain,
sum(additive_inverse(additive_identity),multiplicative_inverse(a),additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_2016,c_12030]) ).
tff(c_1190,plain,
! [Y_219,X_13,V_220,X_222] :
( ~ sum(Y_219,X_13,V_220)
| ~ sum(X_222,Y_219,additive_identity)
| sum(X_222,V_220,X_13)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_6,c_1161]) ).
tff(c_12090,plain,
! [X_222] :
( ~ sum(X_222,additive_inverse(additive_identity),additive_identity)
| sum(X_222,additive_identity,multiplicative_inverse(a))
| ~ defined(multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[c_12066,c_1190]) ).
tff(c_12140,plain,
! [X_222] :
( ~ sum(X_222,additive_inverse(additive_identity),additive_identity)
| sum(X_222,additive_identity,multiplicative_inverse(a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_1005,c_12090]) ).
tff(c_20326,plain,
sum(additive_inverse(multiplicative_inverse(a)),additive_identity,multiplicative_inverse(a)),
inference(resolution,[status(thm)],[c_19872,c_12140]) ).
tff(c_20659,plain,
sum(additive_identity,additive_inverse(multiplicative_inverse(a)),multiplicative_inverse(a)),
inference(resolution,[status(thm)],[c_20326,c_10]) ).
tff(c_38,plain,
! [Y_56,X_55] :
( ~ defined(Y_56)
| ~ defined(X_55)
| sum(X_55,Y_56,add(X_55,Y_56)) ),
inference(cnfTransformation,[status(thm)],[f_188]) ).
tff(c_11345,plain,
! [U_438,Y_439,Y_441,X_440,Z_442] :
( ~ sum(Y_439,Z_442,Y_441)
| ~ sum(X_440,Y_439,U_438)
| sum(U_438,Z_442,add(X_440,Y_441))
| ~ defined(Y_441)
| ~ defined(X_440) ),
inference(resolution,[status(thm)],[c_38,c_1070]) ).
tff(c_11497,plain,
! [X_440,X_14,U_438] :
( ~ sum(X_440,additive_inverse(X_14),U_438)
| sum(U_438,X_14,add(X_440,additive_identity))
| ~ defined(additive_identity)
| ~ defined(X_440)
| ~ defined(X_14) ),
inference(resolution,[status(thm)],[c_8,c_11345]) ).
tff(c_62215,plain,
! [X_761,X_762,U_763] :
( ~ sum(X_761,additive_inverse(X_762),U_763)
| sum(U_763,X_762,add(X_761,additive_identity))
| ~ defined(X_761)
| ~ defined(X_762) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_11497]) ).
tff(c_62288,plain,
( sum(multiplicative_inverse(a),multiplicative_inverse(a),add(additive_identity,additive_identity))
| ~ defined(additive_identity)
| ~ defined(multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[c_20659,c_62215]) ).
tff(c_62524,plain,
sum(multiplicative_inverse(a),multiplicative_inverse(a),add(additive_identity,additive_identity)),
inference(demodulation,[status(thm),theory(equality)],[c_1005,c_28,c_62288]) ).
tff(c_26,plain,
! [Y_50,X_49] :
( ~ defined(Y_50)
| ~ defined(X_49)
| defined(add(X_49,Y_50)) ),
inference(cnfTransformation,[status(thm)],[f_158]) ).
tff(c_1004,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(multiplicative_inverse(a),additive_identity) ),
inference(splitRight,[status(thm)],[c_993]) ).
tff(c_1025,plain,
~ less_or_equal(additive_identity,additive_identity),
inference(splitLeft,[status(thm)],[c_1004]) ).
tff(c_1029,plain,
~ defined(additive_identity),
inference(resolution,[status(thm)],[c_775,c_1025]) ).
tff(c_1035,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_1029]) ).
tff(c_1036,plain,
less_or_equal(multiplicative_inverse(a),additive_identity),
inference(splitRight,[status(thm)],[c_1004]) ).
tff(c_2486,plain,
! [Y_281,Z_282,U_283] :
( ~ sum(Y_281,Z_282,multiplicative_inverse(a))
| ~ sum(additive_identity,Y_281,U_283)
| sum(U_283,Z_282,additive_identity) ),
inference(resolution,[status(thm)],[c_58,c_1070]) ).
tff(c_2498,plain,
! [U_283] :
( ~ sum(additive_identity,additive_identity,U_283)
| sum(U_283,multiplicative_inverse(a),additive_identity)
| ~ defined(multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[c_6,c_2486]) ).
tff(c_2632,plain,
! [U_286] :
( ~ sum(additive_identity,additive_identity,U_286)
| sum(U_286,multiplicative_inverse(a),additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_1005,c_2498]) ).
tff(c_2938,plain,
! [U_289] :
( sum(multiplicative_inverse(a),U_289,additive_identity)
| ~ sum(additive_identity,additive_identity,U_289) ),
inference(resolution,[status(thm)],[c_2632,c_10]) ).
tff(c_963,plain,
! [X_198,X_13,U_197] :
( ~ sum(X_198,X_13,U_197)
| ~ less_or_equal(X_198,additive_identity)
| less_or_equal(U_197,X_13)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_6,c_934]) ).
tff(c_2954,plain,
! [U_289] :
( ~ less_or_equal(multiplicative_inverse(a),additive_identity)
| less_or_equal(additive_identity,U_289)
| ~ defined(U_289)
| ~ sum(additive_identity,additive_identity,U_289) ),
inference(resolution,[status(thm)],[c_2938,c_963]) ).
tff(c_3262,plain,
! [U_296] :
( less_or_equal(additive_identity,U_296)
| ~ defined(U_296)
| ~ sum(additive_identity,additive_identity,U_296) ),
inference(demodulation,[status(thm),theory(equality)],[c_1036,c_2954]) ).
tff(c_3277,plain,
( less_or_equal(additive_identity,add(additive_identity,additive_identity))
| ~ defined(add(additive_identity,additive_identity))
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_38,c_3262]) ).
tff(c_3299,plain,
( less_or_equal(additive_identity,add(additive_identity,additive_identity))
| ~ defined(add(additive_identity,additive_identity)) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_3277]) ).
tff(c_3510,plain,
~ defined(add(additive_identity,additive_identity)),
inference(splitLeft,[status(thm)],[c_3299]) ).
tff(c_3513,plain,
~ defined(additive_identity),
inference(resolution,[status(thm)],[c_26,c_3510]) ).
tff(c_3517,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_3513]) ).
tff(c_3519,plain,
defined(add(additive_identity,additive_identity)),
inference(splitRight,[status(thm)],[c_3299]) ).
tff(c_79,plain,
! [X_14] :
( sum(X_14,additive_inverse(X_14),additive_identity)
| ~ defined(X_14) ),
inference(resolution,[status(thm)],[c_8,c_72]) ).
tff(c_7768,plain,
! [X_387,U_388] :
( ~ sum(additive_identity,X_387,U_388)
| sum(U_388,additive_identity,X_387)
| ~ defined(X_387) ),
inference(resolution,[status(thm)],[c_80,c_3158]) ).
tff(c_7853,plain,
( sum(additive_identity,additive_identity,additive_inverse(additive_identity))
| ~ defined(additive_inverse(additive_identity))
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_79,c_7768]) ).
tff(c_7941,plain,
sum(additive_identity,additive_identity,additive_inverse(additive_identity)),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_2016,c_7853]) ).
tff(c_42698,plain,
( ~ product(additive_identity,multiplicative_identity,additive_identity)
| product(additive_inverse(additive_identity),multiplicative_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_7941,c_42062]) ).
tff(c_43363,plain,
( ~ product(additive_identity,multiplicative_identity,additive_identity)
| product(additive_inverse(additive_identity),multiplicative_identity,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_42698]) ).
tff(c_46366,plain,
product(additive_inverse(additive_identity),multiplicative_identity,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_44665,c_43363]) ).
tff(c_15847,plain,
! [X_509] :
( ~ sum(X_509,additive_inverse(additive_identity),additive_identity)
| sum(X_509,additive_identity,multiplicative_inverse(a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_1005,c_12090]) ).
tff(c_15894,plain,
( sum(additive_inverse(additive_inverse(additive_identity)),additive_identity,multiplicative_inverse(a))
| ~ defined(additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[c_8,c_15847]) ).
tff(c_15924,plain,
sum(additive_inverse(additive_inverse(additive_identity)),additive_identity,multiplicative_inverse(a)),
inference(demodulation,[status(thm),theory(equality)],[c_2016,c_15894]) ).
tff(c_16793,plain,
sum(additive_identity,additive_inverse(additive_inverse(additive_identity)),multiplicative_inverse(a)),
inference(resolution,[status(thm)],[c_15924,c_10]) ).
tff(c_62320,plain,
( sum(multiplicative_inverse(a),additive_inverse(additive_identity),add(additive_identity,additive_identity))
| ~ defined(additive_identity)
| ~ defined(additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[c_16793,c_62215]) ).
tff(c_62570,plain,
sum(multiplicative_inverse(a),additive_inverse(additive_identity),add(additive_identity,additive_identity)),
inference(demodulation,[status(thm),theory(equality)],[c_2016,c_28,c_62320]) ).
tff(c_65615,plain,
sum(additive_inverse(additive_identity),multiplicative_inverse(a),add(additive_identity,additive_identity)),
inference(resolution,[status(thm)],[c_62570,c_10]) ).
tff(c_9943,plain,
! [X_416,X_30,A_419] :
( ~ product(X_416,multiplicative_identity,additive_identity)
| ~ sum(X_416,X_30,A_419)
| product(A_419,multiplicative_identity,X_30)
| ~ defined(X_30) ),
inference(resolution,[status(thm)],[c_67,c_9916]) ).
tff(c_66073,plain,
( ~ product(additive_inverse(additive_identity),multiplicative_identity,additive_identity)
| product(add(additive_identity,additive_identity),multiplicative_identity,multiplicative_inverse(a))
| ~ defined(multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[c_65615,c_9943]) ).
tff(c_66129,plain,
product(add(additive_identity,additive_identity),multiplicative_identity,multiplicative_inverse(a)),
inference(demodulation,[status(thm),theory(equality)],[c_1005,c_46366,c_66073]) ).
tff(c_66281,plain,
product(multiplicative_identity,add(additive_identity,additive_identity),multiplicative_inverse(a)),
inference(resolution,[status(thm)],[c_66129,c_20]) ).
tff(c_66297,plain,
( product(multiplicative_inverse(a),multiplicative_identity,add(additive_identity,additive_identity))
| ~ defined(add(additive_identity,additive_identity)) ),
inference(resolution,[status(thm)],[c_66281,c_4113]) ).
tff(c_66346,plain,
product(multiplicative_inverse(a),multiplicative_identity,add(additive_identity,additive_identity)),
inference(demodulation,[status(thm),theory(equality)],[c_3519,c_66297]) ).
tff(c_66476,plain,
product(multiplicative_identity,multiplicative_inverse(a),add(additive_identity,additive_identity)),
inference(resolution,[status(thm)],[c_66346,c_20]) ).
tff(c_9657,plain,
! [U_413,Z_414,Y_411,Y_412,X_410] :
( ~ product(Y_411,Z_414,Y_412)
| ~ product(X_410,Y_411,U_413)
| product(U_413,Z_414,multiply(X_410,Y_412))
| ~ defined(Y_412)
| ~ defined(X_410) ),
inference(resolution,[status(thm)],[c_40,c_1311]) ).
tff(c_9665,plain,
! [X_410,X_31,U_413] :
( ~ product(X_410,multiplicative_inverse(X_31),U_413)
| product(U_413,X_31,multiply(X_410,multiplicative_identity))
| ~ defined(multiplicative_identity)
| ~ defined(X_410)
| ~ defined(X_31)
| sum(additive_identity,X_31,additive_identity) ),
inference(resolution,[status(thm)],[c_18,c_9657]) ).
tff(c_161780,plain,
! [X_1144,X_1145,U_1146] :
( ~ product(X_1144,multiplicative_inverse(X_1145),U_1146)
| product(U_1146,X_1145,multiply(X_1144,multiplicative_identity))
| ~ defined(X_1144)
| ~ defined(X_1145)
| sum(additive_identity,X_1145,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_9665]) ).
tff(c_161917,plain,
( product(add(additive_identity,additive_identity),a,multiply(multiplicative_identity,multiplicative_identity))
| ~ defined(multiplicative_identity)
| ~ defined(a)
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[status(thm)],[c_66476,c_161780]) ).
tff(c_162129,plain,
( product(add(additive_identity,additive_identity),a,multiply(multiplicative_identity,multiplicative_identity))
| sum(additive_identity,a,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_34,c_161917]) ).
tff(c_162130,plain,
product(add(additive_identity,additive_identity),a,multiply(multiplicative_identity,multiplicative_identity)),
inference(negUnitSimplification,[status(thm)],[c_56,c_162129]) ).
tff(c_16253,plain,
! [X_513,B_515,C_514,A_511,X_512] :
( ~ product(X_513,X_512,C_514)
| ~ product(A_511,X_512,B_515)
| ~ sum(X_513,multiplicative_inverse(X_512),A_511)
| sum(C_514,multiplicative_identity,B_515)
| ~ defined(X_512)
| sum(additive_identity,X_512,additive_identity) ),
inference(resolution,[status(thm)],[c_18,c_1330]) ).
tff(c_182199,plain,
! [A_1219,X_1220,B_1221] :
( ~ product(A_1219,X_1220,B_1221)
| ~ sum(multiplicative_inverse(X_1220),multiplicative_inverse(X_1220),A_1219)
| sum(multiplicative_identity,multiplicative_identity,B_1221)
| ~ defined(X_1220)
| sum(additive_identity,X_1220,additive_identity) ),
inference(resolution,[status(thm)],[c_18,c_16253]) ).
tff(c_182225,plain,
( ~ sum(multiplicative_inverse(a),multiplicative_inverse(a),add(additive_identity,additive_identity))
| sum(multiplicative_identity,multiplicative_identity,multiply(multiplicative_identity,multiplicative_identity))
| ~ defined(a)
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[status(thm)],[c_162130,c_182199]) ).
tff(c_183166,plain,
( sum(multiplicative_identity,multiplicative_identity,multiply(multiplicative_identity,multiplicative_identity))
| sum(additive_identity,a,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_62524,c_182225]) ).
tff(c_183168,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_56,c_167581,c_183166]) ).
tff(c_183169,plain,
sum(a,a,a),
inference(splitRight,[status(thm)],[c_54207]) ).
tff(c_183191,plain,
! [X_222] :
( ~ sum(X_222,a,additive_identity)
| sum(X_222,a,a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_183169,c_1190]) ).
tff(c_187582,plain,
! [X_1252] :
( ~ sum(X_1252,a,additive_identity)
| sum(X_1252,a,a) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_183191]) ).
tff(c_187606,plain,
( sum(additive_inverse(a),a,a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_8,c_187582]) ).
tff(c_187616,plain,
sum(additive_inverse(a),a,a),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_187606]) ).
tff(c_4654,plain,
! [X_13,U_333] :
( ~ sum(additive_inverse(X_13),X_13,U_333)
| sum(U_333,additive_identity,additive_identity)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_80,c_4524]) ).
tff(c_187622,plain,
( sum(a,additive_identity,additive_identity)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_187616,c_4654]) ).
tff(c_187663,plain,
sum(a,additive_identity,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_187622]) ).
tff(c_187757,plain,
sum(additive_identity,a,additive_identity),
inference(resolution,[status(thm)],[c_187663,c_10]) ).
tff(c_187811,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_56,c_187757]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : FLD040-5 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.14 % 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 : n023.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 20:12:37 EDT 2023
% 0.14/0.36 % CPUTime :
% 94.77/80.53 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 94.77/80.55
% 94.77/80.55 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 94.96/80.62
% 94.96/80.62 Inference rules
% 94.96/80.62 ----------------------
% 94.96/80.62 #Ref : 0
% 94.96/80.62 #Sup : 42451
% 94.96/80.62 #Fact : 14
% 94.96/80.62 #Define : 0
% 94.96/80.62 #Split : 27
% 94.96/80.62 #Chain : 0
% 94.96/80.62 #Close : 0
% 94.96/80.62
% 94.96/80.62 Ordering : KBO
% 94.96/80.62
% 94.96/80.62 Simplification rules
% 94.96/80.62 ----------------------
% 94.96/80.62 #Subsume : 2005
% 94.96/80.62 #Demod : 31618
% 94.96/80.62 #Tautology : 7136
% 94.96/80.62 #SimpNegUnit : 1350
% 94.96/80.62 #BackRed : 0
% 94.96/80.62
% 94.96/80.62 #Partial instantiations: 0
% 94.96/80.62 #Strategies tried : 1
% 94.96/80.62
% 94.96/80.62 Timing (in seconds)
% 94.96/80.62 ----------------------
% 94.96/80.62 Preprocessing : 0.49
% 94.96/80.62 Parsing : 0.27
% 94.96/80.62 CNF conversion : 0.03
% 94.96/80.62 Main loop : 78.92
% 94.96/80.62 Inferencing : 5.38
% 94.96/80.62 Reduction : 46.90
% 94.96/80.62 Demodulation : 42.53
% 94.96/80.62 BG Simplification : 0.23
% 94.96/80.62 Subsumption : 22.76
% 94.96/80.62 Abstraction : 0.35
% 94.96/80.62 MUC search : 0.00
% 94.96/80.62 Cooper : 0.00
% 94.96/80.62 Total : 79.51
% 94.96/80.62 Index Insertion : 0.00
% 94.96/80.62 Index Deletion : 0.00
% 94.96/80.62 Index Matching : 0.00
% 94.96/80.62 BG Taut test : 0.00
%------------------------------------------------------------------------------