TSTP Solution File: GRP002-10 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP002-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n010.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 10:39:34 EDT 2023
% Result : Timeout 289.56s 242.20s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 31
% Syntax : Number of formulae : 238 ( 224 unt; 14 typ; 0 def)
% Number of atoms : 224 ( 223 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 14 ( 5 >; 9 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-4 aty)
% Number of variables : 305 (; 305 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ ifeq2 > ifeq > product > multiply > #nlpp > inverse > true > k > j > identity > h > d > c > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(j,type,
j: $i ).
tff(h,type,
h: $i ).
tff(a,type,
a: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(k,type,
k: $i ).
tff(ifeq2,type,
ifeq2: ( $i * $i * $i * $i ) > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(b,type,
b: $i ).
tff(d,type,
d: $i ).
tff(identity,type,
identity: $i ).
tff(true,type,
true: $i ).
tff(product,type,
product: ( $i * $i * $i ) > $i ).
tff(ifeq,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(c,type,
c: $i ).
tff(f_34,axiom,
! [X] : ( product(X,inverse(X),identity) = true ),
file(unknown,unknown) ).
tff(f_24,axiom,
! [A,B,C] : ( ifeq2(A,A,B,C) = B ),
file(unknown,unknown) ).
tff(f_36,axiom,
! [X,Y] : ( product(X,Y,multiply(X,Y)) = true ),
file(unknown,unknown) ).
tff(f_28,axiom,
! [X] : ( product(identity,X,X) = true ),
file(unknown,unknown) ).
tff(f_38,axiom,
! [X,Y,W,Z] : ( ifeq2(product(X,Y,W),true,ifeq2(product(X,Y,Z),true,Z,W),W) = W ),
file(unknown,unknown) ).
tff(f_46,axiom,
! [X,Y] : ( ifeq(product(X,X,Y),true,product(Y,X,identity),true) = true ),
file(unknown,unknown) ).
tff(f_26,axiom,
! [A,B,C] : ( ifeq(A,A,B,C) = B ),
file(unknown,unknown) ).
tff(f_30,axiom,
! [X] : ( product(X,identity,X) = true ),
file(unknown,unknown) ).
tff(f_42,axiom,
! [W,U,Z,X,Y,V] : ( ifeq(product(Y,Z,V),true,ifeq(product(X,V,W),true,ifeq(product(X,Y,U),true,product(U,Z,W),true),true),true) = true ),
file(unknown,unknown) ).
tff(f_50,axiom,
product(h,b,j) = true,
file(unknown,unknown) ).
tff(f_32,axiom,
! [X] : ( product(inverse(X),X,identity) = true ),
file(unknown,unknown) ).
tff(f_49,axiom,
product(d,inverse(b),h) = true,
file(unknown,unknown) ).
tff(f_40,axiom,
! [W,U,Z,X,Y,V] : ( ifeq(product(U,Z,W),true,ifeq(product(Y,Z,V),true,ifeq(product(X,Y,U),true,product(X,V,W),true),true),true) = true ),
file(unknown,unknown) ).
tff(f_51,axiom,
product(j,inverse(h),k) = true,
file(unknown,unknown) ).
tff(f_48,axiom,
product(c,inverse(a),d) = true,
file(unknown,unknown) ).
tff(f_47,axiom,
product(a,b,c) = true,
file(unknown,unknown) ).
tff(f_53,axiom,
product(k,inverse(b),identity) != true,
file(unknown,unknown) ).
tff(c_12,plain,
! [X_10] : ( product(X_10,inverse(X_10),identity) = true ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_2,plain,
! [A_1,B_2,C_3] : ( ifeq2(A_1,A_1,B_2,C_3) = B_2 ),
inference(cnfTransformation,[status(thm)],[f_24]) ).
tff(c_14,plain,
! [X_11,Y_12] : ( product(X_11,Y_12,multiply(X_11,Y_12)) = true ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_6,plain,
! [X_7] : ( product(identity,X_7,X_7) = true ),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_229,plain,
! [X_52,Y_53,W_54,Z_55] : ( ifeq2(product(X_52,Y_53,W_54),true,ifeq2(product(X_52,Y_53,Z_55),true,Z_55,W_54),W_54) = W_54 ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_289,plain,
! [X_7,W_54] : ( ifeq2(product(identity,X_7,W_54),true,ifeq2(true,true,X_7,W_54),W_54) = W_54 ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_229]) ).
tff(c_794,plain,
! [X_73,W_74] : ( ifeq2(product(identity,X_73,W_74),true,X_73,W_74) = W_74 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_289]) ).
tff(c_820,plain,
! [Y_12] : ( ifeq2(true,true,Y_12,multiply(identity,Y_12)) = multiply(identity,Y_12) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_794]) ).
tff(c_838,plain,
! [Y_12] : ( multiply(identity,Y_12) = Y_12 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_820]) ).
tff(c_162,plain,
! [X_48,Y_49] : ( ifeq(product(X_48,X_48,Y_49),true,product(Y_49,X_48,identity),true) = true ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_989,plain,
! [Y_81] : ( ifeq(true,true,product(multiply(Y_81,Y_81),Y_81,identity),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_162]) ).
tff(c_4,plain,
! [A_4,B_5,C_6] : ( ifeq(A_4,A_4,B_5,C_6) = B_5 ),
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_994,plain,
! [Y_81] : ( product(multiply(Y_81,Y_81),Y_81,identity) = true ),
inference(superposition,[status(thm),theory(equality)],[c_989,c_4]) ).
tff(c_241,plain,
! [X_11,Y_12,W_54] : ( ifeq2(product(X_11,Y_12,W_54),true,ifeq2(true,true,multiply(X_11,Y_12),W_54),W_54) = W_54 ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_229]) ).
tff(c_1198,plain,
! [X_88,Y_89,W_90] : ( ifeq2(product(X_88,Y_89,W_90),true,multiply(X_88,Y_89),W_90) = W_90 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_241]) ).
tff(c_1354,plain,
! [Y_93] : ( ifeq2(true,true,multiply(multiply(Y_93,Y_93),Y_93),identity) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_994,c_1198]) ).
tff(c_1359,plain,
! [Y_93] : ( multiply(multiply(Y_93,Y_93),Y_93) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_1354,c_2]) ).
tff(c_8,plain,
! [X_8] : ( product(X_8,identity,X_8) = true ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_392,plain,
! [Z_62,X_60,W_64,V_63,Y_65,U_61] : ( ifeq(product(Y_65,Z_62,V_63),true,ifeq(product(X_60,V_63,W_64),true,ifeq(product(X_60,Y_65,U_61),true,product(U_61,Z_62,W_64),true),true),true) = true ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_31977,plain,
! [X_618,W_619,X_620,U_621] : ( ifeq(true,true,ifeq(product(X_618,identity,W_619),true,ifeq(product(X_618,X_620,U_621),true,product(U_621,inverse(X_620),W_619),true),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_392]) ).
tff(c_32129,plain,
! [X_8,X_620,U_621] : ( ifeq(true,true,ifeq(true,true,ifeq(product(X_8,X_620,U_621),true,product(U_621,inverse(X_620),X_8),true),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_31977]) ).
tff(c_35773,plain,
! [X_673,X_674,U_675] : ( ifeq(product(X_673,X_674,U_675),true,product(U_675,inverse(X_674),X_673),true) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_32129]) ).
tff(c_37166,plain,
! [X_685,Y_686] : ( ifeq(true,true,product(multiply(X_685,Y_686),inverse(Y_686),X_685),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_35773]) ).
tff(c_37300,plain,
! [X_687,Y_688] : ( product(multiply(X_687,Y_688),inverse(Y_688),X_687) = true ),
inference(superposition,[status(thm),theory(equality)],[c_37166,c_4]) ).
tff(c_8572,plain,
! [X_272,Y_273,Z_274] : ( ifeq2(true,true,ifeq2(product(X_272,Y_273,Z_274),true,Z_274,multiply(X_272,Y_273)),multiply(X_272,Y_273)) = multiply(X_272,Y_273) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_229]) ).
tff(c_8578,plain,
! [X_272,Y_273,Z_274] : ( ifeq2(product(X_272,Y_273,Z_274),true,Z_274,multiply(X_272,Y_273)) = multiply(X_272,Y_273) ),
inference(superposition,[status(thm),theory(equality)],[c_8572,c_2]) ).
tff(c_37590,plain,
! [X_687,Y_688] : ( ifeq2(true,true,X_687,multiply(multiply(X_687,Y_688),inverse(Y_688))) = multiply(multiply(X_687,Y_688),inverse(Y_688)) ),
inference(superposition,[status(thm),theory(equality)],[c_37300,c_8578]) ).
tff(c_37902,plain,
! [X_689,Y_690] : ( multiply(multiply(X_689,Y_690),inverse(Y_690)) = X_689 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_37590]) ).
tff(c_38016,plain,
! [Y_93] : ( multiply(identity,inverse(Y_93)) = multiply(Y_93,Y_93) ),
inference(superposition,[status(thm),theory(equality)],[c_1359,c_37902]) ).
tff(c_38214,plain,
! [Y_691] : ( multiply(Y_691,Y_691) = inverse(Y_691) ),
inference(demodulation,[status(thm),theory(equality)],[c_838,c_38016]) ).
tff(c_37860,plain,
! [X_687,Y_688] : ( multiply(multiply(X_687,Y_688),inverse(Y_688)) = X_687 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_37590]) ).
tff(c_38220,plain,
! [Y_691] : ( multiply(inverse(Y_691),inverse(Y_691)) = Y_691 ),
inference(superposition,[status(thm),theory(equality)],[c_38214,c_37860]) ).
tff(c_277,plain,
! [X_8,W_54] : ( ifeq2(product(X_8,identity,W_54),true,ifeq2(true,true,X_8,W_54),W_54) = W_54 ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_229]) ).
tff(c_332,plain,
! [X_57,W_58] : ( ifeq2(product(X_57,identity,W_58),true,X_57,W_58) = W_58 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_277]) ).
tff(c_346,plain,
! [X_11] : ( ifeq2(true,true,X_11,multiply(X_11,identity)) = multiply(X_11,identity) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_332]) ).
tff(c_361,plain,
! [X_11] : ( multiply(X_11,identity) = X_11 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_346]) ).
tff(c_32,plain,
product(h,b,j) = true,
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_295,plain,
! [W_54] : ( ifeq2(product(h,b,W_54),true,ifeq2(true,true,j,W_54),W_54) = W_54 ),
inference(superposition,[status(thm),theory(equality)],[c_32,c_229]) ).
tff(c_587,plain,
! [W_66] : ( ifeq2(product(h,b,W_66),true,j,W_66) = W_66 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_295]) ).
tff(c_601,plain,
ifeq2(true,true,j,multiply(h,b)) = multiply(h,b),
inference(superposition,[status(thm),theory(equality)],[c_14,c_587]) ).
tff(c_608,plain,
multiply(h,b) = j,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_601]) ).
tff(c_10,plain,
! [X_9] : ( product(inverse(X_9),X_9,identity) = true ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_30,plain,
product(d,inverse(b),h) = true,
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_610,plain,
! [X_68,V_70,U_69,Y_67,Z_72,W_71] : ( ifeq(product(U_69,Z_72,W_71),true,ifeq(product(Y_67,Z_72,V_70),true,ifeq(product(X_68,Y_67,U_69),true,product(X_68,V_70,W_71),true),true),true) = true ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_696,plain,
! [Z_72,W_71,V_70] : ( ifeq(product(h,Z_72,W_71),true,ifeq(product(inverse(b),Z_72,V_70),true,ifeq(true,true,product(d,V_70,W_71),true),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_30,c_610]) ).
tff(c_11003,plain,
! [Z_319,W_320,V_321] : ( ifeq(product(h,Z_319,W_320),true,ifeq(product(inverse(b),Z_319,V_321),true,product(d,V_321,W_320),true),true) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_696]) ).
tff(c_11035,plain,
! [W_320] : ( ifeq(product(h,b,W_320),true,ifeq(true,true,product(d,identity,W_320),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_11003]) ).
tff(c_11142,plain,
! [W_323] : ( ifeq(product(h,b,W_323),true,product(d,identity,W_323),true) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_11035]) ).
tff(c_11154,plain,
ifeq(true,true,product(d,identity,multiply(h,b)),true) = true,
inference(superposition,[status(thm),theory(equality)],[c_14,c_11142]) ).
tff(c_11169,plain,
product(d,identity,j) = true,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_608,c_11154]) ).
tff(c_11184,plain,
ifeq2(true,true,j,multiply(d,identity)) = multiply(d,identity),
inference(superposition,[status(thm),theory(equality)],[c_11169,c_8578]) ).
tff(c_11299,plain,
j = d,
inference(demodulation,[status(thm),theory(equality)],[c_361,c_2,c_11184]) ).
tff(c_34,plain,
product(j,inverse(h),k) = true,
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_271,plain,
! [W_54] : ( ifeq2(product(j,inverse(h),W_54),true,ifeq2(true,true,k,W_54),W_54) = W_54 ),
inference(superposition,[status(thm),theory(equality)],[c_34,c_229]) ).
tff(c_1110,plain,
! [W_84] : ( ifeq2(product(j,inverse(h),W_84),true,k,W_84) = W_84 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_271]) ).
tff(c_1124,plain,
ifeq2(true,true,k,multiply(j,inverse(h))) = multiply(j,inverse(h)),
inference(superposition,[status(thm),theory(equality)],[c_14,c_1110]) ).
tff(c_1131,plain,
multiply(j,inverse(h)) = k,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1124]) ).
tff(c_11362,plain,
multiply(d,inverse(h)) = k,
inference(demodulation,[status(thm),theory(equality)],[c_11299,c_1131]) ).
tff(c_23341,plain,
! [Y_501,X_502,V_503,X_504] : ( ifeq(true,true,ifeq(product(Y_501,X_502,V_503),true,ifeq(product(X_504,Y_501,identity),true,product(X_504,V_503,X_502),true),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_610]) ).
tff(c_23496,plain,
! [X_504,X_9] : ( ifeq(true,true,ifeq(true,true,ifeq(product(X_504,inverse(X_9),identity),true,product(X_504,identity,X_9),true),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_23341]) ).
tff(c_33283,plain,
! [X_639,X_640] : ( ifeq(product(X_639,inverse(X_640),identity),true,product(X_639,identity,X_640),true) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_23496]) ).
tff(c_33423,plain,
! [X_641] : ( ifeq(true,true,product(inverse(inverse(X_641)),identity,X_641),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_33283]) ).
tff(c_33442,plain,
! [X_642] : ( product(inverse(inverse(X_642)),identity,X_642) = true ),
inference(superposition,[status(thm),theory(equality)],[c_33423,c_4]) ).
tff(c_33708,plain,
! [X_642] : ( ifeq2(true,true,X_642,multiply(inverse(inverse(X_642)),identity)) = multiply(inverse(inverse(X_642)),identity) ),
inference(superposition,[status(thm),theory(equality)],[c_33442,c_8578]) ).
tff(c_33893,plain,
! [X_642] : ( inverse(inverse(X_642)) = X_642 ),
inference(demodulation,[status(thm),theory(equality)],[c_361,c_2,c_33708]) ).
tff(c_37171,plain,
! [X_685,Y_686] : ( product(multiply(X_685,Y_686),inverse(Y_686),X_685) = true ),
inference(superposition,[status(thm),theory(equality)],[c_37166,c_4]) ).
tff(c_39677,plain,
! [Y_696] : ( product(inverse(Y_696),inverse(Y_696),Y_696) = true ),
inference(superposition,[status(thm),theory(equality)],[c_38214,c_37171]) ).
tff(c_481,plain,
! [Y_65,Z_62,U_61] : ( ifeq(product(Y_65,Z_62,inverse(h)),true,ifeq(true,true,ifeq(product(j,Y_65,U_61),true,product(U_61,Z_62,k),true),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_34,c_392]) ).
tff(c_550,plain,
! [Y_65,Z_62,U_61] : ( ifeq(product(Y_65,Z_62,inverse(h)),true,ifeq(product(j,Y_65,U_61),true,product(U_61,Z_62,k),true),true) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_481]) ).
tff(c_12833,plain,
! [Y_65,Z_62,U_61] : ( ifeq(product(Y_65,Z_62,inverse(h)),true,ifeq(product(d,Y_65,U_61),true,product(U_61,Z_62,k),true),true) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_11299,c_550]) ).
tff(c_39943,plain,
! [U_61] : ( ifeq(true,true,ifeq(product(d,inverse(inverse(h)),U_61),true,product(U_61,inverse(inverse(h)),k),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_39677,c_12833]) ).
tff(c_69733,plain,
! [U_855] : ( ifeq(product(d,h,U_855),true,product(U_855,h,k),true) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_33893,c_4,c_33893,c_39943]) ).
tff(c_69774,plain,
ifeq(true,true,product(multiply(d,h),h,k),true) = true,
inference(superposition,[status(thm),theory(equality)],[c_14,c_69733]) ).
tff(c_69844,plain,
product(multiply(d,h),h,k) = true,
inference(superposition,[status(thm),theory(equality)],[c_69774,c_4]) ).
tff(c_69987,plain,
ifeq2(true,true,k,multiply(multiply(d,h),h)) = multiply(multiply(d,h),h),
inference(superposition,[status(thm),theory(equality)],[c_69844,c_8578]) ).
tff(c_70112,plain,
multiply(multiply(d,h),h) = k,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_69987]) ).
tff(c_753,plain,
! [U_69,W_71,X_68] : ( ifeq(product(U_69,b,W_71),true,ifeq(true,true,ifeq(product(X_68,h,U_69),true,product(X_68,j,W_71),true),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_32,c_610]) ).
tff(c_3118,plain,
! [U_152,W_153,X_154] : ( ifeq(product(U_152,b,W_153),true,ifeq(product(X_154,h,U_152),true,product(X_154,j,W_153),true),true) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_753]) ).
tff(c_3154,plain,
! [X_11,W_153] : ( ifeq(product(multiply(X_11,h),b,W_153),true,ifeq(true,true,product(X_11,j,W_153),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_3118]) ).
tff(c_3194,plain,
! [X_11,W_153] : ( ifeq(product(multiply(X_11,h),b,W_153),true,product(X_11,j,W_153),true) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_3154]) ).
tff(c_92696,plain,
! [X_950,W_951] : ( ifeq(product(multiply(X_950,h),b,W_951),true,product(X_950,d,W_951),true) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_11299,c_3194]) ).
tff(c_92879,plain,
! [X_953] : ( ifeq(true,true,product(X_953,d,multiply(multiply(X_953,h),b)),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_92696]) ).
tff(c_92931,plain,
! [X_954] : ( product(X_954,d,multiply(multiply(X_954,h),b)) = true ),
inference(superposition,[status(thm),theory(equality)],[c_92879,c_4]) ).
tff(c_298,plain,
! [X_11,Y_12,W_54] : ( ifeq2(product(X_11,Y_12,W_54),true,multiply(X_11,Y_12),W_54) = W_54 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_241]) ).
tff(c_93473,plain,
! [X_954] : ( ifeq2(true,true,multiply(X_954,d),multiply(multiply(X_954,h),b)) = multiply(multiply(X_954,h),b) ),
inference(superposition,[status(thm),theory(equality)],[c_92931,c_298]) ).
tff(c_96991,plain,
! [X_960] : ( multiply(multiply(X_960,h),b) = multiply(X_960,d) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_93473]) ).
tff(c_97092,plain,
multiply(multiply(d,h),d) = multiply(k,b),
inference(superposition,[status(thm),theory(equality)],[c_70112,c_96991]) ).
tff(c_38241,plain,
! [Y_691,W_54] : ( ifeq2(product(Y_691,Y_691,W_54),true,inverse(Y_691),W_54) = W_54 ),
inference(superposition,[status(thm),theory(equality)],[c_38214,c_298]) ).
tff(c_93025,plain,
ifeq2(true,true,inverse(d),multiply(multiply(d,h),b)) = multiply(multiply(d,h),b),
inference(superposition,[status(thm),theory(equality)],[c_92931,c_38241]) ).
tff(c_93572,plain,
multiply(multiply(d,h),b) = inverse(d),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_93025]) ).
tff(c_40301,plain,
! [Y_699,V_700,X_701,X_697,Y_698] : ( ifeq(true,true,ifeq(product(Y_699,Y_698,V_700),true,ifeq(product(X_697,Y_699,X_701),true,product(X_697,V_700,multiply(X_701,Y_698)),true),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_610]) ).
tff(c_40561,plain,
! [X_9,Y_698,V_700] : ( ifeq(true,true,ifeq(product(X_9,Y_698,V_700),true,ifeq(true,true,product(inverse(X_9),V_700,multiply(identity,Y_698)),true),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_40301]) ).
tff(c_45553,plain,
! [X_737,Y_738,V_739] : ( ifeq(product(X_737,Y_738,V_739),true,product(inverse(X_737),V_739,Y_738),true) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_838,c_4,c_4,c_40561]) ).
tff(c_48213,plain,
! [X_745,Y_746] : ( ifeq(true,true,product(inverse(X_745),multiply(X_745,Y_746),Y_746),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_45553]) ).
tff(c_48379,plain,
! [X_747,Y_748] : ( product(inverse(X_747),multiply(X_747,Y_748),Y_748) = true ),
inference(superposition,[status(thm),theory(equality)],[c_48213,c_4]) ).
tff(c_48668,plain,
! [Y_748,X_747] : ( ifeq2(true,true,Y_748,multiply(inverse(X_747),multiply(X_747,Y_748))) = multiply(inverse(X_747),multiply(X_747,Y_748)) ),
inference(superposition,[status(thm),theory(equality)],[c_48379,c_8578]) ).
tff(c_49019,plain,
! [X_749,Y_750] : ( multiply(inverse(X_749),multiply(X_749,Y_750)) = Y_750 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_48668]) ).
tff(c_49040,plain,
! [Y_750,X_749] : ( multiply(Y_750,inverse(multiply(X_749,Y_750))) = inverse(X_749) ),
inference(superposition,[status(thm),theory(equality)],[c_49019,c_37860]) ).
tff(c_93718,plain,
multiply(b,inverse(inverse(d))) = inverse(multiply(d,h)),
inference(superposition,[status(thm),theory(equality)],[c_93572,c_49040]) ).
tff(c_93770,plain,
inverse(multiply(d,h)) = multiply(b,d),
inference(demodulation,[status(thm),theory(equality)],[c_33893,c_93718]) ).
tff(c_38252,plain,
! [Y_691] : ( product(Y_691,Y_691,inverse(Y_691)) = true ),
inference(superposition,[status(thm),theory(equality)],[c_38214,c_14]) ).
tff(c_94016,plain,
product(multiply(d,h),multiply(d,h),multiply(b,d)) = true,
inference(superposition,[status(thm),theory(equality)],[c_93770,c_38252]) ).
tff(c_41290,plain,
! [Y_704,W_703,U_702,X_705,X_706] : ( ifeq(true,true,ifeq(product(X_705,multiply(X_706,Y_704),W_703),true,ifeq(product(X_705,X_706,U_702),true,product(U_702,Y_704,W_703),true),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_392]) ).
tff(c_41828,plain,
! [X_11,Y_12,Y_704,W_703] : ( ifeq(true,true,ifeq(product(X_11,multiply(Y_12,Y_704),W_703),true,ifeq(true,true,product(multiply(X_11,Y_12),Y_704,W_703),true),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_41290]) ).
tff(c_42020,plain,
! [X_11,Y_12,Y_704,W_703] : ( ifeq(product(X_11,multiply(Y_12,Y_704),W_703),true,product(multiply(X_11,Y_12),Y_704,W_703),true) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_41828]) ).
tff(c_394106,plain,
ifeq(true,true,product(multiply(multiply(d,h),d),h,multiply(b,d)),true) = true,
inference(superposition,[status(thm),theory(equality)],[c_94016,c_42020]) ).
tff(c_394375,plain,
product(multiply(k,b),h,multiply(b,d)) = true,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_97092,c_394106]) ).
tff(c_394641,plain,
ifeq2(true,true,multiply(b,d),multiply(multiply(k,b),h)) = multiply(multiply(k,b),h),
inference(superposition,[status(thm),theory(equality)],[c_394375,c_8578]) ).
tff(c_394772,plain,
multiply(multiply(k,b),h) = multiply(b,d),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_394641]) ).
tff(c_394978,plain,
product(multiply(b,d),inverse(h),multiply(k,b)) = true,
inference(superposition,[status(thm),theory(equality)],[c_394772,c_37171]) ).
tff(c_645,plain,
! [X_68,X_11,Y_12,U_69,W_71] : ( ifeq(product(U_69,Y_12,W_71),true,ifeq(true,true,ifeq(product(X_68,X_11,U_69),true,product(X_68,multiply(X_11,Y_12),W_71),true),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_610]) ).
tff(c_20716,plain,
! [W_472,X_471,X_468,U_470,Y_469] : ( ifeq(product(U_470,Y_469,W_472),true,ifeq(product(X_468,X_471,U_470),true,product(X_468,multiply(X_471,Y_469),W_472),true),true) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_645]) ).
tff(c_20895,plain,
! [X_11,Y_12,Y_469,W_472] : ( ifeq(product(multiply(X_11,Y_12),Y_469,W_472),true,ifeq(true,true,product(X_11,multiply(Y_12,Y_469),W_472),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_20716]) ).
tff(c_20979,plain,
! [X_11,Y_12,Y_469,W_472] : ( ifeq(product(multiply(X_11,Y_12),Y_469,W_472),true,product(X_11,multiply(Y_12,Y_469),W_472),true) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_20895]) ).
tff(c_397137,plain,
ifeq(true,true,product(b,multiply(d,inverse(h)),multiply(k,b)),true) = true,
inference(superposition,[status(thm),theory(equality)],[c_394978,c_20979]) ).
tff(c_397413,plain,
product(b,k,multiply(k,b)) = true,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_11362,c_397137]) ).
tff(c_397729,plain,
ifeq2(true,true,multiply(b,k),multiply(k,b)) = multiply(k,b),
inference(superposition,[status(thm),theory(equality)],[c_397413,c_298]) ).
tff(c_397809,plain,
multiply(k,b) = multiply(b,k),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_397729]) ).
tff(c_397842,plain,
multiply(multiply(d,h),d) = multiply(b,k),
inference(demodulation,[status(thm),theory(equality)],[c_397809,c_97092]) ).
tff(c_49547,plain,
! [X_753,Y_754] : ( multiply(inverse(multiply(X_753,Y_754)),X_753) = inverse(Y_754) ),
inference(superposition,[status(thm),theory(equality)],[c_37860,c_49019]) ).
tff(c_49586,plain,
! [Y_754,X_753] : ( multiply(inverse(Y_754),inverse(X_753)) = inverse(multiply(X_753,Y_754)) ),
inference(superposition,[status(thm),theory(equality)],[c_49547,c_37860]) ).
tff(c_38223,plain,
! [Y_691] : ( product(inverse(Y_691),inverse(Y_691),Y_691) = true ),
inference(superposition,[status(thm),theory(equality)],[c_38214,c_37171]) ).
tff(c_28,plain,
product(c,inverse(a),d) = true,
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_34032,plain,
! [Y_644,V_645,X_646] : ( ifeq(true,true,ifeq(product(Y_644,inverse(a),V_645),true,ifeq(product(X_646,Y_644,c),true,product(X_646,V_645,d),true),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_28,c_610]) ).
tff(c_34072,plain,
! [X_646,X_11] : ( ifeq(true,true,ifeq(true,true,ifeq(product(X_646,X_11,c),true,product(X_646,multiply(X_11,inverse(a)),d),true),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_34032]) ).
tff(c_161129,plain,
! [X_1106,X_1107] : ( ifeq(product(X_1106,X_1107,c),true,product(X_1106,multiply(X_1107,inverse(a)),d),true) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_34072]) ).
tff(c_161257,plain,
ifeq(true,true,product(inverse(c),multiply(inverse(c),inverse(a)),d),true) = true,
inference(superposition,[status(thm),theory(equality)],[c_38223,c_161129]) ).
tff(c_161326,plain,
product(inverse(c),inverse(multiply(a,c)),d) = true,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_49586,c_161257]) ).
tff(c_163098,plain,
ifeq2(true,true,d,multiply(inverse(c),inverse(multiply(a,c)))) = multiply(inverse(c),inverse(multiply(a,c))),
inference(superposition,[status(thm),theory(equality)],[c_161326,c_8578]) ).
tff(c_163244,plain,
inverse(multiply(multiply(a,c),c)) = d,
inference(demodulation,[status(thm),theory(equality)],[c_49586,c_2,c_163098]) ).
tff(c_163837,plain,
inverse(multiply(a,c)) = multiply(c,d),
inference(superposition,[status(thm),theory(equality)],[c_163244,c_49040]) ).
tff(c_37950,plain,
! [X_689,X_642] : ( multiply(multiply(X_689,inverse(X_642)),X_642) = X_689 ),
inference(superposition,[status(thm),theory(equality)],[c_33893,c_37902]) ).
tff(c_49583,plain,
! [X_642,Y_754] : ( inverse(multiply(inverse(X_642),Y_754)) = multiply(inverse(Y_754),X_642) ),
inference(superposition,[status(thm),theory(equality)],[c_49547,c_37950]) ).
tff(c_49133,plain,
! [X_642,Y_750] : ( multiply(X_642,multiply(inverse(X_642),Y_750)) = Y_750 ),
inference(superposition,[status(thm),theory(equality)],[c_33893,c_49019]) ).
tff(c_49229,plain,
! [X_751,Y_752] : ( multiply(X_751,multiply(inverse(X_751),Y_752)) = Y_752 ),
inference(superposition,[status(thm),theory(equality)],[c_33893,c_49019]) ).
tff(c_49282,plain,
! [X_751,Y_752] : ( product(X_751,multiply(inverse(X_751),Y_752),Y_752) = true ),
inference(superposition,[status(thm),theory(equality)],[c_49229,c_14]) ).
tff(c_40570,plain,
! [Y_698,V_700] : ( ifeq(true,true,ifeq(product(inverse(a),Y_698,V_700),true,ifeq(true,true,product(c,V_700,multiply(d,Y_698)),true),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_28,c_40301]) ).
tff(c_162748,plain,
! [Y_1111,V_1112] : ( ifeq(product(inverse(a),Y_1111,V_1112),true,product(c,V_1112,multiply(d,Y_1111)),true) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_40570]) ).
tff(c_162814,plain,
! [Y_752] : ( ifeq(true,true,product(c,Y_752,multiply(d,multiply(inverse(inverse(a)),Y_752))),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_49282,c_162748]) ).
tff(c_169777,plain,
! [Y_1126] : ( product(c,Y_1126,multiply(d,multiply(a,Y_1126))) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_33893,c_162814]) ).
tff(c_170420,plain,
! [Y_1126] : ( ifeq2(true,true,multiply(c,Y_1126),multiply(d,multiply(a,Y_1126))) = multiply(d,multiply(a,Y_1126)) ),
inference(superposition,[status(thm),theory(equality)],[c_169777,c_298]) ).
tff(c_170683,plain,
! [Y_1127] : ( multiply(d,multiply(a,Y_1127)) = multiply(c,Y_1127) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_170420]) ).
tff(c_181697,plain,
! [Y_1145] : ( multiply(c,multiply(inverse(a),Y_1145)) = multiply(d,Y_1145) ),
inference(superposition,[status(thm),theory(equality)],[c_49133,c_170683]) ).
tff(c_49121,plain,
! [X_687,Y_688] : ( multiply(inverse(multiply(X_687,Y_688)),X_687) = inverse(Y_688) ),
inference(superposition,[status(thm),theory(equality)],[c_37860,c_49019]) ).
tff(c_181804,plain,
! [Y_1145] : ( multiply(inverse(multiply(d,Y_1145)),c) = inverse(multiply(inverse(a),Y_1145)) ),
inference(superposition,[status(thm),theory(equality)],[c_181697,c_49121]) ).
tff(c_181913,plain,
! [Y_1145] : ( multiply(inverse(multiply(d,Y_1145)),c) = multiply(inverse(Y_1145),a) ),
inference(demodulation,[status(thm),theory(equality)],[c_49583,c_181804]) ).
tff(c_38060,plain,
! [Y_93] : ( multiply(Y_93,Y_93) = inverse(Y_93) ),
inference(demodulation,[status(thm),theory(equality)],[c_838,c_38016]) ).
tff(c_39278,plain,
! [X_694,X_695] : ( multiply(multiply(X_694,inverse(X_695)),X_695) = X_694 ),
inference(superposition,[status(thm),theory(equality)],[c_33893,c_37902]) ).
tff(c_39316,plain,
! [X_694,X_695] : ( product(multiply(X_694,inverse(X_695)),X_695,X_694) = true ),
inference(superposition,[status(thm),theory(equality)],[c_39278,c_14]) ).
tff(c_424,plain,
! [Z_62,W_64,V_63,X_11,Y_12] : ( ifeq(product(Y_12,Z_62,V_63),true,ifeq(product(X_11,V_63,W_64),true,ifeq(true,true,product(multiply(X_11,Y_12),Z_62,W_64),true),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_392]) ).
tff(c_18635,plain,
! [Z_449,W_447,Y_448,V_446,X_450] : ( ifeq(product(Y_448,Z_449,V_446),true,ifeq(product(X_450,V_446,W_447),true,product(multiply(X_450,Y_448),Z_449,W_447),true),true) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_424]) ).
tff(c_18796,plain,
! [Y_448,Z_449] : ( ifeq(product(Y_448,Z_449,inverse(a)),true,ifeq(true,true,product(multiply(c,Y_448),Z_449,d),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_28,c_18635]) ).
tff(c_175995,plain,
! [Y_1133,Z_1134] : ( ifeq(product(Y_1133,Z_1134,inverse(a)),true,product(multiply(c,Y_1133),Z_1134,d),true) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_18796]) ).
tff(c_176111,plain,
! [X_695] : ( ifeq(true,true,product(multiply(c,multiply(inverse(a),inverse(X_695))),X_695,d),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_39316,c_175995]) ).
tff(c_217141,plain,
! [X_1209] : ( product(multiply(c,inverse(multiply(X_1209,a))),X_1209,d) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_49586,c_176111]) ).
tff(c_26,plain,
product(a,b,c) = true,
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_40595,plain,
! [X_697,X_701] : ( ifeq(true,true,ifeq(true,true,ifeq(product(X_697,a,X_701),true,product(X_697,c,multiply(X_701,b)),true),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_40301]) ).
tff(c_40681,plain,
! [X_697,X_701] : ( ifeq(product(X_697,a,X_701),true,product(X_697,c,multiply(X_701,b)),true) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_40595]) ).
tff(c_217256,plain,
ifeq(true,true,product(multiply(c,inverse(multiply(a,a))),c,multiply(d,b)),true) = true,
inference(superposition,[status(thm),theory(equality)],[c_217141,c_40681]) ).
tff(c_217934,plain,
product(multiply(c,a),c,multiply(d,b)) = true,
inference(demodulation,[status(thm),theory(equality)],[c_33893,c_4,c_38060,c_217256]) ).
tff(c_218287,plain,
ifeq2(true,true,multiply(d,b),multiply(multiply(c,a),c)) = multiply(multiply(c,a),c),
inference(superposition,[status(thm),theory(equality)],[c_217934,c_8578]) ).
tff(c_218423,plain,
multiply(multiply(c,a),c) = multiply(d,b),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_218287]) ).
tff(c_218569,plain,
multiply(inverse(multiply(d,b)),multiply(c,a)) = inverse(c),
inference(superposition,[status(thm),theory(equality)],[c_218423,c_49121]) ).
tff(c_250635,plain,
product(inverse(multiply(d,b)),multiply(c,a),inverse(c)) = true,
inference(superposition,[status(thm),theory(equality)],[c_218569,c_14]) ).
tff(c_300765,plain,
ifeq(true,true,product(multiply(inverse(multiply(d,b)),c),a,inverse(c)),true) = true,
inference(superposition,[status(thm),theory(equality)],[c_250635,c_42020]) ).
tff(c_301049,plain,
product(multiply(inverse(b),a),a,inverse(c)) = true,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_181913,c_300765]) ).
tff(c_301318,plain,
ifeq2(true,true,inverse(c),multiply(multiply(inverse(b),a),a)) = multiply(multiply(inverse(b),a),a),
inference(superposition,[status(thm),theory(equality)],[c_301049,c_8578]) ).
tff(c_301454,plain,
multiply(multiply(inverse(b),a),a) = inverse(c),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_301318]) ).
tff(c_301633,plain,
multiply(a,inverse(inverse(c))) = inverse(multiply(inverse(b),a)),
inference(superposition,[status(thm),theory(equality)],[c_301454,c_49040]) ).
tff(c_301697,plain,
multiply(inverse(a),b) = multiply(a,c),
inference(demodulation,[status(thm),theory(equality)],[c_49583,c_33893,c_301633]) ).
tff(c_301939,plain,
multiply(inverse(multiply(a,c)),inverse(a)) = inverse(b),
inference(superposition,[status(thm),theory(equality)],[c_301697,c_49121]) ).
tff(c_302007,plain,
multiply(multiply(c,d),inverse(a)) = inverse(b),
inference(demodulation,[status(thm),theory(equality)],[c_163837,c_301939]) ).
tff(c_164303,plain,
inverse(multiply(c,d)) = multiply(a,c),
inference(superposition,[status(thm),theory(equality)],[c_163837,c_33893]) ).
tff(c_94043,plain,
inverse(multiply(b,d)) = multiply(d,h),
inference(superposition,[status(thm),theory(equality)],[c_93770,c_33893]) ).
tff(c_93739,plain,
multiply(inverse(d),inverse(b)) = multiply(d,h),
inference(superposition,[status(thm),theory(equality)],[c_93572,c_37860]) ).
tff(c_58321,plain,
! [X_782,Y_783] : ( inverse(multiply(inverse(X_782),Y_783)) = multiply(inverse(Y_783),X_782) ),
inference(superposition,[status(thm),theory(equality)],[c_49547,c_37950]) ).
tff(c_58415,plain,
! [X_689,Y_783,X_782] : ( multiply(multiply(X_689,multiply(inverse(Y_783),X_782)),multiply(inverse(X_782),Y_783)) = X_689 ),
inference(superposition,[status(thm),theory(equality)],[c_58321,c_37950]) ).
tff(c_99820,plain,
! [X_689] : ( multiply(multiply(X_689,multiply(inverse(inverse(b)),d)),multiply(d,h)) = X_689 ),
inference(superposition,[status(thm),theory(equality)],[c_93739,c_58415]) ).
tff(c_134108,plain,
! [X_1047] : ( multiply(multiply(X_1047,multiply(b,d)),multiply(d,h)) = X_1047 ),
inference(demodulation,[status(thm),theory(equality)],[c_33893,c_99820]) ).
tff(c_287673,plain,
! [X_1274] : ( product(multiply(X_1274,multiply(b,d)),multiply(d,h),X_1274) = true ),
inference(superposition,[status(thm),theory(equality)],[c_134108,c_14]) ).
tff(c_24305,plain,
! [Y_515,V_516,X_517] : ( ifeq(true,true,ifeq(product(Y_515,b,V_516),true,ifeq(product(X_517,Y_515,a),true,product(X_517,V_516,c),true),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_610]) ).
tff(c_24338,plain,
! [X_517,X_11] : ( ifeq(true,true,ifeq(true,true,ifeq(product(X_517,X_11,a),true,product(X_517,multiply(X_11,b),c),true),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_24305]) ).
tff(c_24381,plain,
! [X_517,X_11] : ( ifeq(product(X_517,X_11,a),true,product(X_517,multiply(X_11,b),c),true) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_24338]) ).
tff(c_287774,plain,
ifeq(true,true,product(multiply(a,multiply(b,d)),multiply(multiply(d,h),b),c),true) = true,
inference(superposition,[status(thm),theory(equality)],[c_287673,c_24381]) ).
tff(c_288266,plain,
product(multiply(a,multiply(b,d)),inverse(d),c) = true,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_93572,c_287774]) ).
tff(c_32192,plain,
! [X_8,X_620,U_621] : ( ifeq(product(X_8,X_620,U_621),true,product(U_621,inverse(X_620),X_8),true) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_32129]) ).
tff(c_288475,plain,
ifeq(true,true,product(c,inverse(inverse(d)),multiply(a,multiply(b,d))),true) = true,
inference(superposition,[status(thm),theory(equality)],[c_288266,c_32192]) ).
tff(c_288697,plain,
product(c,d,multiply(a,multiply(b,d))) = true,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_33893,c_288475]) ).
tff(c_289032,plain,
ifeq2(true,true,multiply(c,d),multiply(a,multiply(b,d))) = multiply(a,multiply(b,d)),
inference(superposition,[status(thm),theory(equality)],[c_288697,c_298]) ).
tff(c_289129,plain,
multiply(a,multiply(b,d)) = multiply(c,d),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_289032]) ).
tff(c_289304,plain,
multiply(inverse(multiply(c,d)),a) = inverse(multiply(b,d)),
inference(superposition,[status(thm),theory(equality)],[c_289129,c_49121]) ).
tff(c_289362,plain,
multiply(multiply(a,c),a) = multiply(d,h),
inference(demodulation,[status(thm),theory(equality)],[c_164303,c_94043,c_289304]) ).
tff(c_164276,plain,
product(multiply(a,c),multiply(a,c),multiply(c,d)) = true,
inference(superposition,[status(thm),theory(equality)],[c_163837,c_38252]) ).
tff(c_447637,plain,
ifeq(true,true,product(multiply(multiply(a,c),a),c,multiply(c,d)),true) = true,
inference(superposition,[status(thm),theory(equality)],[c_164276,c_42020]) ).
tff(c_447881,plain,
product(multiply(d,h),c,multiply(c,d)) = true,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_289362,c_447637]) ).
tff(c_40567,plain,
! [X_697,X_701] : ( ifeq(true,true,ifeq(true,true,ifeq(product(X_697,c,X_701),true,product(X_697,d,multiply(X_701,inverse(a))),true),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_28,c_40301]) ).
tff(c_40672,plain,
! [X_697,X_701] : ( ifeq(product(X_697,c,X_701),true,product(X_697,d,multiply(X_701,inverse(a))),true) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_40567]) ).
tff(c_448027,plain,
ifeq(true,true,product(multiply(d,h),d,multiply(multiply(c,d),inverse(a))),true) = true,
inference(superposition,[status(thm),theory(equality)],[c_447881,c_40672]) ).
tff(c_448249,plain,
product(multiply(d,h),d,inverse(b)) = true,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_302007,c_448027]) ).
tff(c_448525,plain,
ifeq2(true,true,inverse(b),multiply(multiply(d,h),d)) = multiply(multiply(d,h),d),
inference(superposition,[status(thm),theory(equality)],[c_448249,c_8578]) ).
tff(c_448668,plain,
multiply(b,k) = inverse(b),
inference(demodulation,[status(thm),theory(equality)],[c_397842,c_2,c_448525]) ).
tff(c_398021,plain,
multiply(multiply(b,k),inverse(b)) = k,
inference(superposition,[status(thm),theory(equality)],[c_397809,c_37860]) ).
tff(c_449120,plain,
multiply(inverse(b),inverse(b)) = k,
inference(demodulation,[status(thm),theory(equality)],[c_448668,c_398021]) ).
tff(c_449151,plain,
k = b,
inference(demodulation,[status(thm),theory(equality)],[c_38220,c_449120]) ).
tff(c_36,plain,
product(k,inverse(b),identity) != true,
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_449560,plain,
product(b,inverse(b),identity) != true,
inference(demodulation,[status(thm),theory(equality)],[c_449151,c_36]) ).
tff(c_449581,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12,c_449560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP002-10 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 21:55:43 EDT 2023
% 0.13/0.35 % CPUTime :
% 289.56/242.20 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 289.77/242.24
% 289.77/242.24 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 289.92/242.33
% 289.92/242.33 Inference rules
% 289.92/242.33 ----------------------
% 289.92/242.33 #Ref : 0
% 289.92/242.33 #Sup : 120957
% 289.92/242.33 #Fact : 0
% 289.92/242.33 #Define : 0
% 289.92/242.33 #Split : 0
% 289.92/242.33 #Chain : 0
% 289.92/242.33 #Close : 0
% 289.92/242.33
% 289.92/242.33 Ordering : KBO
% 289.92/242.33
% 289.92/242.33 Simplification rules
% 289.92/242.33 ----------------------
% 289.92/242.33 #Subsume : 0
% 289.92/242.33 #Demod : 141530
% 289.92/242.33 #Tautology : 52729
% 289.92/242.33 #SimpNegUnit : 0
% 289.92/242.33 #BackRed : 655
% 289.92/242.33
% 289.92/242.33 #Partial instantiations: 0
% 289.92/242.33 #Strategies tried : 1
% 289.92/242.33
% 289.92/242.33 Timing (in seconds)
% 289.92/242.33 ----------------------
% 289.92/242.34 Preprocessing : 0.46
% 289.92/242.34 Parsing : 0.26
% 289.92/242.34 CNF conversion : 0.02
% 289.92/242.34 Main loop : 240.66
% 289.92/242.34 Inferencing : 9.82
% 289.92/242.34 Reduction : 169.20
% 289.92/242.34 Demodulation : 160.21
% 289.92/242.34 BG Simplification : 0.50
% 289.92/242.34 Subsumption : 42.21
% 289.92/242.34 Abstraction : 0.58
% 289.92/242.34 MUC search : 0.00
% 289.92/242.34 Cooper : 0.00
% 289.92/242.34 Total : 241.27
% 289.92/242.34 Index Insertion : 0.00
% 289.92/242.34 Index Deletion : 0.00
% 289.92/242.34 Index Matching : 0.00
% 289.92/242.34 BG Taut test : 0.00
%------------------------------------------------------------------------------