TSTP Solution File: FLD040-3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : FLD040-3 : 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 : n029.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 164.64s 144.70s
% Output : CNFRefutation 165.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 39
% Syntax : Number of formulae : 436 ( 135 unt; 11 typ; 0 def)
% Number of atoms : 1034 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 1204 ( 595 ~; 609 |; 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 : 528 (; 528 !; 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_173,axiom,
defined(multiplicative_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_251,axiom,
~ sum(additive_identity,a,additive_identity),
file(unknown,unknown) ).
tff(f_249,axiom,
defined(a),
file(unknown,unknown) ).
tff(f_159,axiom,
defined(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,additive_identity,multiplicative_inverse(a)),
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_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_246,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
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_244,axiom,
! [Z,X,Y] :
( less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,X)
| ~ less_or_equal(additive_identity,Y)
| ~ product(X,Y,Z) ),
file(unknown,unknown) ).
tff(f_78,axiom,
! [X] :
( sum(additive_inverse(X),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_110,axiom,
! [X] :
( product(multiplicative_identity,X,X)
| ~ defined(X) ),
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_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_180,axiom,
! [X] :
( defined(multiplicative_inverse(X))
| ~ defined(X)
| sum(additive_identity,X,additive_identity) ),
file(unknown,unknown) ).
tff(f_196,axiom,
! [X,Y] :
( product(X,Y,multiply(X,Y))
| ~ 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(f_164,axiom,
! [X] :
( defined(additive_inverse(X))
| ~ defined(X) ),
file(unknown,unknown) ).
tff(c_34,plain,
defined(multiplicative_identity),
inference(cnfTransformation,[status(thm)],[f_173]) ).
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_106,plain,
! [Y_65] :
( ~ defined(Y_65)
| less_or_equal(Y_65,Y_65) ),
inference(factorization,[status(thm),theory(equality)],[c_46]) ).
tff(c_127,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_56,plain,
~ sum(additive_identity,a,additive_identity),
inference(cnfTransformation,[status(thm)],[f_251]) ).
tff(c_137,plain,
( ~ less_or_equal(additive_identity,a)
| ~ less_or_equal(a,additive_identity) ),
inference(resolution,[status(thm)],[c_127,c_56]) ).
tff(c_143,plain,
~ less_or_equal(a,additive_identity),
inference(splitLeft,[status(thm)],[c_137]) ).
tff(c_54,plain,
defined(a),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_28,plain,
defined(additive_identity),
inference(cnfTransformation,[status(thm)],[f_159]) ).
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,additive_identity,multiplicative_inverse(a)),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_196,plain,
! [V_119,X_116,Y_118,Z_117,U_115] :
( ~ sum(Y_118,Z_117,V_119)
| ~ sum(X_116,Z_117,U_115)
| ~ less_or_equal(X_116,Y_118)
| less_or_equal(U_115,V_119) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_224,plain,
! [X_120,U_121] :
( ~ sum(X_120,additive_identity,U_121)
| ~ less_or_equal(X_120,additive_identity)
| less_or_equal(U_121,multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[c_58,c_196]) ).
tff(c_243,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(additive_identity,multiplicative_inverse(a))
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_6,c_224]) ).
tff(c_260,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(additive_identity,multiplicative_inverse(a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_243]) ).
tff(c_262,plain,
~ less_or_equal(additive_identity,additive_identity),
inference(splitLeft,[status(thm)],[c_260]) ).
tff(c_265,plain,
~ defined(additive_identity),
inference(resolution,[status(thm)],[c_106,c_262]) ).
tff(c_271,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_265]) ).
tff(c_273,plain,
less_or_equal(additive_identity,additive_identity),
inference(splitRight,[status(thm)],[c_260]) ).
tff(c_108,plain,
! [Y_95,X_96] :
( ~ defined(Y_95)
| ~ defined(X_96)
| less_or_equal(Y_95,X_96)
| less_or_equal(X_96,Y_95) ),
inference(cnfTransformation,[status(thm)],[f_222]) ).
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_865,plain,
! [X_185,Y_186,X_187] :
( ~ less_or_equal(X_185,Y_186)
| less_or_equal(X_185,X_187)
| ~ defined(Y_186)
| ~ defined(X_187)
| less_or_equal(X_187,Y_186) ),
inference(resolution,[status(thm)],[c_108,c_44]) ).
tff(c_897,plain,
! [X_187] :
( less_or_equal(additive_identity,X_187)
| ~ defined(additive_identity)
| ~ defined(X_187)
| less_or_equal(X_187,additive_identity) ),
inference(resolution,[status(thm)],[c_273,c_865]) ).
tff(c_937,plain,
! [X_187] :
( less_or_equal(additive_identity,X_187)
| ~ defined(X_187)
| less_or_equal(X_187,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_897]) ).
tff(c_272,plain,
less_or_equal(additive_identity,multiplicative_inverse(a)),
inference(splitRight,[status(thm)],[c_260]) ).
tff(c_52,plain,
~ sum(additive_identity,additive_identity,multiplicative_identity),
inference(cnfTransformation,[status(thm)],[f_246]) ).
tff(c_138,plain,
( ~ less_or_equal(multiplicative_identity,additive_identity)
| ~ less_or_equal(additive_identity,multiplicative_identity) ),
inference(resolution,[status(thm)],[c_127,c_52]) ).
tff(c_146,plain,
~ less_or_equal(additive_identity,multiplicative_identity),
inference(splitLeft,[status(thm)],[c_138]) ).
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_147,plain,
! [X_105,Y_106,Z_107] :
( ~ product(X_105,Y_106,Z_107)
| ~ less_or_equal(additive_identity,Y_106)
| ~ less_or_equal(additive_identity,X_105)
| less_or_equal(additive_identity,Z_107) ),
inference(cnfTransformation,[status(thm)],[f_244]) ).
tff(c_160,plain,
! [X_31] :
( ~ less_or_equal(additive_identity,X_31)
| ~ less_or_equal(additive_identity,multiplicative_inverse(X_31))
| less_or_equal(additive_identity,multiplicative_identity)
| ~ defined(X_31)
| sum(additive_identity,X_31,additive_identity) ),
inference(resolution,[status(thm)],[c_18,c_147]) ).
tff(c_6144,plain,
! [X_304] :
( ~ less_or_equal(additive_identity,X_304)
| ~ less_or_equal(additive_identity,multiplicative_inverse(X_304))
| ~ defined(X_304)
| sum(additive_identity,X_304,additive_identity) ),
inference(negUnitSimplification,[status(thm)],[c_146,c_160]) ).
tff(c_6160,plain,
( ~ less_or_equal(additive_identity,a)
| ~ defined(a)
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[status(thm)],[c_272,c_6144]) ).
tff(c_6177,plain,
( ~ less_or_equal(additive_identity,a)
| sum(additive_identity,a,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_6160]) ).
tff(c_6178,plain,
~ less_or_equal(additive_identity,a),
inference(negUnitSimplification,[status(thm)],[c_56,c_6177]) ).
tff(c_6181,plain,
( ~ defined(a)
| less_or_equal(a,additive_identity) ),
inference(resolution,[status(thm)],[c_937,c_6178]) ).
tff(c_6190,plain,
less_or_equal(a,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_6181]) ).
tff(c_6192,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_143,c_6190]) ).
tff(c_6193,plain,
~ less_or_equal(multiplicative_identity,additive_identity),
inference(splitRight,[status(thm)],[c_138]) ).
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_139,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_142,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_139,c_20]) ).
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_6761,plain,
! [C_371,Z_373,A_372,D_374,Y_370,X_376,B_375] :
( ~ sum(C_371,D_374,B_375)
| ~ product(Y_370,Z_373,D_374)
| ~ product(X_376,Z_373,C_371)
| ~ sum(X_376,Y_370,A_372)
| product(A_372,Z_373,B_375) ),
inference(cnfTransformation,[status(thm)],[f_150]) ).
tff(c_13358,plain,
! [Y_512,Z_513,X_514,A_515] :
( ~ product(Y_512,Z_513,additive_identity)
| ~ product(X_514,Z_513,additive_identity)
| ~ sum(X_514,Y_512,A_515)
| product(A_515,Z_513,multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[c_58,c_6761]) ).
tff(c_13379,plain,
! [X_514,A_515] :
( ~ product(X_514,multiplicative_identity,additive_identity)
| ~ sum(X_514,additive_identity,A_515)
| product(A_515,multiplicative_identity,multiplicative_inverse(a))
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_67,c_13358]) ).
tff(c_47522,plain,
! [X_786,A_787] :
( ~ product(X_786,multiplicative_identity,additive_identity)
| ~ sum(X_786,additive_identity,A_787)
| product(A_787,multiplicative_identity,multiplicative_inverse(a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_13379]) ).
tff(c_47766,plain,
( ~ product(additive_identity,multiplicative_identity,additive_identity)
| product(additive_identity,multiplicative_identity,multiplicative_inverse(a))
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_6,c_47522]) ).
tff(c_47940,plain,
( ~ product(additive_identity,multiplicative_identity,additive_identity)
| product(additive_identity,multiplicative_identity,multiplicative_inverse(a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_47766]) ).
tff(c_47942,plain,
~ product(additive_identity,multiplicative_identity,additive_identity),
inference(splitLeft,[status(thm)],[c_47940]) ).
tff(c_47945,plain,
~ defined(additive_identity),
inference(resolution,[status(thm)],[c_67,c_47942]) ).
tff(c_47949,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_47945]) ).
tff(c_47950,plain,
product(additive_identity,multiplicative_identity,multiplicative_inverse(a)),
inference(splitRight,[status(thm)],[c_47940]) ).
tff(c_48259,plain,
product(multiplicative_identity,additive_identity,multiplicative_inverse(a)),
inference(resolution,[status(thm)],[c_47950,c_20]) ).
tff(c_6405,plain,
! [X_334,Y_331,Z_332,V_336,W_335,U_333] :
( ~ product(X_334,V_336,W_335)
| ~ product(Y_331,Z_332,V_336)
| ~ product(X_334,Y_331,U_333)
| product(U_333,Z_332,W_335) ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_10523,plain,
! [Y_460,Z_461,X_462,U_463] :
( ~ product(Y_460,Z_461,X_462)
| ~ product(multiplicative_identity,Y_460,U_463)
| product(U_463,Z_461,X_462)
| ~ defined(X_462) ),
inference(resolution,[status(thm)],[c_16,c_6405]) ).
tff(c_10544,plain,
! [X_30,U_463] :
( ~ product(multiplicative_identity,X_30,U_463)
| product(U_463,multiplicative_identity,X_30)
| ~ defined(X_30) ),
inference(resolution,[status(thm)],[c_67,c_10523]) ).
tff(c_48283,plain,
( product(multiplicative_inverse(a),multiplicative_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_48259,c_10544]) ).
tff(c_48332,plain,
product(multiplicative_inverse(a),multiplicative_identity,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_48283]) ).
tff(c_6570,plain,
! [W_353,V_355,X_354,U_351,Y_356,Z_352] :
( ~ product(U_351,Z_352,W_353)
| ~ product(Y_356,Z_352,V_355)
| ~ product(X_354,Y_356,U_351)
| product(X_354,V_355,W_353) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_6588,plain,
! [Y_356,X_30,V_355,X_354] :
( ~ product(Y_356,X_30,V_355)
| ~ product(X_354,Y_356,multiplicative_identity)
| product(X_354,V_355,X_30)
| ~ defined(X_30) ),
inference(resolution,[status(thm)],[c_16,c_6570]) ).
tff(c_48374,plain,
! [X_354] :
( ~ product(X_354,multiplicative_inverse(a),multiplicative_identity)
| product(X_354,additive_identity,multiplicative_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[c_48332,c_6588]) ).
tff(c_50929,plain,
! [X_808] :
( ~ product(X_808,multiplicative_inverse(a),multiplicative_identity)
| product(X_808,additive_identity,multiplicative_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_48374]) ).
tff(c_50948,plain,
( product(a,additive_identity,multiplicative_identity)
| ~ defined(a)
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[status(thm)],[c_142,c_50929]) ).
tff(c_50959,plain,
( product(a,additive_identity,multiplicative_identity)
| sum(additive_identity,a,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_50948]) ).
tff(c_50960,plain,
product(a,additive_identity,multiplicative_identity),
inference(negUnitSimplification,[status(thm)],[c_56,c_50959]) ).
tff(c_51045,plain,
product(additive_identity,a,multiplicative_identity),
inference(resolution,[status(thm)],[c_50960,c_20]) ).
tff(c_51071,plain,
! [X_354] :
( ~ product(X_354,additive_identity,multiplicative_identity)
| product(X_354,multiplicative_identity,a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_51045,c_6588]) ).
tff(c_52480,plain,
! [X_820] :
( ~ product(X_820,additive_identity,multiplicative_identity)
| product(X_820,multiplicative_identity,a) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_51071]) ).
tff(c_54261,plain,
! [X_824] :
( product(multiplicative_identity,X_824,a)
| ~ product(X_824,additive_identity,multiplicative_identity) ),
inference(resolution,[status(thm)],[c_52480,c_20]) ).
tff(c_54282,plain,
product(multiplicative_identity,a,a),
inference(resolution,[status(thm)],[c_50960,c_54261]) ).
tff(c_6652,plain,
! [B_361,A_358,X_362,Y_359,Z_360,D_364,C_363] :
( ~ product(Y_359,Z_360,D_364)
| ~ product(X_362,Z_360,C_363)
| ~ product(A_358,Z_360,B_361)
| ~ sum(X_362,Y_359,A_358)
| sum(C_363,D_364,B_361) ),
inference(cnfTransformation,[status(thm)],[f_136]) ).
tff(c_17635,plain,
! [X_575,X_576,A_573,B_572,C_574] :
( ~ product(X_576,X_575,C_574)
| ~ product(A_573,X_575,B_572)
| ~ sum(X_576,multiplicative_identity,A_573)
| sum(C_574,X_575,B_572)
| ~ defined(X_575) ),
inference(resolution,[status(thm)],[c_16,c_6652]) ).
tff(c_57666,plain,
! [A_840,X_841,B_842] :
( ~ product(A_840,X_841,B_842)
| ~ sum(multiplicative_identity,multiplicative_identity,A_840)
| sum(X_841,X_841,B_842)
| ~ defined(X_841) ),
inference(resolution,[status(thm)],[c_16,c_17635]) ).
tff(c_57724,plain,
( ~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| sum(a,a,a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_54282,c_57666]) ).
tff(c_57941,plain,
( ~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| sum(a,a,a) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_57724]) ).
tff(c_67640,plain,
~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(splitLeft,[status(thm)],[c_57941]) ).
tff(c_47951,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(splitRight,[status(thm)],[c_47940]) ).
tff(c_48088,plain,
product(multiplicative_identity,additive_identity,additive_identity),
inference(resolution,[status(thm)],[c_47951,c_20]) ).
tff(c_48118,plain,
! [X_354] :
( ~ product(X_354,multiplicative_identity,multiplicative_identity)
| product(X_354,additive_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_48088,c_6588]) ).
tff(c_49452,plain,
! [X_796] :
( ~ product(X_796,multiplicative_identity,multiplicative_identity)
| product(X_796,additive_identity,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_48118]) ).
tff(c_49496,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_49452]) ).
tff(c_49534,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_49496]) ).
tff(c_50406,plain,
sum(additive_identity,multiplicative_identity,additive_identity),
inference(splitLeft,[status(thm)],[c_49534]) ).
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_6430,plain,
! [Z_337,V_340,W_338,X_341,Y_342,U_339] :
( ~ sum(X_341,V_340,W_338)
| ~ sum(Y_342,Z_337,V_340)
| ~ sum(X_341,Y_342,U_339)
| sum(U_339,Z_337,W_338) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_9887,plain,
! [Y_452,Z_453,X_454,U_455] :
( ~ sum(Y_452,Z_453,X_454)
| ~ sum(additive_identity,Y_452,U_455)
| sum(U_455,Z_453,X_454)
| ~ defined(X_454) ),
inference(resolution,[status(thm)],[c_6,c_6430]) ).
tff(c_9977,plain,
! [X_13,U_455] :
( ~ sum(additive_identity,X_13,U_455)
| sum(U_455,additive_identity,X_13)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_80,c_9887]) ).
tff(c_50414,plain,
( sum(additive_identity,additive_identity,multiplicative_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[c_50406,c_9977]) ).
tff(c_50455,plain,
sum(additive_identity,additive_identity,multiplicative_identity),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_50414]) ).
tff(c_50457,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_50455]) ).
tff(c_50459,plain,
~ sum(additive_identity,multiplicative_identity,additive_identity),
inference(splitRight,[status(thm)],[c_49534]) ).
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_20532,plain,
! [Y_606,Z_607,X_608,U_609] :
( ~ product(Y_606,Z_607,X_608)
| ~ product(multiplicative_inverse(X_608),Y_606,U_609)
| product(U_609,Z_607,multiplicative_identity)
| ~ defined(X_608)
| sum(additive_identity,X_608,additive_identity) ),
inference(resolution,[status(thm)],[c_18,c_6405]) ).
tff(c_71508,plain,
! [X_918,U_919] :
( ~ product(multiplicative_inverse(X_918),X_918,U_919)
| product(U_919,multiplicative_identity,multiplicative_identity)
| sum(additive_identity,X_918,additive_identity)
| ~ defined(X_918) ),
inference(resolution,[status(thm)],[c_67,c_20532]) ).
tff(c_71606,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_71508]) ).
tff(c_71665,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_71606]) ).
tff(c_71666,plain,
( product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| ~ defined(multiplicative_inverse(multiplicative_identity)) ),
inference(negUnitSimplification,[status(thm)],[c_50459,c_71665]) ).
tff(c_71667,plain,
~ defined(multiplicative_inverse(multiplicative_identity)),
inference(splitLeft,[status(thm)],[c_71666]) ).
tff(c_71670,plain,
( sum(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[c_36,c_71667]) ).
tff(c_71673,plain,
sum(additive_identity,multiplicative_identity,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_71670]) ).
tff(c_71675,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_50459,c_71673]) ).
tff(c_71676,plain,
product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity),
inference(splitRight,[status(thm)],[c_71666]) ).
tff(c_17690,plain,
! [A_573,X_30,B_572] :
( ~ product(A_573,X_30,B_572)
| ~ sum(multiplicative_identity,multiplicative_identity,A_573)
| sum(X_30,X_30,B_572)
| ~ defined(X_30) ),
inference(resolution,[status(thm)],[c_16,c_17635]) ).
tff(c_71742,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_71676,c_17690]) ).
tff(c_71797,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_71742]) ).
tff(c_71798,plain,
~ sum(multiplicative_identity,multiplicative_identity,multiplicative_inverse(multiplicative_identity)),
inference(negUnitSimplification,[status(thm)],[c_67640,c_71797]) ).
tff(c_71677,plain,
defined(multiplicative_inverse(multiplicative_identity)),
inference(splitRight,[status(thm)],[c_71666]) ).
tff(c_9457,plain,
! [Y_444,X_445,V_446,X_447] :
( ~ product(Y_444,X_445,V_446)
| ~ product(X_447,Y_444,multiplicative_identity)
| product(X_447,V_446,X_445)
| ~ defined(X_445) ),
inference(resolution,[status(thm)],[c_16,c_6570]) ).
tff(c_9477,plain,
! [X_447,X_30] :
( ~ product(X_447,multiplicative_identity,multiplicative_identity)
| product(X_447,X_30,X_30)
| ~ defined(X_30) ),
inference(resolution,[status(thm)],[c_16,c_9457]) ).
tff(c_71839,plain,
! [X_30] :
( product(multiplicative_inverse(multiplicative_identity),X_30,X_30)
| ~ defined(X_30) ),
inference(resolution,[status(thm)],[c_71676,c_9477]) ).
tff(c_21319,plain,
! [Y_612,X_613,V_614,X_615] :
( ~ product(Y_612,X_613,V_614)
| ~ product(X_615,Y_612,multiplicative_inverse(X_613))
| product(X_615,V_614,multiplicative_identity)
| ~ defined(X_613)
| sum(additive_identity,X_613,additive_identity) ),
inference(resolution,[status(thm)],[c_18,c_6570]) ).
tff(c_21347,plain,
! [X_615,X_30] :
( ~ product(X_615,X_30,multiplicative_inverse(multiplicative_identity))
| product(X_615,X_30,multiplicative_identity)
| ~ defined(multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(X_30) ),
inference(resolution,[status(thm)],[c_67,c_21319]) ).
tff(c_21373,plain,
! [X_615,X_30] :
( ~ product(X_615,X_30,multiplicative_inverse(multiplicative_identity))
| product(X_615,X_30,multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(X_30) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_21347]) ).
tff(c_80396,plain,
! [X_962,X_963] :
( ~ product(X_962,X_963,multiplicative_inverse(multiplicative_identity))
| product(X_962,X_963,multiplicative_identity)
| ~ defined(X_963) ),
inference(negUnitSimplification,[status(thm)],[c_50459,c_21373]) ).
tff(c_80410,plain,
( product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ defined(multiplicative_inverse(multiplicative_identity)) ),
inference(resolution,[status(thm)],[c_71839,c_80396]) ).
tff(c_80495,plain,
product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(demodulation,[status(thm),theory(equality)],[c_71677,c_80410]) ).
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_17319,plain,
! [Y_569,V_566,Y_568,X_567,X_570] :
( ~ product(Y_569,Y_568,V_566)
| ~ product(X_570,Y_569,X_567)
| product(X_570,V_566,multiply(X_567,Y_568))
| ~ defined(Y_568)
| ~ defined(X_567) ),
inference(resolution,[status(thm)],[c_40,c_6570]) ).
tff(c_160520,plain,
! [X_1277,X_1278,X_1279] :
( ~ product(X_1277,multiplicative_inverse(X_1278),X_1279)
| product(X_1277,multiplicative_identity,multiply(X_1279,X_1278))
| ~ defined(X_1279)
| ~ defined(X_1278)
| sum(additive_identity,X_1278,additive_identity) ),
inference(resolution,[status(thm)],[c_18,c_17319]) ).
tff(c_160644,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_80495,c_160520]) ).
tff(c_160871,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_160644]) ).
tff(c_160872,plain,
product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiply(multiplicative_identity,multiplicative_identity)),
inference(negUnitSimplification,[status(thm)],[c_50459,c_160871]) ).
tff(c_162479,plain,
product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiply(multiplicative_identity,multiplicative_identity)),
inference(resolution,[status(thm)],[c_160872,c_20]) ).
tff(c_162533,plain,
( product(multiply(multiplicative_identity,multiplicative_identity),multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| ~ defined(multiplicative_inverse(multiplicative_identity)) ),
inference(resolution,[status(thm)],[c_162479,c_10544]) ).
tff(c_162622,plain,
product(multiply(multiplicative_identity,multiplicative_identity),multiplicative_identity,multiplicative_inverse(multiplicative_identity)),
inference(demodulation,[status(thm),theory(equality)],[c_71677,c_162533]) ).
tff(c_162670,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_162622,c_17690]) ).
tff(c_162752,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_162670]) ).
tff(c_162753,plain,
~ sum(multiplicative_identity,multiplicative_identity,multiply(multiplicative_identity,multiplicative_identity)),
inference(negUnitSimplification,[status(thm)],[c_71798,c_162752]) ).
tff(c_6343,plain,
! [W_329,U_327,X_328,Z_324,Y_325,V_326] :
( ~ sum(U_327,Z_324,W_329)
| ~ sum(Y_325,Z_324,V_326)
| ~ sum(X_328,Y_325,U_327)
| sum(X_328,V_326,W_329) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_9006,plain,
! [Y_432,X_433,V_434,X_435] :
( ~ sum(Y_432,X_433,V_434)
| ~ sum(X_435,Y_432,additive_identity)
| sum(X_435,V_434,X_433)
| ~ defined(X_433) ),
inference(resolution,[status(thm)],[c_6,c_6343]) ).
tff(c_9194,plain,
! [X_439,X_440] :
( ~ sum(X_439,additive_identity,additive_identity)
| sum(X_439,X_440,X_440)
| ~ defined(X_440) ),
inference(resolution,[status(thm)],[c_6,c_9006]) ).
tff(c_9209,plain,
! [X_440] :
( sum(additive_inverse(additive_identity),X_440,X_440)
| ~ defined(X_440)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_8,c_9194]) ).
tff(c_9227,plain,
! [X_441] :
( sum(additive_inverse(additive_identity),X_441,X_441)
| ~ defined(X_441) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_9209]) ).
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_9291,plain,
! [X_441] :
( sum(X_441,additive_inverse(additive_identity),X_441)
| ~ defined(X_441) ),
inference(resolution,[status(thm)],[c_9227,c_10]) ).
tff(c_11489,plain,
! [X_487,X_488] :
( ~ sum(X_487,additive_inverse(X_488),additive_identity)
| sum(X_487,additive_identity,X_488)
| ~ defined(X_488) ),
inference(resolution,[status(thm)],[c_8,c_9006]) ).
tff(c_11493,plain,
( sum(additive_identity,additive_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_9291,c_11489]) ).
tff(c_11511,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_11493]) ).
tff(c_8156,plain,
! [Y_414,Z_415,U_416] :
( ~ sum(Y_414,Z_415,additive_identity)
| ~ sum(additive_identity,Y_414,U_416)
| sum(U_416,Z_415,multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[c_58,c_6430]) ).
tff(c_8172,plain,
! [U_416] :
( ~ sum(additive_identity,additive_identity,U_416)
| sum(U_416,additive_identity,multiplicative_inverse(a))
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_6,c_8156]) ).
tff(c_8474,plain,
! [U_420] :
( ~ sum(additive_identity,additive_identity,U_420)
| sum(U_420,additive_identity,multiplicative_inverse(a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_8172]) ).
tff(c_8510,plain,
! [U_420] :
( sum(additive_identity,U_420,multiplicative_inverse(a))
| ~ sum(additive_identity,additive_identity,U_420) ),
inference(resolution,[status(thm)],[c_8474,c_10]) ).
tff(c_6456,plain,
! [Y_342,Z_337,X_13,U_339] :
( ~ sum(Y_342,Z_337,X_13)
| ~ sum(additive_identity,Y_342,U_339)
| sum(U_339,Z_337,X_13)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_6,c_6430]) ).
tff(c_11524,plain,
! [U_339] :
( ~ sum(additive_identity,additive_identity,U_339)
| sum(U_339,additive_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_11511,c_6456]) ).
tff(c_11916,plain,
! [U_498] :
( ~ sum(additive_identity,additive_identity,U_498)
| sum(U_498,additive_identity,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_11524]) ).
tff(c_11921,plain,
( sum(multiplicative_inverse(a),additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[c_8510,c_11916]) ).
tff(c_11955,plain,
sum(multiplicative_inverse(a),additive_identity,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_11511,c_11921]) ).
tff(c_6369,plain,
! [Y_325,X_13,V_326,X_328] :
( ~ sum(Y_325,X_13,V_326)
| ~ sum(X_328,Y_325,additive_identity)
| sum(X_328,V_326,X_13)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_6,c_6343]) ).
tff(c_11992,plain,
! [X_328] :
( ~ sum(X_328,multiplicative_inverse(a),additive_identity)
| sum(X_328,additive_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_11955,c_6369]) ).
tff(c_13822,plain,
! [X_521] :
( ~ sum(X_521,multiplicative_inverse(a),additive_identity)
| sum(X_521,additive_identity,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_11992]) ).
tff(c_13857,plain,
( sum(additive_inverse(multiplicative_inverse(a)),additive_identity,additive_identity)
| ~ defined(multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[c_8,c_13822]) ).
tff(c_14265,plain,
~ defined(multiplicative_inverse(a)),
inference(splitLeft,[status(thm)],[c_13857]) ).
tff(c_14268,plain,
( sum(additive_identity,a,additive_identity)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_36,c_14265]) ).
tff(c_14271,plain,
sum(additive_identity,a,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_14268]) ).
tff(c_14273,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_56,c_14271]) ).
tff(c_14275,plain,
defined(multiplicative_inverse(a)),
inference(splitRight,[status(thm)],[c_13857]) ).
tff(c_10546,plain,
! [U_464,X_465] :
( ~ sum(additive_identity,additive_identity,U_464)
| sum(U_464,X_465,X_465)
| ~ defined(X_465) ),
inference(resolution,[status(thm)],[c_6,c_9887]) ).
tff(c_10598,plain,
! [X_466] :
( sum(multiplicative_inverse(a),X_466,X_466)
| ~ defined(X_466) ),
inference(resolution,[status(thm)],[c_58,c_10546]) ).
tff(c_6370,plain,
! [Y_325,V_326,X_328] :
( ~ sum(Y_325,additive_identity,V_326)
| ~ sum(X_328,Y_325,additive_identity)
| sum(X_328,V_326,multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[c_58,c_6343]) ).
tff(c_10615,plain,
! [X_328] :
( ~ sum(X_328,multiplicative_inverse(a),additive_identity)
| sum(X_328,additive_identity,multiplicative_inverse(a))
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_10598,c_6370]) ).
tff(c_20356,plain,
! [X_605] :
( ~ sum(X_605,multiplicative_inverse(a),additive_identity)
| sum(X_605,additive_identity,multiplicative_inverse(a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_10615]) ).
tff(c_20408,plain,
( sum(additive_inverse(multiplicative_inverse(a)),additive_identity,multiplicative_inverse(a))
| ~ defined(multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[c_8,c_20356]) ).
tff(c_20442,plain,
sum(additive_inverse(multiplicative_inverse(a)),additive_identity,multiplicative_inverse(a)),
inference(demodulation,[status(thm),theory(equality)],[c_14275,c_20408]) ).
tff(c_20531,plain,
sum(additive_identity,additive_inverse(multiplicative_inverse(a)),multiplicative_inverse(a)),
inference(resolution,[status(thm)],[c_20442,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_16215,plain,
! [X_557,Y_558,U_554,Y_555,Z_556] :
( ~ sum(Y_555,Z_556,Y_558)
| ~ sum(X_557,Y_555,U_554)
| sum(U_554,Z_556,add(X_557,Y_558))
| ~ defined(Y_558)
| ~ defined(X_557) ),
inference(resolution,[status(thm)],[c_38,c_6430]) ).
tff(c_16347,plain,
! [X_557,X_14,U_554] :
( ~ sum(X_557,additive_inverse(X_14),U_554)
| sum(U_554,X_14,add(X_557,additive_identity))
| ~ defined(additive_identity)
| ~ defined(X_557)
| ~ defined(X_14) ),
inference(resolution,[status(thm)],[c_8,c_16215]) ).
tff(c_87763,plain,
! [X_998,X_999,U_1000] :
( ~ sum(X_998,additive_inverse(X_999),U_1000)
| sum(U_1000,X_999,add(X_998,additive_identity))
| ~ defined(X_998)
| ~ defined(X_999) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_16347]) ).
tff(c_87944,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_20531,c_87763]) ).
tff(c_88239,plain,
sum(multiplicative_inverse(a),multiplicative_inverse(a),add(additive_identity,additive_identity)),
inference(demodulation,[status(thm),theory(equality)],[c_14275,c_28,c_87944]) ).
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_10570,plain,
! [X_465] :
( sum(add(additive_identity,additive_identity),X_465,X_465)
| ~ defined(X_465)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_38,c_10546]) ).
tff(c_10726,plain,
! [X_470] :
( sum(add(additive_identity,additive_identity),X_470,X_470)
| ~ defined(X_470) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_10570]) ).
tff(c_6265,plain,
! [Z_315,V_317,Y_316,X_314,U_313] :
( ~ sum(Y_316,Z_315,V_317)
| ~ sum(X_314,Z_315,U_313)
| ~ less_or_equal(X_314,Y_316)
| less_or_equal(U_313,V_317) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_6305,plain,
! [X_322,U_323] :
( ~ sum(X_322,additive_identity,U_323)
| ~ less_or_equal(X_322,additive_identity)
| less_or_equal(U_323,multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[c_58,c_6265]) ).
tff(c_6324,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(additive_identity,multiplicative_inverse(a))
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_6,c_6305]) ).
tff(c_6341,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(additive_identity,multiplicative_inverse(a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_6324]) ).
tff(c_6371,plain,
~ less_or_equal(additive_identity,additive_identity),
inference(splitLeft,[status(thm)],[c_6341]) ).
tff(c_6374,plain,
~ defined(additive_identity),
inference(resolution,[status(thm)],[c_106,c_6371]) ).
tff(c_6380,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_6374]) ).
tff(c_6382,plain,
less_or_equal(additive_identity,additive_identity),
inference(splitRight,[status(thm)],[c_6341]) ).
tff(c_6523,plain,
! [X_348,X_349,U_350] :
( ~ sum(X_348,X_349,U_350)
| ~ less_or_equal(X_348,additive_identity)
| less_or_equal(U_350,X_349)
| ~ defined(X_349) ),
inference(resolution,[status(thm)],[c_6,c_6265]) ).
tff(c_6550,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(multiplicative_inverse(a),additive_identity)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_58,c_6523]) ).
tff(c_6569,plain,
less_or_equal(multiplicative_inverse(a),additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_6382,c_6550]) ).
tff(c_9040,plain,
! [X_435] :
( ~ sum(X_435,additive_identity,additive_identity)
| sum(X_435,multiplicative_inverse(a),additive_identity)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_58,c_9006]) ).
tff(c_9072,plain,
! [X_436] :
( ~ sum(X_436,additive_identity,additive_identity)
| sum(X_436,multiplicative_inverse(a),additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_9040]) ).
tff(c_9103,plain,
! [X_437] :
( sum(multiplicative_inverse(a),X_437,additive_identity)
| ~ sum(X_437,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[c_9072,c_10]) ).
tff(c_6288,plain,
! [X_314,X_13,U_313] :
( ~ sum(X_314,X_13,U_313)
| ~ less_or_equal(X_314,additive_identity)
| less_or_equal(U_313,X_13)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_6,c_6265]) ).
tff(c_9124,plain,
! [X_437] :
( ~ less_or_equal(multiplicative_inverse(a),additive_identity)
| less_or_equal(additive_identity,X_437)
| ~ defined(X_437)
| ~ sum(X_437,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[c_9103,c_6288]) ).
tff(c_9146,plain,
! [X_437] :
( less_or_equal(additive_identity,X_437)
| ~ defined(X_437)
| ~ sum(X_437,additive_identity,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_6569,c_9124]) ).
tff(c_10735,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_10726,c_9146]) ).
tff(c_10771,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_10735]) ).
tff(c_11057,plain,
~ defined(add(additive_identity,additive_identity)),
inference(splitLeft,[status(thm)],[c_10771]) ).
tff(c_11150,plain,
~ defined(additive_identity),
inference(resolution,[status(thm)],[c_26,c_11057]) ).
tff(c_11154,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_11150]) ).
tff(c_11156,plain,
defined(add(additive_identity,additive_identity)),
inference(splitRight,[status(thm)],[c_10771]) ).
tff(c_30,plain,
! [X_51] :
( ~ defined(X_51)
| defined(additive_inverse(X_51)) ),
inference(cnfTransformation,[status(thm)],[f_164]) ).
tff(c_6799,plain,
! [X_378,U_379,X_380] :
( ~ sum(X_378,additive_identity,U_379)
| ~ less_or_equal(X_378,X_380)
| less_or_equal(U_379,X_380)
| ~ defined(X_380) ),
inference(resolution,[status(thm)],[c_80,c_6265]) ).
tff(c_6815,plain,
! [X_380] :
( ~ less_or_equal(additive_inverse(additive_identity),X_380)
| less_or_equal(additive_identity,X_380)
| ~ defined(X_380)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_8,c_6799]) ).
tff(c_6837,plain,
! [X_381] :
( ~ less_or_equal(additive_inverse(additive_identity),X_381)
| less_or_equal(additive_identity,X_381)
| ~ defined(X_381) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_6815]) ).
tff(c_6863,plain,
( less_or_equal(additive_identity,additive_inverse(additive_identity))
| ~ defined(additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[c_106,c_6837]) ).
tff(c_6866,plain,
~ defined(additive_inverse(additive_identity)),
inference(splitLeft,[status(thm)],[c_6863]) ).
tff(c_6869,plain,
~ defined(additive_identity),
inference(resolution,[status(thm)],[c_30,c_6866]) ).
tff(c_6873,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_6869]) ).
tff(c_6875,plain,
defined(additive_inverse(additive_identity)),
inference(splitRight,[status(thm)],[c_6863]) ).
tff(c_10590,plain,
! [X_465] :
( sum(add(additive_identity,additive_identity),X_465,X_465)
| ~ defined(X_465) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_10570]) ).
tff(c_11219,plain,
! [Y_480,X_481,V_482,X_483] :
( ~ sum(Y_480,X_481,V_482)
| ~ sum(X_483,Y_480,additive_inverse(X_481))
| sum(X_483,V_482,additive_identity)
| ~ defined(X_481) ),
inference(resolution,[status(thm)],[c_8,c_6343]) ).
tff(c_11279,plain,
! [X_483,X_13] :
( ~ sum(X_483,X_13,additive_inverse(additive_identity))
| sum(X_483,X_13,additive_identity)
| ~ defined(additive_identity)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_80,c_11219]) ).
tff(c_26936,plain,
! [X_671,X_672] :
( ~ sum(X_671,X_672,additive_inverse(additive_identity))
| sum(X_671,X_672,additive_identity)
| ~ defined(X_672) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_11279]) ).
tff(c_27053,plain,
( sum(add(additive_identity,additive_identity),additive_inverse(additive_identity),additive_identity)
| ~ defined(additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[c_10590,c_26936]) ).
tff(c_27178,plain,
sum(add(additive_identity,additive_identity),additive_inverse(additive_identity),additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_6875,c_27053]) ).
tff(c_7147,plain,
! [Y_391,V_392,X_393] :
( ~ sum(Y_391,additive_identity,V_392)
| ~ sum(X_393,Y_391,additive_identity)
| sum(X_393,V_392,multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[c_58,c_6343]) ).
tff(c_7163,plain,
! [X_393] :
( ~ sum(X_393,additive_inverse(additive_identity),additive_identity)
| sum(X_393,additive_identity,multiplicative_inverse(a))
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_8,c_7147]) ).
tff(c_7180,plain,
! [X_393] :
( ~ sum(X_393,additive_inverse(additive_identity),additive_identity)
| sum(X_393,additive_identity,multiplicative_inverse(a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_7163]) ).
tff(c_27279,plain,
sum(add(additive_identity,additive_identity),additive_identity,multiplicative_inverse(a)),
inference(resolution,[status(thm)],[c_27178,c_7180]) ).
tff(c_27455,plain,
sum(additive_identity,add(additive_identity,additive_identity),multiplicative_inverse(a)),
inference(resolution,[status(thm)],[c_27279,c_10]) ).
tff(c_16830,plain,
! [X_564,Y_563,X_562,A_560,Z_561] :
( ~ product(Y_563,Z_561,X_562)
| ~ product(X_564,Z_561,additive_identity)
| ~ sum(X_564,Y_563,A_560)
| product(A_560,Z_561,X_562)
| ~ defined(X_562) ),
inference(resolution,[status(thm)],[c_6,c_6761]) ).
tff(c_52584,plain,
! [X_821,X_822,A_823] :
( ~ product(X_821,multiplicative_identity,additive_identity)
| ~ sum(X_821,X_822,A_823)
| product(A_823,multiplicative_identity,X_822)
| ~ defined(X_822) ),
inference(resolution,[status(thm)],[c_67,c_16830]) ).
tff(c_52986,plain,
( ~ product(additive_identity,multiplicative_identity,additive_identity)
| product(multiplicative_inverse(a),multiplicative_identity,add(additive_identity,additive_identity))
| ~ defined(add(additive_identity,additive_identity)) ),
inference(resolution,[status(thm)],[c_27455,c_52584]) ).
tff(c_53727,plain,
product(multiplicative_inverse(a),multiplicative_identity,add(additive_identity,additive_identity)),
inference(demodulation,[status(thm),theory(equality)],[c_11156,c_47951,c_52986]) ).
tff(c_59220,plain,
product(multiplicative_identity,multiplicative_inverse(a),add(additive_identity,additive_identity)),
inference(resolution,[status(thm)],[c_53727,c_20]) ).
tff(c_14603,plain,
! [Y_534,U_535,Z_537,X_533,Y_536] :
( ~ product(Y_534,Z_537,Y_536)
| ~ product(X_533,Y_534,U_535)
| product(U_535,Z_537,multiply(X_533,Y_536))
| ~ defined(Y_536)
| ~ defined(X_533) ),
inference(resolution,[status(thm)],[c_40,c_6405]) ).
tff(c_14627,plain,
! [X_533,X_31,U_535] :
( ~ product(X_533,multiplicative_inverse(X_31),U_535)
| product(U_535,X_31,multiply(X_533,multiplicative_identity))
| ~ defined(multiplicative_identity)
| ~ defined(X_533)
| ~ defined(X_31)
| sum(additive_identity,X_31,additive_identity) ),
inference(resolution,[status(thm)],[c_18,c_14603]) ).
tff(c_163116,plain,
! [X_1285,X_1286,U_1287] :
( ~ product(X_1285,multiplicative_inverse(X_1286),U_1287)
| product(U_1287,X_1286,multiply(X_1285,multiplicative_identity))
| ~ defined(X_1285)
| ~ defined(X_1286)
| sum(additive_identity,X_1286,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_14627]) ).
tff(c_163237,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_59220,c_163116]) ).
tff(c_163437,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_163237]) ).
tff(c_163438,plain,
product(add(additive_identity,additive_identity),a,multiply(multiplicative_identity,multiplicative_identity)),
inference(negUnitSimplification,[status(thm)],[c_56,c_163437]) ).
tff(c_23775,plain,
! [C_647,B_645,X_648,A_646,X_649] :
( ~ product(X_649,X_648,C_647)
| ~ product(A_646,X_648,B_645)
| ~ sum(X_649,multiplicative_inverse(X_648),A_646)
| sum(C_647,multiplicative_identity,B_645)
| ~ defined(X_648)
| sum(additive_identity,X_648,additive_identity) ),
inference(resolution,[status(thm)],[c_18,c_6652]) ).
tff(c_178451,plain,
! [A_1334,X_1335,B_1336] :
( ~ product(A_1334,X_1335,B_1336)
| ~ sum(multiplicative_inverse(X_1335),multiplicative_inverse(X_1335),A_1334)
| sum(multiplicative_identity,multiplicative_identity,B_1336)
| ~ defined(X_1335)
| sum(additive_identity,X_1335,additive_identity) ),
inference(resolution,[status(thm)],[c_18,c_23775]) ).
tff(c_178461,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_163438,c_178451]) ).
tff(c_179437,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_88239,c_178461]) ).
tff(c_179439,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_56,c_162753,c_179437]) ).
tff(c_179441,plain,
sum(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(splitRight,[status(thm)],[c_57941]) ).
tff(c_179547,plain,
! [X_328] :
( ~ sum(X_328,multiplicative_identity,additive_identity)
| sum(X_328,multiplicative_identity,multiplicative_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[c_179441,c_6369]) ).
tff(c_184941,plain,
! [X_1365] :
( ~ sum(X_1365,multiplicative_identity,additive_identity)
| sum(X_1365,multiplicative_identity,multiplicative_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_179547]) ).
tff(c_185238,plain,
! [X_1366] :
( sum(multiplicative_identity,X_1366,multiplicative_identity)
| ~ sum(X_1366,multiplicative_identity,additive_identity) ),
inference(resolution,[status(thm)],[c_184941,c_10]) ).
tff(c_185259,plain,
( sum(multiplicative_identity,additive_inverse(multiplicative_identity),multiplicative_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[c_8,c_185238]) ).
tff(c_185270,plain,
sum(multiplicative_identity,additive_inverse(multiplicative_identity),multiplicative_identity),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_185259]) ).
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_6285,plain,
! [X_314,X_14,U_313] :
( ~ sum(X_314,additive_inverse(X_14),U_313)
| ~ less_or_equal(X_314,X_14)
| less_or_equal(U_313,additive_identity)
| ~ defined(X_14) ),
inference(resolution,[status(thm)],[c_79,c_6265]) ).
tff(c_185278,plain,
( ~ less_or_equal(multiplicative_identity,multiplicative_identity)
| less_or_equal(multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[c_185270,c_6285]) ).
tff(c_185320,plain,
( ~ less_or_equal(multiplicative_identity,multiplicative_identity)
| less_or_equal(multiplicative_identity,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_185278]) ).
tff(c_185321,plain,
~ less_or_equal(multiplicative_identity,multiplicative_identity),
inference(negUnitSimplification,[status(thm)],[c_6193,c_185320]) ).
tff(c_185365,plain,
~ defined(multiplicative_identity),
inference(resolution,[status(thm)],[c_106,c_185321]) ).
tff(c_185384,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_34,c_185365]) ).
tff(c_185385,plain,
~ less_or_equal(additive_identity,a),
inference(splitRight,[status(thm)],[c_137]) ).
tff(c_185885,plain,
! [Z_1432,D_1433,A_1431,C_1430,B_1434,X_1435,Y_1429] :
( ~ sum(C_1430,D_1433,B_1434)
| ~ product(Y_1429,Z_1432,D_1433)
| ~ product(X_1435,Z_1432,C_1430)
| ~ sum(X_1435,Y_1429,A_1431)
| product(A_1431,Z_1432,B_1434) ),
inference(cnfTransformation,[status(thm)],[f_150]) ).
tff(c_193895,plain,
! [Y_1592,Z_1593,X_1594,A_1595] :
( ~ product(Y_1592,Z_1593,additive_identity)
| ~ product(X_1594,Z_1593,additive_identity)
| ~ sum(X_1594,Y_1592,A_1595)
| product(A_1595,Z_1593,multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[c_58,c_185885]) ).
tff(c_193916,plain,
! [X_1594,A_1595] :
( ~ product(X_1594,multiplicative_identity,additive_identity)
| ~ sum(X_1594,additive_identity,A_1595)
| product(A_1595,multiplicative_identity,multiplicative_inverse(a))
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_67,c_193895]) ).
tff(c_227714,plain,
! [X_1856,A_1857] :
( ~ product(X_1856,multiplicative_identity,additive_identity)
| ~ sum(X_1856,additive_identity,A_1857)
| product(A_1857,multiplicative_identity,multiplicative_inverse(a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_193916]) ).
tff(c_227995,plain,
( ~ product(additive_identity,multiplicative_identity,additive_identity)
| product(additive_identity,multiplicative_identity,multiplicative_inverse(a))
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_6,c_227714]) ).
tff(c_228200,plain,
( ~ product(additive_identity,multiplicative_identity,additive_identity)
| product(additive_identity,multiplicative_identity,multiplicative_inverse(a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_227995]) ).
tff(c_228202,plain,
~ product(additive_identity,multiplicative_identity,additive_identity),
inference(splitLeft,[status(thm)],[c_228200]) ).
tff(c_228205,plain,
~ defined(additive_identity),
inference(resolution,[status(thm)],[c_67,c_228202]) ).
tff(c_228209,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_228205]) ).
tff(c_228210,plain,
product(additive_identity,multiplicative_identity,multiplicative_inverse(a)),
inference(splitRight,[status(thm)],[c_228200]) ).
tff(c_228466,plain,
product(multiplicative_identity,additive_identity,multiplicative_inverse(a)),
inference(resolution,[status(thm)],[c_228210,c_20]) ).
tff(c_185493,plain,
! [Z_1385,U_1386,V_1389,W_1388,X_1387,Y_1384] :
( ~ product(X_1387,V_1389,W_1388)
| ~ product(Y_1384,Z_1385,V_1389)
| ~ product(X_1387,Y_1384,U_1386)
| product(U_1386,Z_1385,W_1388) ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_187571,plain,
! [Y_1483,Z_1484,X_1485,U_1486] :
( ~ product(Y_1483,Z_1484,X_1485)
| ~ product(multiplicative_identity,Y_1483,U_1486)
| product(U_1486,Z_1484,X_1485)
| ~ defined(X_1485) ),
inference(resolution,[status(thm)],[c_16,c_185493]) ).
tff(c_187592,plain,
! [X_30,U_1486] :
( ~ product(multiplicative_identity,X_30,U_1486)
| product(U_1486,multiplicative_identity,X_30)
| ~ defined(X_30) ),
inference(resolution,[status(thm)],[c_67,c_187571]) ).
tff(c_228490,plain,
( product(multiplicative_inverse(a),multiplicative_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_228466,c_187592]) ).
tff(c_228539,plain,
product(multiplicative_inverse(a),multiplicative_identity,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_228490]) ).
tff(c_185563,plain,
! [X_1395,Y_1397,V_1396,W_1394,Z_1393,U_1392] :
( ~ product(U_1392,Z_1393,W_1394)
| ~ product(Y_1397,Z_1393,V_1396)
| ~ product(X_1395,Y_1397,U_1392)
| product(X_1395,V_1396,W_1394) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_185578,plain,
! [Y_1397,X_30,V_1396,X_1395] :
( ~ product(Y_1397,X_30,V_1396)
| ~ product(X_1395,Y_1397,multiplicative_identity)
| product(X_1395,V_1396,X_30)
| ~ defined(X_30) ),
inference(resolution,[status(thm)],[c_16,c_185563]) ).
tff(c_228579,plain,
! [X_1395] :
( ~ product(X_1395,multiplicative_inverse(a),multiplicative_identity)
| product(X_1395,additive_identity,multiplicative_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[c_228539,c_185578]) ).
tff(c_232526,plain,
! [X_1888] :
( ~ product(X_1888,multiplicative_inverse(a),multiplicative_identity)
| product(X_1888,additive_identity,multiplicative_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_228579]) ).
tff(c_232545,plain,
( product(a,additive_identity,multiplicative_identity)
| ~ defined(a)
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[status(thm)],[c_142,c_232526]) ).
tff(c_232556,plain,
( product(a,additive_identity,multiplicative_identity)
| sum(additive_identity,a,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_232545]) ).
tff(c_232557,plain,
product(a,additive_identity,multiplicative_identity),
inference(negUnitSimplification,[status(thm)],[c_56,c_232556]) ).
tff(c_232653,plain,
product(additive_identity,a,multiplicative_identity),
inference(resolution,[status(thm)],[c_232557,c_20]) ).
tff(c_232679,plain,
! [X_1395] :
( ~ product(X_1395,additive_identity,multiplicative_identity)
| product(X_1395,multiplicative_identity,a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_232653,c_185578]) ).
tff(c_233456,plain,
! [X_1898] :
( ~ product(X_1898,additive_identity,multiplicative_identity)
| product(X_1898,multiplicative_identity,a) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_232679]) ).
tff(c_234516,plain,
! [X_1908] :
( product(multiplicative_identity,X_1908,a)
| ~ product(X_1908,additive_identity,multiplicative_identity) ),
inference(resolution,[status(thm)],[c_233456,c_20]) ).
tff(c_234537,plain,
product(multiplicative_identity,a,a),
inference(resolution,[status(thm)],[c_232557,c_234516]) ).
tff(c_185790,plain,
! [C_1423,A_1418,B_1421,X_1422,Y_1419,Z_1420,D_1424] :
( ~ product(Y_1419,Z_1420,D_1424)
| ~ product(X_1422,Z_1420,C_1423)
| ~ product(A_1418,Z_1420,B_1421)
| ~ sum(X_1422,Y_1419,A_1418)
| sum(C_1423,D_1424,B_1421) ),
inference(cnfTransformation,[status(thm)],[f_136]) ).
tff(c_198141,plain,
! [A_1641,X_1645,X_1642,B_1644,C_1643] :
( ~ product(X_1645,X_1642,C_1643)
| ~ product(A_1641,X_1642,B_1644)
| ~ sum(X_1645,multiplicative_identity,A_1641)
| sum(C_1643,X_1642,B_1644)
| ~ defined(X_1642) ),
inference(resolution,[status(thm)],[c_16,c_185790]) ).
tff(c_198196,plain,
! [A_1641,X_30,B_1644] :
( ~ product(A_1641,X_30,B_1644)
| ~ sum(multiplicative_identity,multiplicative_identity,A_1641)
| sum(X_30,X_30,B_1644)
| ~ defined(X_30) ),
inference(resolution,[status(thm)],[c_16,c_198141]) ).
tff(c_234547,plain,
( ~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| sum(a,a,a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_234537,c_198196]) ).
tff(c_234591,plain,
( ~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| sum(a,a,a) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_234547]) ).
tff(c_247427,plain,
~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(splitLeft,[status(thm)],[c_234591]) ).
tff(c_228211,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(splitRight,[status(thm)],[c_228200]) ).
tff(c_228295,plain,
product(multiplicative_identity,additive_identity,additive_identity),
inference(resolution,[status(thm)],[c_228211,c_20]) ).
tff(c_228323,plain,
! [X_1395] :
( ~ product(X_1395,multiplicative_identity,multiplicative_identity)
| product(X_1395,additive_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_228295,c_185578]) ).
tff(c_229298,plain,
! [X_1861] :
( ~ product(X_1861,multiplicative_identity,multiplicative_identity)
| product(X_1861,additive_identity,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_228323]) ).
tff(c_229342,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_229298]) ).
tff(c_229379,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_229342]) ).
tff(c_231999,plain,
sum(additive_identity,multiplicative_identity,additive_identity),
inference(splitLeft,[status(thm)],[c_229379]) ).
tff(c_185684,plain,
! [W_1408,Y_1412,Z_1407,X_1411,U_1409,V_1410] :
( ~ sum(X_1411,V_1410,W_1408)
| ~ sum(Y_1412,Z_1407,V_1410)
| ~ sum(X_1411,Y_1412,U_1409)
| sum(U_1409,Z_1407,W_1408) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_188234,plain,
! [Y_1512,Z_1513,X_1514,U_1515] :
( ~ sum(Y_1512,Z_1513,X_1514)
| ~ sum(additive_identity,Y_1512,U_1515)
| sum(U_1515,Z_1513,X_1514)
| ~ defined(X_1514) ),
inference(resolution,[status(thm)],[c_6,c_185684]) ).
tff(c_188297,plain,
! [X_13,U_1515] :
( ~ sum(additive_identity,X_13,U_1515)
| sum(U_1515,additive_identity,X_13)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_80,c_188234]) ).
tff(c_232019,plain,
( sum(additive_identity,additive_identity,multiplicative_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[c_231999,c_188297]) ).
tff(c_232064,plain,
sum(additive_identity,additive_identity,multiplicative_identity),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_232019]) ).
tff(c_232066,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_232064]) ).
tff(c_232068,plain,
~ sum(additive_identity,multiplicative_identity,additive_identity),
inference(splitRight,[status(thm)],[c_229379]) ).
tff(c_200890,plain,
! [Y_1684,X_1685,V_1686,X_1687] :
( ~ product(Y_1684,X_1685,V_1686)
| ~ product(X_1687,Y_1684,multiplicative_inverse(X_1685))
| product(X_1687,V_1686,multiplicative_identity)
| ~ defined(X_1685)
| sum(additive_identity,X_1685,additive_identity) ),
inference(resolution,[status(thm)],[c_18,c_185563]) ).
tff(c_200920,plain,
! [X_1687,X_30] :
( ~ product(X_1687,X_30,multiplicative_inverse(multiplicative_identity))
| product(X_1687,X_30,multiplicative_identity)
| ~ defined(multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(X_30) ),
inference(resolution,[status(thm)],[c_67,c_200890]) ).
tff(c_200953,plain,
! [X_1687,X_30] :
( ~ product(X_1687,X_30,multiplicative_inverse(multiplicative_identity))
| product(X_1687,X_30,multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(X_30) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_200920]) ).
tff(c_254225,plain,
! [X_1996,X_1997] :
( ~ product(X_1996,X_1997,multiplicative_inverse(multiplicative_identity))
| product(X_1996,X_1997,multiplicative_identity)
| ~ defined(X_1997) ),
inference(negUnitSimplification,[status(thm)],[c_232068,c_200953]) ).
tff(c_254313,plain,
( product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ defined(multiplicative_inverse(multiplicative_identity)) ),
inference(resolution,[status(thm)],[c_16,c_254225]) ).
tff(c_254381,plain,
~ defined(multiplicative_inverse(multiplicative_identity)),
inference(splitLeft,[status(thm)],[c_254313]) ).
tff(c_254384,plain,
( sum(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[c_36,c_254381]) ).
tff(c_254387,plain,
sum(additive_identity,multiplicative_identity,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_254384]) ).
tff(c_254389,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_232068,c_254387]) ).
tff(c_254390,plain,
product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(splitRight,[status(thm)],[c_254313]) ).
tff(c_254485,plain,
product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity),
inference(resolution,[status(thm)],[c_254390,c_20]) ).
tff(c_254620,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_254485,c_198196]) ).
tff(c_254678,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_254620]) ).
tff(c_254679,plain,
~ sum(multiplicative_identity,multiplicative_identity,multiplicative_inverse(multiplicative_identity)),
inference(negUnitSimplification,[status(thm)],[c_247427,c_254678]) ).
tff(c_254391,plain,
defined(multiplicative_inverse(multiplicative_identity)),
inference(splitRight,[status(thm)],[c_254313]) ).
tff(c_187719,plain,
! [Y_1492,X_1493,V_1494,X_1495] :
( ~ product(Y_1492,X_1493,V_1494)
| ~ product(X_1495,Y_1492,multiplicative_identity)
| product(X_1495,V_1494,X_1493)
| ~ defined(X_1493) ),
inference(resolution,[status(thm)],[c_16,c_185563]) ).
tff(c_187745,plain,
! [X_1495,X_30] :
( ~ product(X_1495,multiplicative_identity,multiplicative_identity)
| product(X_1495,X_30,X_30)
| ~ defined(X_30) ),
inference(resolution,[status(thm)],[c_16,c_187719]) ).
tff(c_255513,plain,
! [X_2001] :
( product(multiplicative_inverse(multiplicative_identity),X_2001,X_2001)
| ~ defined(X_2001) ),
inference(resolution,[status(thm)],[c_254485,c_187745]) ).
tff(c_254224,plain,
! [X_1687,X_30] :
( ~ product(X_1687,X_30,multiplicative_inverse(multiplicative_identity))
| product(X_1687,X_30,multiplicative_identity)
| ~ defined(X_30) ),
inference(negUnitSimplification,[status(thm)],[c_232068,c_200953]) ).
tff(c_255517,plain,
( product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ defined(multiplicative_inverse(multiplicative_identity)) ),
inference(resolution,[status(thm)],[c_255513,c_254224]) ).
tff(c_255593,plain,
product(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(demodulation,[status(thm),theory(equality)],[c_254391,c_255517]) ).
tff(c_194450,plain,
! [Y_1604,X_1603,X_1602,Y_1601,V_1605] :
( ~ product(Y_1601,Y_1604,V_1605)
| ~ product(X_1603,Y_1601,X_1602)
| product(X_1603,V_1605,multiply(X_1602,Y_1604))
| ~ defined(Y_1604)
| ~ defined(X_1602) ),
inference(resolution,[status(thm)],[c_40,c_185563]) ).
tff(c_346577,plain,
! [X_2351,X_2352,X_2353] :
( ~ product(X_2351,multiplicative_inverse(X_2352),X_2353)
| product(X_2351,multiplicative_identity,multiply(X_2353,X_2352))
| ~ defined(X_2353)
| ~ defined(X_2352)
| sum(additive_identity,X_2352,additive_identity) ),
inference(resolution,[status(thm)],[c_18,c_194450]) ).
tff(c_346721,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_255593,c_346577]) ).
tff(c_346954,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_346721]) ).
tff(c_346955,plain,
product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiply(multiplicative_identity,multiplicative_identity)),
inference(negUnitSimplification,[status(thm)],[c_232068,c_346954]) ).
tff(c_351072,plain,
product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiply(multiplicative_identity,multiplicative_identity)),
inference(resolution,[status(thm)],[c_346955,c_20]) ).
tff(c_352196,plain,
( product(multiply(multiplicative_identity,multiplicative_identity),multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| ~ defined(multiplicative_inverse(multiplicative_identity)) ),
inference(resolution,[status(thm)],[c_351072,c_187592]) ).
tff(c_352289,plain,
product(multiply(multiplicative_identity,multiplicative_identity),multiplicative_identity,multiplicative_inverse(multiplicative_identity)),
inference(demodulation,[status(thm),theory(equality)],[c_254391,c_352196]) ).
tff(c_352335,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_352289,c_198196]) ).
tff(c_352412,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_352335]) ).
tff(c_352413,plain,
~ sum(multiplicative_identity,multiplicative_identity,multiply(multiplicative_identity,multiplicative_identity)),
inference(negUnitSimplification,[status(thm)],[c_254679,c_352412]) ).
tff(c_188696,plain,
! [X_1524,U_1525] :
( ~ sum(additive_identity,X_1524,U_1525)
| sum(U_1525,additive_identity,X_1524)
| ~ defined(X_1524) ),
inference(resolution,[status(thm)],[c_80,c_188234]) ).
tff(c_188743,plain,
( sum(multiplicative_inverse(a),additive_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_58,c_188696]) ).
tff(c_188784,plain,
sum(multiplicative_inverse(a),additive_identity,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_188743]) ).
tff(c_185609,plain,
! [Y_1400,Z_1399,V_1401,U_1402,W_1404,X_1403] :
( ~ sum(U_1402,Z_1399,W_1404)
| ~ sum(Y_1400,Z_1399,V_1401)
| ~ sum(X_1403,Y_1400,U_1402)
| sum(X_1403,V_1401,W_1404) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_185635,plain,
! [Y_1400,X_13,V_1401,X_1403] :
( ~ sum(Y_1400,X_13,V_1401)
| ~ sum(X_1403,Y_1400,additive_identity)
| sum(X_1403,V_1401,X_13)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_6,c_185609]) ).
tff(c_188858,plain,
! [X_1403] :
( ~ sum(X_1403,multiplicative_inverse(a),additive_identity)
| sum(X_1403,additive_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_188784,c_185635]) ).
tff(c_190313,plain,
! [X_1547] :
( ~ sum(X_1547,multiplicative_inverse(a),additive_identity)
| sum(X_1547,additive_identity,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_188858]) ).
tff(c_190348,plain,
( sum(additive_inverse(multiplicative_inverse(a)),additive_identity,additive_identity)
| ~ defined(multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[c_8,c_190313]) ).
tff(c_191230,plain,
~ defined(multiplicative_inverse(a)),
inference(splitLeft,[status(thm)],[c_190348]) ).
tff(c_191425,plain,
( sum(additive_identity,a,additive_identity)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_36,c_191230]) ).
tff(c_191428,plain,
sum(additive_identity,a,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_191425]) ).
tff(c_191430,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_56,c_191428]) ).
tff(c_191432,plain,
defined(multiplicative_inverse(a)),
inference(splitRight,[status(thm)],[c_190348]) ).
tff(c_185636,plain,
! [Y_1400,V_1401,X_1403] :
( ~ sum(Y_1400,additive_identity,V_1401)
| ~ sum(X_1403,Y_1400,additive_identity)
| sum(X_1403,V_1401,multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[c_58,c_185609]) ).
tff(c_196121,plain,
! [X_1621] :
( ~ sum(X_1621,multiplicative_inverse(a),additive_identity)
| sum(X_1621,additive_identity,multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[c_188784,c_185636]) ).
tff(c_196173,plain,
( sum(additive_inverse(multiplicative_inverse(a)),additive_identity,multiplicative_inverse(a))
| ~ defined(multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[c_8,c_196121]) ).
tff(c_196205,plain,
sum(additive_inverse(multiplicative_inverse(a)),additive_identity,multiplicative_inverse(a)),
inference(demodulation,[status(thm),theory(equality)],[c_191432,c_196173]) ).
tff(c_196277,plain,
sum(additive_identity,additive_inverse(multiplicative_inverse(a)),multiplicative_inverse(a)),
inference(resolution,[status(thm)],[c_196205,c_10]) ).
tff(c_186021,plain,
! [Y_1441,Z_1442,U_1443] :
( ~ sum(Y_1441,Z_1442,additive_identity)
| ~ sum(additive_identity,Y_1441,U_1443)
| sum(U_1443,Z_1442,multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[c_58,c_185684]) ).
tff(c_186044,plain,
! [X_14,U_1443] :
( ~ sum(additive_identity,additive_inverse(X_14),U_1443)
| sum(U_1443,X_14,multiplicative_inverse(a))
| ~ defined(X_14) ),
inference(resolution,[status(thm)],[c_8,c_186021]) ).
tff(c_196299,plain,
( sum(multiplicative_inverse(a),multiplicative_inverse(a),multiplicative_inverse(a))
| ~ defined(multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[c_196277,c_186044]) ).
tff(c_196343,plain,
sum(multiplicative_inverse(a),multiplicative_inverse(a),multiplicative_inverse(a)),
inference(demodulation,[status(thm),theory(equality)],[c_191432,c_196299]) ).
tff(c_228201,plain,
( ~ product(additive_identity,multiplicative_identity,additive_identity)
| product(multiplicative_inverse(a),multiplicative_identity,multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[c_58,c_227714]) ).
tff(c_229671,plain,
product(multiplicative_inverse(a),multiplicative_identity,multiplicative_inverse(a)),
inference(demodulation,[status(thm),theory(equality)],[c_228211,c_228201]) ).
tff(c_229752,plain,
product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(a)),
inference(resolution,[status(thm)],[c_229671,c_20]) ).
tff(c_199785,plain,
! [Z_1664,Y_1666,U_1665,X_1663,Y_1667] :
( ~ product(Y_1667,Z_1664,Y_1666)
| ~ product(X_1663,Y_1667,U_1665)
| product(U_1665,Z_1664,multiply(X_1663,Y_1666))
| ~ defined(Y_1666)
| ~ defined(X_1663) ),
inference(resolution,[status(thm)],[c_40,c_185493]) ).
tff(c_199809,plain,
! [X_1663,X_31,U_1665] :
( ~ product(X_1663,multiplicative_inverse(X_31),U_1665)
| product(U_1665,X_31,multiply(X_1663,multiplicative_identity))
| ~ defined(multiplicative_identity)
| ~ defined(X_1663)
| ~ defined(X_31)
| sum(additive_identity,X_31,additive_identity) ),
inference(resolution,[status(thm)],[c_18,c_199785]) ).
tff(c_351073,plain,
! [X_2365,X_2366,U_2367] :
( ~ product(X_2365,multiplicative_inverse(X_2366),U_2367)
| product(U_2367,X_2366,multiply(X_2365,multiplicative_identity))
| ~ defined(X_2365)
| ~ defined(X_2366)
| sum(additive_identity,X_2366,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_199809]) ).
tff(c_351231,plain,
( product(multiplicative_inverse(a),a,multiply(multiplicative_identity,multiplicative_identity))
| ~ defined(multiplicative_identity)
| ~ defined(a)
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[status(thm)],[c_229752,c_351073]) ).
tff(c_351442,plain,
( product(multiplicative_inverse(a),a,multiply(multiplicative_identity,multiplicative_identity))
| sum(additive_identity,a,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_34,c_351231]) ).
tff(c_351443,plain,
product(multiplicative_inverse(a),a,multiply(multiplicative_identity,multiplicative_identity)),
inference(negUnitSimplification,[status(thm)],[c_56,c_351442]) ).
tff(c_203893,plain,
! [X_1730,X_1729,A_1726,C_1727,B_1728] :
( ~ product(X_1730,X_1729,C_1727)
| ~ product(A_1726,X_1729,B_1728)
| ~ sum(X_1730,multiplicative_inverse(X_1729),A_1726)
| sum(C_1727,multiplicative_identity,B_1728)
| ~ defined(X_1729)
| sum(additive_identity,X_1729,additive_identity) ),
inference(resolution,[status(thm)],[c_18,c_185790]) ).
tff(c_365880,plain,
! [A_2421,X_2422,B_2423] :
( ~ product(A_2421,X_2422,B_2423)
| ~ sum(multiplicative_inverse(X_2422),multiplicative_inverse(X_2422),A_2421)
| sum(multiplicative_identity,multiplicative_identity,B_2423)
| ~ defined(X_2422)
| sum(additive_identity,X_2422,additive_identity) ),
inference(resolution,[status(thm)],[c_18,c_203893]) ).
tff(c_365958,plain,
( ~ sum(multiplicative_inverse(a),multiplicative_inverse(a),multiplicative_inverse(a))
| sum(multiplicative_identity,multiplicative_identity,multiply(multiplicative_identity,multiplicative_identity))
| ~ defined(a)
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[status(thm)],[c_351443,c_365880]) ).
tff(c_367016,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_196343,c_365958]) ).
tff(c_367018,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_56,c_352413,c_367016]) ).
tff(c_367019,plain,
sum(a,a,a),
inference(splitRight,[status(thm)],[c_234591]) ).
tff(c_367043,plain,
! [X_1403] :
( ~ sum(X_1403,a,additive_identity)
| sum(X_1403,a,a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_367019,c_185635]) ).
tff(c_368761,plain,
! [X_2436] :
( ~ sum(X_2436,a,additive_identity)
| sum(X_2436,a,a) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_367043]) ).
tff(c_368797,plain,
( sum(additive_inverse(a),a,a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_8,c_368761]) ).
tff(c_368810,plain,
sum(additive_inverse(a),a,a),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_368797]) ).
tff(c_189164,plain,
! [Y_1526,Z_1527,X_1528,U_1529] :
( ~ sum(Y_1526,Z_1527,X_1528)
| ~ sum(additive_inverse(X_1528),Y_1526,U_1529)
| sum(U_1529,Z_1527,additive_identity)
| ~ defined(X_1528) ),
inference(resolution,[status(thm)],[c_8,c_185684]) ).
tff(c_189280,plain,
! [X_13,U_1529] :
( ~ sum(additive_inverse(X_13),X_13,U_1529)
| sum(U_1529,additive_identity,additive_identity)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_80,c_189164]) ).
tff(c_368816,plain,
( sum(a,additive_identity,additive_identity)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_368810,c_189280]) ).
tff(c_368857,plain,
sum(a,additive_identity,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_368816]) ).
tff(c_185424,plain,
! [X_1371,V_1374,Z_1372,Y_1373,U_1370] :
( ~ sum(Y_1373,Z_1372,V_1374)
| ~ sum(X_1371,Z_1372,U_1370)
| ~ less_or_equal(X_1371,Y_1373)
| less_or_equal(U_1370,V_1374) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_185509,plain,
! [X_1390,U_1391] :
( ~ sum(X_1390,additive_identity,U_1391)
| ~ less_or_equal(X_1390,additive_identity)
| less_or_equal(U_1391,multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[c_58,c_185424]) ).
tff(c_185528,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(additive_identity,multiplicative_inverse(a))
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_6,c_185509]) ).
tff(c_185545,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(additive_identity,multiplicative_inverse(a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_185528]) ).
tff(c_185547,plain,
~ less_or_equal(additive_identity,additive_identity),
inference(splitLeft,[status(thm)],[c_185545]) ).
tff(c_185553,plain,
~ defined(additive_identity),
inference(resolution,[status(thm)],[c_106,c_185547]) ).
tff(c_185560,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_185553]) ).
tff(c_185562,plain,
less_or_equal(additive_identity,additive_identity),
inference(splitRight,[status(thm)],[c_185545]) ).
tff(c_185822,plain,
! [X_1426,X_1427,U_1428] :
( ~ sum(X_1426,X_1427,U_1428)
| ~ less_or_equal(X_1426,additive_identity)
| less_or_equal(U_1428,X_1427)
| ~ defined(X_1427) ),
inference(resolution,[status(thm)],[c_6,c_185424]) ).
tff(c_185849,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(multiplicative_inverse(a),additive_identity)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_58,c_185822]) ).
tff(c_185868,plain,
less_or_equal(multiplicative_inverse(a),additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_185562,c_185849]) ).
tff(c_187918,plain,
! [Y_1502,X_1503,V_1504,X_1505] :
( ~ sum(Y_1502,X_1503,V_1504)
| ~ sum(X_1505,Y_1502,additive_identity)
| sum(X_1505,V_1504,X_1503)
| ~ defined(X_1503) ),
inference(resolution,[status(thm)],[c_6,c_185609]) ).
tff(c_187954,plain,
! [X_1505] :
( ~ sum(X_1505,additive_identity,additive_identity)
| sum(X_1505,multiplicative_inverse(a),additive_identity)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_58,c_187918]) ).
tff(c_188157,plain,
! [X_1510] :
( ~ sum(X_1510,additive_identity,additive_identity)
| sum(X_1510,multiplicative_inverse(a),additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_187954]) ).
tff(c_188188,plain,
! [X_1511] :
( sum(multiplicative_inverse(a),X_1511,additive_identity)
| ~ sum(X_1511,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[c_188157,c_10]) ).
tff(c_185444,plain,
! [X_1371,X_13,U_1370] :
( ~ sum(X_1371,X_13,U_1370)
| ~ less_or_equal(X_1371,additive_identity)
| less_or_equal(U_1370,X_13)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_6,c_185424]) ).
tff(c_188205,plain,
! [X_1511] :
( ~ less_or_equal(multiplicative_inverse(a),additive_identity)
| less_or_equal(additive_identity,X_1511)
| ~ defined(X_1511)
| ~ sum(X_1511,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[c_188188,c_185444]) ).
tff(c_188226,plain,
! [X_1511] :
( less_or_equal(additive_identity,X_1511)
| ~ defined(X_1511)
| ~ sum(X_1511,additive_identity,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_185868,c_188205]) ).
tff(c_368927,plain,
( less_or_equal(additive_identity,a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_368857,c_188226]) ).
tff(c_368989,plain,
less_or_equal(additive_identity,a),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_368927]) ).
tff(c_368991,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_185385,c_368989]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : FLD040-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 20:04:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 164.64/144.70 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 164.79/144.76
% 164.79/144.76 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 165.09/144.84
% 165.09/144.84 Inference rules
% 165.09/144.84 ----------------------
% 165.09/144.84 #Ref : 0
% 165.09/144.84 #Sup : 82319
% 165.09/144.84 #Fact : 34
% 165.09/144.84 #Define : 0
% 165.09/144.84 #Split : 51
% 165.09/144.84 #Chain : 0
% 165.09/144.84 #Close : 0
% 165.09/144.84
% 165.09/144.84 Ordering : KBO
% 165.09/144.84
% 165.09/144.84 Simplification rules
% 165.09/144.84 ----------------------
% 165.09/144.84 #Subsume : 4548
% 165.09/144.84 #Demod : 62698
% 165.09/144.84 #Tautology : 14760
% 165.09/144.84 #SimpNegUnit : 3302
% 165.09/144.84 #BackRed : 0
% 165.09/144.84
% 165.09/144.84 #Partial instantiations: 0
% 165.09/144.84 #Strategies tried : 1
% 165.09/144.84
% 165.09/144.84 Timing (in seconds)
% 165.09/144.84 ----------------------
% 165.09/144.84 Preprocessing : 0.50
% 165.09/144.84 Parsing : 0.28
% 165.09/144.84 CNF conversion : 0.03
% 165.09/144.84 Main loop : 143.11
% 165.09/144.84 Inferencing : 10.08
% 165.09/144.84 Reduction : 81.43
% 165.09/144.85 Demodulation : 73.62
% 165.09/144.85 BG Simplification : 0.44
% 165.09/144.85 Subsumption : 44.55
% 165.09/144.85 Abstraction : 0.65
% 165.09/144.85 MUC search : 0.00
% 165.09/144.85 Cooper : 0.00
% 165.09/144.85 Total : 143.76
% 165.09/144.85 Index Insertion : 0.00
% 165.09/144.85 Index Deletion : 0.00
% 165.09/144.85 Index Matching : 0.00
% 165.09/144.85 BG Taut test : 0.00
%------------------------------------------------------------------------------