TSTP Solution File: GRP348-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP348-1 : TPTP v8.1.2. Released v2.5.0.
% 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 : n008.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 10:41:01 EDT 2023
% Result : Unsatisfiable 11.85s 3.88s
% Output : CNFRefutation 12.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 31
% Syntax : Number of formulae : 436 ( 373 unt; 9 typ; 0 def)
% Number of atoms : 548 ( 528 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 262 ( 141 ~; 121 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 194 (; 194 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > sk_c6 > sk_c5 > sk_c4 > sk_c3 > sk_c2 > sk_c1 > identity
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(sk_c4,type,
sk_c4: $i ).
tff(sk_c5,type,
sk_c5: $i ).
tff(sk_c2,type,
sk_c2: $i ).
tff(sk_c3,type,
sk_c3: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(sk_c6,type,
sk_c6: $i ).
tff(sk_c1,type,
sk_c1: $i ).
tff(identity,type,
identity: $i ).
tff(f_57,axiom,
! [X] : ( multiply(inverse(X),X) = identity ),
file(unknown,unknown) ).
tff(f_53,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_71,axiom,
( ( multiply(sk_c5,sk_c6) = sk_c4 )
| ( inverse(sk_c3) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_60,axiom,
! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_113,axiom,
( ( multiply(sk_c2,sk_c4) = sk_c5 )
| ( inverse(sk_c4) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_107,axiom,
( ( inverse(sk_c2) = sk_c5 )
| ( inverse(sk_c3) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_89,axiom,
( ( multiply(sk_c1,sk_c5) = sk_c6 )
| ( inverse(sk_c4) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_77,axiom,
( ( inverse(sk_c1) = sk_c6 )
| ( inverse(sk_c4) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_149,axiom,
! [X2,X3,X1] :
( ( multiply(sk_c5,sk_c6) != sk_c4 )
| ( inverse(X2) != sk_c6 )
| ( multiply(X2,sk_c5) != sk_c6 )
| ( inverse(X3) != sk_c5 )
| ( multiply(X3,sk_c4) != sk_c5 )
| ( inverse(sk_c4) != sk_c5 )
| ( multiply(sk_c4,sk_c5) != sk_c6 )
| ( inverse(X1) != sk_c6 )
| ( multiply(X1,sk_c5) != sk_c6 ) ),
file(unknown,unknown) ).
tff(f_92,axiom,
( ( multiply(sk_c1,sk_c5) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_65,axiom,
( ( multiply(sk_c5,sk_c6) = sk_c4 )
| ( inverse(sk_c4) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_68,axiom,
( ( multiply(sk_c5,sk_c6) = sk_c4 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_74,axiom,
( ( multiply(sk_c5,sk_c6) = sk_c4 )
| ( multiply(sk_c3,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_116,axiom,
( ( multiply(sk_c2,sk_c4) = sk_c5 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_119,axiom,
( ( multiply(sk_c2,sk_c4) = sk_c5 )
| ( inverse(sk_c3) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_122,axiom,
( ( multiply(sk_c2,sk_c4) = sk_c5 )
| ( multiply(sk_c3,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_80,axiom,
( ( inverse(sk_c1) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_86,axiom,
( ( inverse(sk_c1) = sk_c6 )
| ( multiply(sk_c3,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_83,axiom,
( ( inverse(sk_c1) = sk_c6 )
| ( inverse(sk_c3) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_104,axiom,
( ( inverse(sk_c2) = sk_c5 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_101,axiom,
( ( inverse(sk_c2) = sk_c5 )
| ( inverse(sk_c4) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_110,axiom,
( ( inverse(sk_c2) = sk_c5 )
| ( multiply(sk_c3,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(c_4,plain,
! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_2,plain,
! [X_1] : ( multiply(identity,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_12,plain,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(sk_c5,sk_c6) = sk_c4 ) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_99,plain,
multiply(sk_c5,sk_c6) = sk_c4,
inference(splitLeft,[status(thm)],[c_12]) ).
tff(c_119,plain,
! [X_11,Y_12,Z_13] : ( multiply(multiply(X_11,Y_12),Z_13) = multiply(X_11,multiply(Y_12,Z_13)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_149,plain,
! [X_2,Z_13] : ( multiply(inverse(X_2),multiply(X_2,Z_13)) = multiply(identity,Z_13) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_119]) ).
tff(c_159,plain,
! [X_2,Z_13] : ( multiply(inverse(X_2),multiply(X_2,Z_13)) = Z_13 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_149]) ).
tff(c_207,plain,
! [X_16,Z_17] : ( multiply(inverse(X_16),multiply(X_16,Z_17)) = Z_17 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_149]) ).
tff(c_1245,plain,
! [X_30,Z_31] : ( multiply(inverse(inverse(X_30)),Z_31) = multiply(X_30,Z_31) ),
inference(superposition,[status(thm),theory(equality)],[c_159,c_207]) ).
tff(c_261,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_207]) ).
tff(c_1252,plain,
! [X_30] : ( multiply(X_30,identity) = X_30 ),
inference(superposition,[status(thm),theory(equality)],[c_1245,c_261]) ).
tff(c_40,plain,
( ( inverse(sk_c4) = sk_c5 )
| ( multiply(sk_c2,sk_c4) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_91,plain,
multiply(sk_c2,sk_c4) = sk_c5,
inference(splitLeft,[status(thm)],[c_40]) ).
tff(c_36,plain,
( ( inverse(sk_c3) = sk_c6 )
| ( inverse(sk_c2) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_65,plain,
inverse(sk_c2) = sk_c5,
inference(splitLeft,[status(thm)],[c_36]) ).
tff(c_69,plain,
multiply(sk_c5,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_65,c_4]) ).
tff(c_146,plain,
! [Z_13] : ( multiply(sk_c5,multiply(sk_c2,Z_13)) = multiply(identity,Z_13) ),
inference(superposition,[status(thm),theory(equality)],[c_69,c_119]) ).
tff(c_184,plain,
! [Z_15] : ( multiply(sk_c5,multiply(sk_c2,Z_15)) = Z_15 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_146]) ).
tff(c_196,plain,
multiply(sk_c5,sk_c5) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_91,c_184]) ).
tff(c_225,plain,
multiply(inverse(sk_c5),sk_c4) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_196,c_207]) ).
tff(c_243,plain,
multiply(inverse(sk_c5),sk_c4) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_99,c_207]) ).
tff(c_367,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_225,c_243]) ).
tff(c_24,plain,
( ( inverse(sk_c4) = sk_c5 )
| ( multiply(sk_c1,sk_c5) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_104,plain,
multiply(sk_c1,sk_c5) = sk_c6,
inference(splitLeft,[status(thm)],[c_24]) ).
tff(c_16,plain,
( ( inverse(sk_c4) = sk_c5 )
| ( inverse(sk_c1) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_77,plain,
inverse(sk_c1) = sk_c6,
inference(splitLeft,[status(thm)],[c_16]) ).
tff(c_81,plain,
multiply(sk_c6,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_77,c_4]) ).
tff(c_143,plain,
! [Z_13] : ( multiply(sk_c6,multiply(sk_c1,Z_13)) = multiply(identity,Z_13) ),
inference(superposition,[status(thm),theory(equality)],[c_81,c_119]) ).
tff(c_161,plain,
! [Z_14] : ( multiply(sk_c6,multiply(sk_c1,Z_14)) = Z_14 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_143]) ).
tff(c_173,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_104,c_161]) ).
tff(c_379,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_367,c_367,c_173]) ).
tff(c_385,plain,
sk_c5 = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_196,c_379]) ).
tff(c_422,plain,
multiply(inverse(sk_c4),sk_c4) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_385,c_385,c_225]) ).
tff(c_430,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_422]) ).
tff(c_48,plain,
! [X1_8,X3_7,X2_6] :
( ( multiply(X1_8,sk_c5) != sk_c6 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(sk_c4,sk_c5) != sk_c6 )
| ( inverse(sk_c4) != sk_c5 )
| ( multiply(X3_7,sk_c4) != sk_c5 )
| ( inverse(X3_7) != sk_c5 )
| ( multiply(X2_6,sk_c5) != sk_c6 )
| ( inverse(X2_6) != sk_c6 )
| ( multiply(sk_c5,sk_c6) != sk_c4 ) ),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_273,plain,
! [X1_8,X3_7,X2_6] :
( ( multiply(X1_8,sk_c5) != sk_c6 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(sk_c4,sk_c5) != sk_c6 )
| ( inverse(sk_c4) != sk_c5 )
| ( multiply(X3_7,sk_c4) != sk_c5 )
| ( inverse(X3_7) != sk_c5 )
| ( multiply(X2_6,sk_c5) != sk_c6 )
| ( inverse(X2_6) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_99,c_48]) ).
tff(c_274,plain,
inverse(sk_c4) != sk_c5,
inference(splitLeft,[status(thm)],[c_273]) ).
tff(c_424,plain,
inverse(sk_c4) != sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_385,c_274]) ).
tff(c_532,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_430,c_430,c_424]) ).
tff(c_440,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_430,c_385]) ).
tff(c_384,plain,
inverse(sk_c1) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_367,c_77]) ).
tff(c_472,plain,
inverse(sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_440,c_384]) ).
tff(c_476,plain,
multiply(inverse(identity),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_472,c_261]) ).
tff(c_485,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_476]) ).
tff(c_487,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_485,c_472]) ).
tff(c_533,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_532,c_487]) ).
tff(c_535,plain,
inverse(sk_c4) = sk_c5,
inference(splitRight,[status(thm)],[c_273]) ).
tff(c_255,plain,
multiply(inverse(sk_c5),identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_69,c_207]) ).
tff(c_578,plain,
multiply(sk_c5,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_535,c_4]) ).
tff(c_585,plain,
multiply(inverse(sk_c5),identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_578,c_159]) ).
tff(c_626,plain,
sk_c4 = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_255,c_585]) ).
tff(c_633,plain,
multiply(sk_c2,sk_c2) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_626,c_91]) ).
tff(c_140,plain,
! [Z_13] : ( multiply(sk_c2,multiply(sk_c4,Z_13)) = multiply(sk_c5,Z_13) ),
inference(superposition,[status(thm),theory(equality)],[c_91,c_119]) ).
tff(c_759,plain,
! [Z_26] : ( multiply(sk_c2,multiply(sk_c2,Z_26)) = multiply(sk_c5,Z_26) ),
inference(demodulation,[status(thm),theory(equality)],[c_626,c_140]) ).
tff(c_783,plain,
multiply(sk_c5,sk_c2) = multiply(sk_c2,sk_c5),
inference(superposition,[status(thm),theory(equality)],[c_633,c_759]) ).
tff(c_790,plain,
multiply(sk_c2,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_69,c_783]) ).
tff(c_534,plain,
! [X2_6,X3_7,X1_8] :
( ( multiply(sk_c4,sk_c5) != sk_c6 )
| ( multiply(X2_6,sk_c5) != sk_c6 )
| ( inverse(X2_6) != sk_c6 )
| ( multiply(X3_7,sk_c4) != sk_c5 )
| ( inverse(X3_7) != sk_c5 )
| ( multiply(X1_8,sk_c5) != sk_c6 )
| ( inverse(X1_8) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_273]) ).
tff(c_625,plain,
multiply(sk_c4,sk_c5) != sk_c6,
inference(splitLeft,[status(thm)],[c_534]) ).
tff(c_627,plain,
multiply(sk_c2,sk_c5) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_626,c_625]) ).
tff(c_791,plain,
sk_c6 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_790,c_627]) ).
tff(c_631,plain,
multiply(sk_c5,sk_c5) = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_626,c_196]) ).
tff(c_137,plain,
! [Z_13] : ( multiply(sk_c5,multiply(sk_c6,Z_13)) = multiply(sk_c4,Z_13) ),
inference(superposition,[status(thm),theory(equality)],[c_99,c_119]) ).
tff(c_849,plain,
! [Z_27] : ( multiply(sk_c5,multiply(sk_c6,Z_27)) = multiply(sk_c2,Z_27) ),
inference(demodulation,[status(thm),theory(equality)],[c_626,c_137]) ).
tff(c_870,plain,
multiply(sk_c5,sk_c5) = multiply(sk_c2,sk_c6),
inference(superposition,[status(thm),theory(equality)],[c_173,c_849]) ).
tff(c_881,plain,
multiply(sk_c2,sk_c6) = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_631,c_870]) ).
tff(c_889,plain,
multiply(inverse(sk_c2),sk_c2) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_881,c_159]) ).
tff(c_899,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_69,c_65,c_889]) ).
tff(c_901,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_791,c_899]) ).
tff(c_903,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(splitRight,[status(thm)],[c_534]) ).
tff(c_907,plain,
multiply(inverse(sk_c4),sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_903,c_159]) ).
tff(c_913,plain,
sk_c5 = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_99,c_535,c_907]) ).
tff(c_917,plain,
multiply(inverse(sk_c4),sk_c4) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_913,c_243]) ).
tff(c_928,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_917]) ).
tff(c_915,plain,
multiply(sk_c4,sk_c4) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_913,c_903]) ).
tff(c_1141,plain,
multiply(sk_c4,sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_928,c_915]) ).
tff(c_927,plain,
inverse(sk_c2) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_913,c_65]) ).
tff(c_925,plain,
multiply(sk_c2,sk_c4) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_913,c_91]) ).
tff(c_1171,plain,
multiply(inverse(sk_c2),sk_c4) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_925,c_159]) ).
tff(c_1177,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_1141,c_927,c_1171]) ).
tff(c_264,plain,
! [X_1] : ( multiply(inverse(identity),X_1) = X_1 ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_207]) ).
tff(c_249,plain,
multiply(inverse(sk_c6),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_81,c_207]) ).
tff(c_953,plain,
multiply(inverse(identity),identity) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_928,c_249]) ).
tff(c_957,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_264,c_953]) ).
tff(c_956,plain,
inverse(sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_928,c_77]) ).
tff(c_994,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_957,c_956]) ).
tff(c_1015,plain,
multiply(sk_c4,sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_928,c_915]) ).
tff(c_1045,plain,
multiply(inverse(sk_c2),sk_c4) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_925,c_159]) ).
tff(c_1051,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_1015,c_927,c_1045]) ).
tff(c_902,plain,
! [X1_8,X3_7,X2_6] :
( ( multiply(X1_8,sk_c5) != sk_c6 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(X3_7,sk_c4) != sk_c5 )
| ( inverse(X3_7) != sk_c5 )
| ( multiply(X2_6,sk_c5) != sk_c6 )
| ( inverse(X2_6) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_534]) ).
tff(c_1013,plain,
! [X1_8,X3_7,X2_6] :
( ( multiply(X1_8,sk_c4) != identity )
| ( inverse(X1_8) != identity )
| ( multiply(X3_7,sk_c4) != sk_c4 )
| ( inverse(X3_7) != sk_c4 )
| ( multiply(X2_6,sk_c4) != identity )
| ( inverse(X2_6) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_928,c_928,c_913,c_913,c_913,c_928,c_928,c_913,c_902]) ).
tff(c_1014,plain,
! [X2_6] :
( ( multiply(X2_6,sk_c4) != identity )
| ( inverse(X2_6) != identity ) ),
inference(splitLeft,[status(thm)],[c_1013]) ).
tff(c_1120,plain,
! [X2_29] :
( ( multiply(X2_29,identity) != identity )
| ( inverse(X2_29) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1051,c_1014]) ).
tff(c_1131,plain,
inverse(inverse(identity)) != identity,
inference(superposition,[status(thm),theory(equality)],[c_4,c_1120]) ).
tff(c_1139,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_994,c_994,c_1131]) ).
tff(c_1140,plain,
! [X3_7,X1_8] :
( ( multiply(X3_7,sk_c4) != sk_c4 )
| ( inverse(X3_7) != sk_c4 )
| ( multiply(X1_8,sk_c4) != identity )
| ( inverse(X1_8) != identity ) ),
inference(splitRight,[status(thm)],[c_1013]) ).
tff(c_1795,plain,
! [X3_7,X1_8] :
( ( identity != X3_7 )
| ( inverse(X3_7) != identity )
| ( identity != X1_8 )
| ( inverse(X1_8) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1252,c_1177,c_1177,c_1252,c_1177,c_1177,c_1140]) ).
tff(c_1797,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_1795]) ).
tff(c_1799,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1797,c_994]) ).
tff(c_1801,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_1795]) ).
tff(c_1803,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1801,c_994]) ).
tff(c_1805,plain,
multiply(sk_c1,sk_c5) != sk_c6,
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_26,plain,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c1,sk_c5) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_1840,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_1805,c_26]) ).
tff(c_1804,plain,
inverse(sk_c4) = sk_c5,
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_1809,plain,
multiply(sk_c5,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_1804,c_4]) ).
tff(c_1846,plain,
! [X_44,Y_45,Z_46] : ( multiply(multiply(X_44,Y_45),Z_46) = multiply(X_44,multiply(Y_45,Z_46)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_1870,plain,
! [Z_46] : ( multiply(sk_c5,multiply(sk_c4,Z_46)) = multiply(identity,Z_46) ),
inference(superposition,[status(thm),theory(equality)],[c_1809,c_1846]) ).
tff(c_2106,plain,
! [Z_53] : ( multiply(sk_c5,multiply(sk_c4,Z_53)) = Z_53 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1870]) ).
tff(c_2118,plain,
multiply(sk_c5,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_1840,c_2106]) ).
tff(c_2122,plain,
sk_c5 = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_99,c_2118]) ).
tff(c_1882,plain,
! [Z_46] : ( multiply(sk_c5,multiply(sk_c2,Z_46)) = multiply(identity,Z_46) ),
inference(superposition,[status(thm),theory(equality)],[c_69,c_1846]) ).
tff(c_1912,plain,
! [Z_48] : ( multiply(sk_c5,multiply(sk_c2,Z_48)) = Z_48 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1882]) ).
tff(c_1924,plain,
multiply(sk_c5,sk_c5) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_91,c_1912]) ).
tff(c_2125,plain,
multiply(sk_c4,sk_c4) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_2122,c_2122,c_1924]) ).
tff(c_1885,plain,
! [X_2,Z_46] : ( multiply(inverse(X_2),multiply(X_2,Z_46)) = multiply(identity,Z_46) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_1846]) ).
tff(c_2208,plain,
! [X_54,Z_55] : ( multiply(inverse(X_54),multiply(X_54,Z_55)) = Z_55 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1885]) ).
tff(c_2226,plain,
multiply(inverse(sk_c4),sk_c4) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_2125,c_2208]) ).
tff(c_2251,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_2226]) ).
tff(c_2127,plain,
multiply(sk_c4,sk_c4) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_2122,c_1840]) ).
tff(c_2189,plain,
sk_c6 = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_2125,c_2127]) ).
tff(c_2202,plain,
multiply(sk_c4,sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2189,c_81]) ).
tff(c_2319,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2251,c_2202]) ).
tff(c_2254,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2251,c_2189]) ).
tff(c_2130,plain,
multiply(sk_c1,sk_c4) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_2122,c_1805]) ).
tff(c_2365,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2319,c_2254,c_2251,c_2130]) ).
tff(c_2367,plain,
multiply(sk_c5,sk_c6) != sk_c4,
inference(splitRight,[status(thm)],[c_12]) ).
tff(c_8,plain,
( ( inverse(sk_c4) = sk_c5 )
| ( multiply(sk_c5,sk_c6) = sk_c4 ) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_2379,plain,
inverse(sk_c4) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_2367,c_8]) ).
tff(c_2383,plain,
multiply(sk_c5,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_2379,c_4]) ).
tff(c_2617,plain,
! [X_63,Y_64,Z_65] : ( multiply(multiply(X_63,Y_64),Z_65) = multiply(X_63,multiply(Y_64,Z_65)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_2650,plain,
! [Z_65] : ( multiply(sk_c5,multiply(sk_c2,Z_65)) = multiply(identity,Z_65) ),
inference(superposition,[status(thm),theory(equality)],[c_69,c_2617]) ).
tff(c_2680,plain,
! [Z_67] : ( multiply(sk_c5,multiply(sk_c2,Z_67)) = Z_67 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2650]) ).
tff(c_2692,plain,
multiply(sk_c5,sk_c5) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_91,c_2680]) ).
tff(c_2413,plain,
! [X_56,Y_57,Z_58] : ( multiply(multiply(X_56,Y_57),Z_58) = multiply(X_56,multiply(Y_57,Z_58)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_2449,plain,
! [Z_58] : ( multiply(sk_c5,multiply(sk_c2,Z_58)) = multiply(identity,Z_58) ),
inference(superposition,[status(thm),theory(equality)],[c_69,c_2413]) ).
tff(c_2489,plain,
! [Z_60] : ( multiply(sk_c5,multiply(sk_c2,Z_60)) = Z_60 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2449]) ).
tff(c_2501,plain,
multiply(sk_c5,sk_c5) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_91,c_2489]) ).
tff(c_10,plain,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c5,sk_c6) = sk_c4 ) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_2408,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_2367,c_10]) ).
tff(c_2538,plain,
! [Z_62] : ( multiply(sk_c2,multiply(sk_c4,Z_62)) = multiply(sk_c5,Z_62) ),
inference(superposition,[status(thm),theory(equality)],[c_91,c_2413]) ).
tff(c_2553,plain,
multiply(sk_c5,sk_c5) = multiply(sk_c2,sk_c6),
inference(superposition,[status(thm),theory(equality)],[c_2408,c_2538]) ).
tff(c_2557,plain,
multiply(sk_c2,sk_c6) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_2501,c_2553]) ).
tff(c_2463,plain,
! [Z_58] : ( multiply(sk_c5,multiply(sk_c2,Z_58)) = Z_58 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2449]) ).
tff(c_2561,plain,
multiply(sk_c5,sk_c4) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_2557,c_2463]) ).
tff(c_2567,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2383,c_2561]) ).
tff(c_2397,plain,
multiply(sk_c1,sk_c5) = sk_c6,
inference(splitLeft,[status(thm)],[c_26]) ).
tff(c_2446,plain,
! [Z_58] : ( multiply(sk_c6,multiply(sk_c1,Z_58)) = multiply(identity,Z_58) ),
inference(superposition,[status(thm),theory(equality)],[c_81,c_2413]) ).
tff(c_2466,plain,
! [Z_59] : ( multiply(sk_c6,multiply(sk_c1,Z_59)) = Z_59 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2446]) ).
tff(c_2478,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_2397,c_2466]) ).
tff(c_2571,plain,
multiply(identity,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_2567,c_2567,c_2478]) ).
tff(c_2580,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2571]) ).
tff(c_2437,plain,
! [Z_58] : ( multiply(sk_c5,multiply(sk_c4,Z_58)) = multiply(identity,Z_58) ),
inference(superposition,[status(thm),theory(equality)],[c_2383,c_2413]) ).
tff(c_2514,plain,
! [Z_61] : ( multiply(sk_c5,multiply(sk_c4,Z_61)) = Z_61 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2437]) ).
tff(c_2526,plain,
multiply(sk_c5,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_2408,c_2514]) ).
tff(c_2530,plain,
sk_c5 != sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_2526,c_2367]) ).
tff(c_2586,plain,
sk_c4 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_2580,c_2530]) ).
tff(c_2588,plain,
multiply(identity,identity) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_2580,c_2580,c_2501]) ).
tff(c_2596,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2588]) ).
tff(c_2601,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2586,c_2596]) ).
tff(c_2602,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(splitRight,[status(thm)],[c_26]) ).
tff(c_2752,plain,
! [Z_70] : ( multiply(sk_c2,multiply(sk_c4,Z_70)) = multiply(sk_c5,Z_70) ),
inference(superposition,[status(thm),theory(equality)],[c_91,c_2617]) ).
tff(c_2767,plain,
multiply(sk_c5,sk_c5) = multiply(sk_c2,sk_c6),
inference(superposition,[status(thm),theory(equality)],[c_2602,c_2752]) ).
tff(c_2771,plain,
multiply(sk_c2,sk_c6) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_2692,c_2767]) ).
tff(c_2664,plain,
! [Z_65] : ( multiply(sk_c5,multiply(sk_c2,Z_65)) = Z_65 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2650]) ).
tff(c_2775,plain,
multiply(sk_c5,sk_c4) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_2771,c_2664]) ).
tff(c_2781,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2383,c_2775]) ).
tff(c_14,plain,
( ( multiply(sk_c3,sk_c5) = sk_c6 )
| ( multiply(sk_c5,sk_c6) = sk_c4 ) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_2608,plain,
multiply(sk_c3,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_2367,c_14]) ).
tff(c_2366,plain,
inverse(sk_c3) = sk_c6,
inference(splitRight,[status(thm)],[c_12]) ).
tff(c_2371,plain,
multiply(sk_c6,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_2366,c_4]) ).
tff(c_2641,plain,
! [Z_65] : ( multiply(sk_c6,multiply(sk_c3,Z_65)) = multiply(identity,Z_65) ),
inference(superposition,[status(thm),theory(equality)],[c_2371,c_2617]) ).
tff(c_2703,plain,
! [Z_68] : ( multiply(sk_c6,multiply(sk_c3,Z_68)) = Z_68 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2641]) ).
tff(c_2715,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_2608,c_2703]) ).
tff(c_2785,plain,
multiply(identity,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_2781,c_2781,c_2715]) ).
tff(c_2795,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2785]) ).
tff(c_2638,plain,
! [Z_65] : ( multiply(sk_c5,multiply(sk_c4,Z_65)) = multiply(identity,Z_65) ),
inference(superposition,[status(thm),theory(equality)],[c_2383,c_2617]) ).
tff(c_2728,plain,
! [Z_69] : ( multiply(sk_c5,multiply(sk_c4,Z_69)) = Z_69 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2638]) ).
tff(c_2740,plain,
multiply(sk_c5,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_2602,c_2728]) ).
tff(c_2744,plain,
sk_c5 != sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_2740,c_2367]) ).
tff(c_2800,plain,
sk_c4 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_2795,c_2744]) ).
tff(c_2803,plain,
multiply(identity,identity) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_2795,c_2795,c_2692]) ).
tff(c_2811,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2803]) ).
tff(c_2844,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2800,c_2811]) ).
tff(c_2846,plain,
multiply(sk_c2,sk_c4) != sk_c5,
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_42,plain,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c2,sk_c4) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_2884,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_2846,c_42]) ).
tff(c_2845,plain,
inverse(sk_c4) = sk_c5,
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_2850,plain,
multiply(sk_c5,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_2845,c_4]) ).
tff(c_3443,plain,
! [X_88,Y_89,Z_90] : ( multiply(multiply(X_88,Y_89),Z_90) = multiply(X_88,multiply(Y_89,Z_90)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_3470,plain,
! [Z_90] : ( multiply(sk_c5,multiply(sk_c4,Z_90)) = multiply(identity,Z_90) ),
inference(superposition,[status(thm),theory(equality)],[c_2850,c_3443]) ).
tff(c_3531,plain,
! [Z_93] : ( multiply(sk_c5,multiply(sk_c4,Z_93)) = Z_93 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3470]) ).
tff(c_3543,plain,
multiply(sk_c5,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_2884,c_3531]) ).
tff(c_3479,plain,
! [X_2,Z_90] : ( multiply(inverse(X_2),multiply(X_2,Z_90)) = multiply(identity,Z_90) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_3443]) ).
tff(c_3555,plain,
! [X_94,Z_95] : ( multiply(inverse(X_94),multiply(X_94,Z_95)) = Z_95 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3479]) ).
tff(c_3573,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_3543,c_3555]) ).
tff(c_3631,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_3573]) ).
tff(c_2878,plain,
multiply(sk_c1,sk_c5) = sk_c6,
inference(splitLeft,[status(thm)],[c_26]) ).
tff(c_3473,plain,
! [Z_90] : ( multiply(sk_c6,multiply(sk_c1,Z_90)) = multiply(identity,Z_90) ),
inference(superposition,[status(thm),theory(equality)],[c_81,c_3443]) ).
tff(c_3495,plain,
! [Z_91] : ( multiply(sk_c6,multiply(sk_c1,Z_91)) = Z_91 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3473]) ).
tff(c_3507,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_2878,c_3495]) ).
tff(c_3639,plain,
multiply(identity,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_3631,c_3631,c_3507]) ).
tff(c_3648,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3639]) ).
tff(c_2890,plain,
multiply(sk_c5,sk_c6) = sk_c4,
inference(splitLeft,[status(thm)],[c_14]) ).
tff(c_2900,plain,
! [X_73,Y_74,Z_75] : ( multiply(multiply(X_73,Y_74),Z_75) = multiply(X_73,multiply(Y_74,Z_75)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_2930,plain,
! [Z_75] : ( multiply(sk_c5,multiply(sk_c4,Z_75)) = multiply(identity,Z_75) ),
inference(superposition,[status(thm),theory(equality)],[c_2850,c_2900]) ).
tff(c_3114,plain,
! [Z_84] : ( multiply(sk_c5,multiply(sk_c4,Z_84)) = Z_84 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2930]) ).
tff(c_3126,plain,
multiply(sk_c5,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_2884,c_3114]) ).
tff(c_3130,plain,
sk_c5 = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_2890,c_3126]) ).
tff(c_3139,plain,
multiply(sk_c4,sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_3130,c_2850]) ).
tff(c_3137,plain,
multiply(sk_c4,sk_c4) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_3130,c_2884]) ).
tff(c_3195,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_3139,c_3137]) ).
tff(c_44,plain,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(sk_c2,sk_c4) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_2859,plain,
inverse(sk_c3) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_2846,c_44]) ).
tff(c_3200,plain,
inverse(sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_3195,c_2859]) ).
tff(c_46,plain,
( ( multiply(sk_c3,sk_c5) = sk_c6 )
| ( multiply(sk_c2,sk_c4) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_2895,plain,
multiply(sk_c3,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_2846,c_46]) ).
tff(c_3135,plain,
multiply(sk_c3,sk_c4) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_3130,c_2895]) ).
tff(c_3197,plain,
multiply(sk_c3,sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_3195,c_3135]) ).
tff(c_2939,plain,
! [X_2,Z_75] : ( multiply(inverse(X_2),multiply(X_2,Z_75)) = multiply(identity,Z_75) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_2900]) ).
tff(c_3229,plain,
! [X_85,Z_86] : ( multiply(inverse(X_85),multiply(X_85,Z_86)) = Z_86 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2939]) ).
tff(c_3247,plain,
multiply(inverse(sk_c3),identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_3197,c_3229]) ).
tff(c_3278,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3200,c_3247]) ).
tff(c_3142,plain,
multiply(sk_c4,sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_3130,c_69]) ).
tff(c_3284,plain,
multiply(identity,sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_3278,c_3142]) ).
tff(c_2951,plain,
! [X_2,Z_75] : ( multiply(inverse(X_2),multiply(X_2,Z_75)) = Z_75 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2939]) ).
tff(c_3402,plain,
multiply(inverse(identity),identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_3284,c_2951]) ).
tff(c_3414,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_3402]) ).
tff(c_3140,plain,
multiply(sk_c2,sk_c4) != sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_3130,c_2846]) ).
tff(c_3282,plain,
multiply(sk_c2,identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_3278,c_3278,c_3140]) ).
tff(c_3434,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3414,c_3282]) ).
tff(c_3436,plain,
multiply(sk_c5,sk_c6) != sk_c4,
inference(splitRight,[status(thm)],[c_14]) ).
tff(c_3547,plain,
sk_c5 != sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_3543,c_3436]) ).
tff(c_3653,plain,
sk_c4 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_3648,c_3547]) ).
tff(c_3656,plain,
multiply(identity,sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_3648,c_2850]) ).
tff(c_3491,plain,
! [X_2,Z_90] : ( multiply(inverse(X_2),multiply(X_2,Z_90)) = Z_90 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3479]) ).
tff(c_3900,plain,
multiply(inverse(identity),identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_3656,c_3491]) ).
tff(c_3912,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_3900]) ).
tff(c_3914,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3653,c_3912]) ).
tff(c_3915,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(splitRight,[status(thm)],[c_26]) ).
tff(c_4332,plain,
! [X_109,Y_110,Z_111] : ( multiply(multiply(X_109,Y_110),Z_111) = multiply(X_109,multiply(Y_110,Z_111)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_4356,plain,
! [Z_111] : ( multiply(sk_c5,multiply(sk_c4,Z_111)) = multiply(identity,Z_111) ),
inference(superposition,[status(thm),theory(equality)],[c_2850,c_4332]) ).
tff(c_4407,plain,
! [Z_114] : ( multiply(sk_c5,multiply(sk_c4,Z_114)) = Z_114 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4356]) ).
tff(c_4419,plain,
multiply(sk_c5,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_3915,c_4407]) ).
tff(c_4365,plain,
! [X_2,Z_111] : ( multiply(inverse(X_2),multiply(X_2,Z_111)) = multiply(identity,Z_111) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_4332]) ).
tff(c_4510,plain,
! [X_117,Z_118] : ( multiply(inverse(X_117),multiply(X_117,Z_118)) = Z_118 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4365]) ).
tff(c_4543,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_4419,c_4510]) ).
tff(c_4596,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4543]) ).
tff(c_4576,plain,
multiply(inverse(sk_c6),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_81,c_4510]) ).
tff(c_4794,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4596,c_4576]) ).
tff(c_3921,plain,
multiply(sk_c5,sk_c6) = sk_c4,
inference(splitLeft,[status(thm)],[c_14]) ).
tff(c_3936,plain,
! [X_99,Y_100,Z_101] : ( multiply(multiply(X_99,Y_100),Z_101) = multiply(X_99,multiply(Y_100,Z_101)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_3963,plain,
! [Z_101] : ( multiply(sk_c5,multiply(sk_c4,Z_101)) = multiply(identity,Z_101) ),
inference(superposition,[status(thm),theory(equality)],[c_2850,c_3936]) ).
tff(c_4038,plain,
! [Z_105] : ( multiply(sk_c5,multiply(sk_c4,Z_105)) = Z_105 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3963]) ).
tff(c_4050,plain,
multiply(sk_c5,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_3915,c_4038]) ).
tff(c_4054,plain,
sk_c5 = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_3921,c_4050]) ).
tff(c_4064,plain,
inverse(sk_c4) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_4054,c_2845]) ).
tff(c_4074,plain,
multiply(sk_c4,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_4064,c_4]) ).
tff(c_4061,plain,
multiply(sk_c4,sk_c4) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_4054,c_3915]) ).
tff(c_4134,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4074,c_4061]) ).
tff(c_4143,plain,
multiply(identity,sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4134,c_81]) ).
tff(c_3972,plain,
! [X_2,Z_101] : ( multiply(inverse(X_2),multiply(X_2,Z_101)) = multiply(identity,Z_101) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_3936]) ).
tff(c_3984,plain,
! [X_2,Z_101] : ( multiply(inverse(X_2),multiply(X_2,Z_101)) = Z_101 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3972]) ).
tff(c_4291,plain,
multiply(inverse(identity),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_4143,c_3984]) ).
tff(c_4303,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4291]) ).
tff(c_3926,plain,
multiply(sk_c3,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_2846,c_46]) ).
tff(c_2863,plain,
multiply(sk_c6,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_2859,c_4]) ).
tff(c_3960,plain,
! [Z_101] : ( multiply(sk_c6,multiply(sk_c3,Z_101)) = multiply(identity,Z_101) ),
inference(superposition,[status(thm),theory(equality)],[c_2863,c_3936]) ).
tff(c_4015,plain,
! [Z_104] : ( multiply(sk_c6,multiply(sk_c3,Z_104)) = Z_104 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3960]) ).
tff(c_4027,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_3926,c_4015]) ).
tff(c_4056,plain,
multiply(sk_c6,sk_c6) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_4054,c_4027]) ).
tff(c_4137,plain,
multiply(identity,identity) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_4134,c_4134,c_4056]) ).
tff(c_4145,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4137]) ).
tff(c_3916,plain,
multiply(sk_c1,sk_c5) != sk_c6,
inference(splitRight,[status(thm)],[c_26]) ).
tff(c_4059,plain,
multiply(sk_c1,sk_c4) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_4054,c_3916]) ).
tff(c_4136,plain,
multiply(sk_c1,sk_c4) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_4134,c_4059]) ).
tff(c_4317,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4303,c_4145,c_4136]) ).
tff(c_4318,plain,
multiply(sk_c3,sk_c5) = sk_c6,
inference(splitRight,[status(thm)],[c_14]) ).
tff(c_4353,plain,
! [Z_111] : ( multiply(sk_c6,multiply(sk_c3,Z_111)) = multiply(identity,Z_111) ),
inference(superposition,[status(thm),theory(equality)],[c_2863,c_4332]) ).
tff(c_4486,plain,
! [Z_116] : ( multiply(sk_c6,multiply(sk_c3,Z_116)) = Z_116 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4353]) ).
tff(c_4498,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_4318,c_4486]) ).
tff(c_4431,plain,
! [Z_115] : ( multiply(sk_c4,multiply(sk_c5,Z_115)) = multiply(sk_c6,Z_115) ),
inference(superposition,[status(thm),theory(equality)],[c_3915,c_4332]) ).
tff(c_4446,plain,
multiply(sk_c6,sk_c6) = multiply(sk_c4,sk_c5),
inference(superposition,[status(thm),theory(equality)],[c_4419,c_4431]) ).
tff(c_4462,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_3915,c_4446]) ).
tff(c_4502,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_4498,c_4462]) ).
tff(c_4623,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4596,c_4502]) ).
tff(c_4611,plain,
multiply(sk_c1,sk_c5) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_4502,c_3916]) ).
tff(c_4802,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4794,c_4623,c_4623,c_4611]) ).
tff(c_4804,plain,
inverse(sk_c1) != sk_c6,
inference(splitRight,[status(thm)],[c_16]) ).
tff(c_18,plain,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( inverse(sk_c1) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_4831,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_4804,c_18]) ).
tff(c_4803,plain,
inverse(sk_c4) = sk_c5,
inference(splitRight,[status(thm)],[c_16]) ).
tff(c_4808,plain,
multiply(sk_c5,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_4803,c_4]) ).
tff(c_4853,plain,
! [X_121,Y_122,Z_123] : ( multiply(multiply(X_121,Y_122),Z_123) = multiply(X_121,multiply(Y_122,Z_123)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_4877,plain,
! [Z_123] : ( multiply(sk_c5,multiply(sk_c4,Z_123)) = multiply(identity,Z_123) ),
inference(superposition,[status(thm),theory(equality)],[c_4808,c_4853]) ).
tff(c_4932,plain,
! [Z_126] : ( multiply(sk_c5,multiply(sk_c4,Z_126)) = Z_126 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4877]) ).
tff(c_4944,plain,
multiply(sk_c5,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_4831,c_4932]) ).
tff(c_4883,plain,
! [X_2,Z_123] : ( multiply(inverse(X_2),multiply(X_2,Z_123)) = multiply(identity,Z_123) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_4853]) ).
tff(c_4958,plain,
! [X_127,Z_128] : ( multiply(inverse(X_127),multiply(X_127,Z_128)) = Z_128 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4883]) ).
tff(c_4976,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_4944,c_4958]) ).
tff(c_5025,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4976]) ).
tff(c_22,plain,
( ( multiply(sk_c3,sk_c5) = sk_c6 )
| ( inverse(sk_c1) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_4841,plain,
multiply(sk_c3,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_4804,c_22]) ).
tff(c_20,plain,
( ( inverse(sk_c3) = sk_c6 )
| ( inverse(sk_c1) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_4812,plain,
inverse(sk_c3) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_4804,c_20]) ).
tff(c_4816,plain,
multiply(sk_c6,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_4812,c_4]) ).
tff(c_4874,plain,
! [Z_123] : ( multiply(sk_c6,multiply(sk_c3,Z_123)) = multiply(identity,Z_123) ),
inference(superposition,[status(thm),theory(equality)],[c_4816,c_4853]) ).
tff(c_4896,plain,
! [Z_124] : ( multiply(sk_c6,multiply(sk_c3,Z_124)) = Z_124 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4874]) ).
tff(c_4908,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_4841,c_4896]) ).
tff(c_5032,plain,
multiply(identity,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_5025,c_5025,c_4908]) ).
tff(c_5039,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_5032]) ).
tff(c_4956,plain,
! [X1_8,X3_7,X2_6] :
( ( multiply(X1_8,sk_c5) != sk_c6 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(X3_7,sk_c4) != sk_c5 )
| ( inverse(X3_7) != sk_c5 )
| ( multiply(X2_6,sk_c5) != sk_c6 )
| ( inverse(X2_6) != sk_c6 )
| ( sk_c5 != sk_c4 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4944,c_4803,c_4831,c_48]) ).
tff(c_4957,plain,
sk_c5 != sk_c4,
inference(splitLeft,[status(thm)],[c_4956]) ).
tff(c_5080,plain,
sk_c4 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_5039,c_4957]) ).
tff(c_5084,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_5039,c_4803]) ).
tff(c_5107,plain,
multiply(identity,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_5084,c_4]) ).
tff(c_4894,plain,
! [X_2,Z_123] : ( multiply(inverse(X_2),multiply(X_2,Z_123)) = Z_123 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4883]) ).
tff(c_5233,plain,
multiply(inverse(identity),identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_5107,c_4894]) ).
tff(c_5245,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_5233]) ).
tff(c_5247,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5080,c_5245]) ).
tff(c_5249,plain,
sk_c5 = sk_c4,
inference(splitRight,[status(thm)],[c_4956]) ).
tff(c_5250,plain,
multiply(sk_c4,sk_c6) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_5249,c_5249,c_4944]) ).
tff(c_5350,plain,
multiply(inverse(sk_c4),sk_c4) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_5250,c_4894]) ).
tff(c_5356,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_5350]) ).
tff(c_5296,plain,
! [X_132,Z_133] : ( multiply(inverse(X_132),multiply(X_132,Z_133)) = Z_133 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4883]) ).
tff(c_5492,plain,
! [X_136,Z_137] : ( multiply(inverse(inverse(X_136)),Z_137) = multiply(X_136,Z_137) ),
inference(superposition,[status(thm),theory(equality)],[c_4894,c_5296]) ).
tff(c_5338,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_5296]) ).
tff(c_5499,plain,
! [X_136] : ( multiply(X_136,identity) = X_136 ),
inference(superposition,[status(thm),theory(equality)],[c_5492,c_5338]) ).
tff(c_5253,plain,
multiply(sk_c6,sk_c6) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_5249,c_4908]) ).
tff(c_5360,plain,
multiply(identity,identity) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_5356,c_5356,c_5253]) ).
tff(c_5365,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_5360]) ).
tff(c_5372,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_5365,c_5249]) ).
tff(c_5248,plain,
! [X2_6,X3_7,X1_8] :
( ( multiply(X2_6,sk_c5) != sk_c6 )
| ( inverse(X2_6) != sk_c6 )
| ( multiply(X3_7,sk_c4) != sk_c5 )
| ( inverse(X3_7) != sk_c5 )
| ( multiply(X1_8,sk_c5) != sk_c6 )
| ( inverse(X1_8) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_4956]) ).
tff(c_13678,plain,
! [X2_6,X3_7,X1_8] :
( ( identity != X2_6 )
| ( inverse(X2_6) != identity )
| ( identity != X3_7 )
| ( inverse(X3_7) != identity )
| ( identity != X1_8 )
| ( inverse(X1_8) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_5356,c_5499,c_5372,c_5356,c_5372,c_5499,c_5372,c_5365,c_5356,c_5499,c_5372,c_5356,c_5248]) ).
tff(c_13680,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_13678]) ).
tff(c_5259,plain,
inverse(sk_c2) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_5249,c_65]) ).
tff(c_5274,plain,
multiply(sk_c4,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_5259,c_4]) ).
tff(c_5377,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_5365,c_5274]) ).
tff(c_5370,plain,
inverse(sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_5365,c_5259]) ).
tff(c_5386,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_5377,c_5370]) ).
tff(c_13682,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_13680,c_5386]) ).
tff(c_13683,plain,
! [X3_7,X2_6] :
( ( identity != X3_7 )
| ( inverse(X3_7) != identity )
| ( identity != X2_6 )
| ( inverse(X2_6) != identity ) ),
inference(splitRight,[status(thm)],[c_13678]) ).
tff(c_13685,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_13683]) ).
tff(c_13687,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_13685,c_5386]) ).
tff(c_14009,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_13683]) ).
tff(c_14011,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14009,c_5386]) ).
tff(c_14013,plain,
inverse(sk_c2) != sk_c5,
inference(splitRight,[status(thm)],[c_36]) ).
tff(c_34,plain,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( inverse(sk_c2) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_14058,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_14013,c_34]) ).
tff(c_32,plain,
( ( inverse(sk_c4) = sk_c5 )
| ( inverse(sk_c2) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_14038,plain,
inverse(sk_c4) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_14013,c_32]) ).
tff(c_14042,plain,
multiply(sk_c5,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_14038,c_4]) ).
tff(c_14074,plain,
! [X_229,Y_230,Z_231] : ( multiply(multiply(X_229,Y_230),Z_231) = multiply(X_229,multiply(Y_230,Z_231)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_14095,plain,
! [Z_231] : ( multiply(sk_c5,multiply(sk_c4,Z_231)) = multiply(identity,Z_231) ),
inference(superposition,[status(thm),theory(equality)],[c_14042,c_14074]) ).
tff(c_14117,plain,
! [Z_232] : ( multiply(sk_c5,multiply(sk_c4,Z_232)) = Z_232 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14095]) ).
tff(c_14129,plain,
multiply(sk_c5,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_14058,c_14117]) ).
tff(c_14104,plain,
! [X_2,Z_231] : ( multiply(inverse(X_2),multiply(X_2,Z_231)) = multiply(identity,Z_231) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_14074]) ).
tff(c_14179,plain,
! [X_235,Z_236] : ( multiply(inverse(X_235),multiply(X_235,Z_236)) = Z_236 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14104]) ).
tff(c_14206,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_14129,c_14179]) ).
tff(c_14246,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_14206]) ).
tff(c_38,plain,
( ( multiply(sk_c3,sk_c5) = sk_c6 )
| ( inverse(sk_c2) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_14053,plain,
multiply(sk_c3,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_14013,c_38]) ).
tff(c_14012,plain,
inverse(sk_c3) = sk_c6,
inference(splitRight,[status(thm)],[c_36]) ).
tff(c_14017,plain,
multiply(sk_c6,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_14012,c_4]) ).
tff(c_14101,plain,
! [Z_231] : ( multiply(sk_c6,multiply(sk_c3,Z_231)) = multiply(identity,Z_231) ),
inference(superposition,[status(thm),theory(equality)],[c_14017,c_14074]) ).
tff(c_14143,plain,
! [Z_233] : ( multiply(sk_c6,multiply(sk_c3,Z_233)) = Z_233 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14101]) ).
tff(c_14155,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_14053,c_14143]) ).
tff(c_14252,plain,
! [Z_237] : ( multiply(sk_c4,multiply(sk_c5,Z_237)) = multiply(sk_c6,Z_237) ),
inference(superposition,[status(thm),theory(equality)],[c_14058,c_14074]) ).
tff(c_14270,plain,
multiply(sk_c6,sk_c6) = multiply(sk_c4,sk_c5),
inference(superposition,[status(thm),theory(equality)],[c_14129,c_14252]) ).
tff(c_14281,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_14155,c_14058,c_14270]) ).
tff(c_14299,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_14246,c_14281]) ).
tff(c_14141,plain,
! [X1_8,X3_7,X2_6] :
( ( multiply(X1_8,sk_c5) != sk_c6 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(X3_7,sk_c4) != sk_c5 )
| ( inverse(X3_7) != sk_c5 )
| ( multiply(X2_6,sk_c5) != sk_c6 )
| ( inverse(X2_6) != sk_c6 )
| ( sk_c5 != sk_c4 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_14129,c_14038,c_14058,c_48]) ).
tff(c_14142,plain,
sk_c5 != sk_c4,
inference(splitLeft,[status(thm)],[c_14141]) ).
tff(c_14300,plain,
sk_c4 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_14299,c_14142]) ).
tff(c_14302,plain,
multiply(identity,sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_14299,c_14042]) ).
tff(c_14115,plain,
! [X_2,Z_231] : ( multiply(inverse(X_2),multiply(X_2,Z_231)) = Z_231 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14104]) ).
tff(c_14397,plain,
multiply(inverse(identity),identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_14302,c_14115]) ).
tff(c_14409,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_14397]) ).
tff(c_14411,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14300,c_14409]) ).
tff(c_14413,plain,
sk_c5 = sk_c4,
inference(splitRight,[status(thm)],[c_14141]) ).
tff(c_14419,plain,
inverse(sk_c4) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_14413,c_14038]) ).
tff(c_14428,plain,
multiply(sk_c4,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_14419,c_4]) ).
tff(c_14416,plain,
multiply(sk_c4,sk_c4) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_14413,c_14058]) ).
tff(c_14455,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_14428,c_14416]) ).
tff(c_14466,plain,
! [X_240,Z_241] : ( multiply(inverse(X_240),multiply(X_240,Z_241)) = Z_241 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14104]) ).
tff(c_14668,plain,
! [X_244,Z_245] : ( multiply(inverse(inverse(X_244)),Z_245) = multiply(X_244,Z_245) ),
inference(superposition,[status(thm),theory(equality)],[c_14115,c_14466]) ).
tff(c_14493,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_14466]) ).
tff(c_14675,plain,
! [X_244] : ( multiply(X_244,identity) = X_244 ),
inference(superposition,[status(thm),theory(equality)],[c_14668,c_14493]) ).
tff(c_14461,plain,
inverse(sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_14455,c_14012]) ).
tff(c_14507,plain,
multiply(identity,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_14461,c_4]) ).
tff(c_14536,plain,
multiply(inverse(identity),identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_14507,c_14115]) ).
tff(c_14548,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_14536]) ).
tff(c_14417,plain,
multiply(sk_c3,sk_c4) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_14413,c_14053]) ).
tff(c_14456,plain,
multiply(sk_c3,sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_14455,c_14417]) ).
tff(c_14572,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14548,c_14456]) ).
tff(c_14577,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_14572,c_14413]) ).
tff(c_14412,plain,
! [X2_6,X3_7,X1_8] :
( ( multiply(X2_6,sk_c5) != sk_c6 )
| ( inverse(X2_6) != sk_c6 )
| ( multiply(X3_7,sk_c4) != sk_c5 )
| ( inverse(X3_7) != sk_c5 )
| ( multiply(X1_8,sk_c5) != sk_c6 )
| ( inverse(X1_8) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_14141]) ).
tff(c_22534,plain,
! [X2_6,X3_7,X1_8] :
( ( identity != X2_6 )
| ( inverse(X2_6) != identity )
| ( identity != X3_7 )
| ( inverse(X3_7) != identity )
| ( identity != X1_8 )
| ( inverse(X1_8) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_14455,c_14675,c_14577,c_14455,c_14577,c_14675,c_14577,c_14572,c_14455,c_14675,c_14577,c_14455,c_14412]) ).
tff(c_22536,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_22534]) ).
tff(c_14552,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_14548,c_14461]) ).
tff(c_22538,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22536,c_14552]) ).
tff(c_22539,plain,
! [X3_7,X2_6] :
( ( identity != X3_7 )
| ( inverse(X3_7) != identity )
| ( identity != X2_6 )
| ( inverse(X2_6) != identity ) ),
inference(splitRight,[status(thm)],[c_22534]) ).
tff(c_22541,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_22539]) ).
tff(c_22543,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22541,c_14552]) ).
tff(c_22942,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_22539]) ).
tff(c_22944,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22942,c_14552]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP348-1 : TPTP v8.1.2. Released v2.5.0.
% 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 : n008.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 22:16:03 EDT 2023
% 0.13/0.35 % CPUTime :
% 11.85/3.88 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.85/3.92
% 11.85/3.92 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.21/3.98
% 12.21/3.98 Inference rules
% 12.21/3.98 ----------------------
% 12.21/3.98 #Ref : 0
% 12.21/3.98 #Sup : 5692
% 12.21/3.98 #Fact : 0
% 12.21/3.98 #Define : 0
% 12.21/3.98 #Split : 25
% 12.21/3.98 #Chain : 0
% 12.21/3.98 #Close : 0
% 12.21/3.98
% 12.21/3.98 Ordering : KBO
% 12.21/3.98
% 12.21/3.98 Simplification rules
% 12.21/3.98 ----------------------
% 12.21/3.98 #Subsume : 5
% 12.21/3.98 #Demod : 12512
% 12.21/3.98 #Tautology : 4518
% 12.21/3.98 #SimpNegUnit : 41
% 12.21/3.98 #BackRed : 394
% 12.21/3.98
% 12.21/3.98 #Partial instantiations: 0
% 12.21/3.98 #Strategies tried : 1
% 12.21/3.98
% 12.21/3.98 Timing (in seconds)
% 12.21/3.98 ----------------------
% 12.21/3.99 Preprocessing : 0.47
% 12.21/3.99 Parsing : 0.21
% 12.21/3.99 CNF conversion : 0.02
% 12.21/3.99 Main loop : 2.32
% 12.21/3.99 Inferencing : 0.74
% 12.21/3.99 Reduction : 1.08
% 12.21/3.99 Demodulation : 0.93
% 12.21/3.99 BG Simplification : 0.08
% 12.21/3.99 Subsumption : 0.28
% 12.21/3.99 Abstraction : 0.13
% 12.21/3.99 MUC search : 0.00
% 12.21/3.99 Cooper : 0.00
% 12.21/3.99 Total : 2.92
% 12.21/3.99 Index Insertion : 0.00
% 12.21/3.99 Index Deletion : 0.00
% 12.21/3.99 Index Matching : 0.00
% 12.21/3.99 BG Taut test : 0.00
%------------------------------------------------------------------------------