TSTP Solution File: GRP121-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP121-1 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n027.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 10:39:53 EDT 2023
% Result : Unsatisfiable 123.18s 78.88s
% Output : CNFRefutation 123.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 6
% Syntax : Number of formulae : 161 ( 158 unt; 3 typ; 0 def)
% Number of atoms : 158 ( 157 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 266 (; 266 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > #nlpp > identity > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(identity,type,
identity: $i ).
tff(f_24,axiom,
multiply(identity,identity) = identity,
file(unknown,unknown) ).
tff(f_23,axiom,
! [Y,X,Z] : ( multiply(Y,multiply(multiply(Y,multiply(multiply(Y,Y),multiply(X,Z))),multiply(Z,multiply(Z,Z)))) = X ),
file(unknown,unknown) ).
tff(f_26,axiom,
multiply(a,identity) != a,
file(unknown,unknown) ).
tff(c_4,plain,
multiply(identity,identity) = identity,
inference(cnfTransformation,[status(thm)],[f_24]) ).
tff(c_11,plain,
! [Y_4,X_5,Z_6] : ( multiply(Y_4,multiply(multiply(Y_4,multiply(multiply(Y_4,Y_4),multiply(X_5,Z_6))),multiply(Z_6,multiply(Z_6,Z_6)))) = X_5 ),
inference(cnfTransformation,[status(thm)],[f_23]) ).
tff(c_40,plain,
! [Y_4,X_5] : ( multiply(Y_4,multiply(multiply(Y_4,multiply(multiply(Y_4,Y_4),multiply(X_5,identity))),multiply(identity,identity))) = X_5 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_11]) ).
tff(c_44,plain,
! [Y_4,X_5] : ( multiply(Y_4,multiply(multiply(Y_4,multiply(multiply(Y_4,Y_4),multiply(X_5,identity))),identity)) = X_5 ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_40]) ).
tff(c_100,plain,
! [X_10,Z_11] : ( multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X_10,Z_11))),multiply(Z_11,multiply(Z_11,Z_11)))) = X_10 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_11]) ).
tff(c_128,plain,
! [X_5] : ( multiply(identity,multiply(multiply(identity,X_5),multiply(identity,multiply(identity,identity)))) = multiply(identity,multiply(multiply(identity,identity),multiply(X_5,identity))) ),
inference(superposition,[status(thm),theory(equality)],[c_44,c_100]) ).
tff(c_151,plain,
! [X_5] : ( multiply(identity,multiply(multiply(identity,X_5),identity)) = multiply(identity,multiply(identity,multiply(X_5,identity))) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_4,c_128]) ).
tff(c_64,plain,
! [Y_8,X_9] : ( multiply(Y_8,multiply(multiply(Y_8,multiply(multiply(Y_8,Y_8),multiply(X_9,identity))),identity)) = X_9 ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_40]) ).
tff(c_92,plain,
! [X_9] : ( multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X_9,identity))),identity)) = X_9 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_64]) ).
tff(c_197,plain,
! [X_13] : ( multiply(identity,multiply(multiply(identity,X_13),identity)) = multiply(identity,multiply(identity,multiply(X_13,identity))) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_4,c_128]) ).
tff(c_242,plain,
! [X_9] : ( multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X_9,identity)),identity))) = X_9 ),
inference(superposition,[status(thm),theory(equality)],[c_92,c_197]) ).
tff(c_278,plain,
! [X_9] : ( multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X_9,identity),identity)))) = X_9 ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_242]) ).
tff(c_200,plain,
! [X_13] : ( multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X_13,identity))),identity)) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X_13),identity),identity))) ),
inference(superposition,[status(thm),theory(equality)],[c_197,c_151]) ).
tff(c_508,plain,
! [X_17] : ( multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X_17),identity),identity))) = X_17 ),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_200]) ).
tff(c_532,plain,
! [X_17] : ( multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(multiply(identity,X_17),identity),identity)),identity))) = multiply(identity,multiply(X_17,identity)) ),
inference(superposition,[status(thm),theory(equality)],[c_508,c_151]) ).
tff(c_591,plain,
! [X_17] : ( multiply(multiply(identity,X_17),identity) = multiply(identity,multiply(X_17,identity)) ),
inference(demodulation,[status(thm),theory(equality)],[c_278,c_151,c_532]) ).
tff(c_34,plain,
! [X_5,Z_6] : ( multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X_5,Z_6))),multiply(Z_6,multiply(Z_6,Z_6)))) = X_5 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_11]) ).
tff(c_2,plain,
! [Y_1,X_2,Z_3] : ( multiply(Y_1,multiply(multiply(Y_1,multiply(multiply(Y_1,Y_1),multiply(X_2,Z_3))),multiply(Z_3,multiply(Z_3,Z_3)))) = X_2 ),
inference(cnfTransformation,[status(thm)],[f_23]) ).
tff(c_601,plain,
! [Y_18,X_19,Z_20] : ( multiply(multiply(Y_18,Y_18),multiply(multiply(multiply(Y_18,Y_18),multiply(Y_18,Y_18)),multiply(X_19,Z_20))) = multiply(Y_18,multiply(multiply(Y_18,X_19),multiply(multiply(Z_20,multiply(Z_20,Z_20)),multiply(multiply(Z_20,multiply(Z_20,Z_20)),multiply(Z_20,multiply(Z_20,Z_20)))))) ),
inference(superposition,[status(thm),theory(equality)],[c_11,c_2]) ).
tff(c_677,plain,
! [Y_18,X_19] : ( multiply(multiply(Y_18,Y_18),multiply(multiply(Y_18,multiply(multiply(Y_18,X_19),multiply(multiply(identity,multiply(identity,identity)),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),identity)) = X_19 ),
inference(superposition,[status(thm),theory(equality)],[c_601,c_44]) ).
tff(c_1023,plain,
! [Y_25,X_26] : ( multiply(multiply(Y_25,Y_25),multiply(multiply(Y_25,multiply(multiply(Y_25,X_26),identity)),identity)) = X_26 ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_4,c_4,c_4,c_4,c_4,c_4,c_677]) ).
tff(c_1082,plain,
! [X_5,Z_6] : ( multiply(multiply(identity,multiply(identity,multiply(X_5,Z_6))),multiply(Z_6,multiply(Z_6,Z_6))) = multiply(multiply(identity,identity),multiply(multiply(identity,multiply(X_5,identity)),identity)) ),
inference(superposition,[status(thm),theory(equality)],[c_34,c_1023]) ).
tff(c_1113,plain,
! [X_5,Z_6] : ( multiply(multiply(identity,multiply(identity,multiply(X_5,Z_6))),multiply(Z_6,multiply(Z_6,Z_6))) = multiply(identity,multiply(identity,multiply(multiply(X_5,identity),identity))) ),
inference(demodulation,[status(thm),theory(equality)],[c_591,c_4,c_1082]) ).
tff(c_18,plain,
! [Y_1,X_5,Z_6] : ( multiply(multiply(Y_1,Y_1),multiply(multiply(multiply(Y_1,Y_1),multiply(Y_1,Y_1)),multiply(X_5,Z_6))) = multiply(Y_1,multiply(multiply(Y_1,X_5),multiply(multiply(Z_6,multiply(Z_6,Z_6)),multiply(multiply(Z_6,multiply(Z_6,Z_6)),multiply(Z_6,multiply(Z_6,Z_6)))))) ),
inference(superposition,[status(thm),theory(equality)],[c_11,c_2]) ).
tff(c_819,plain,
! [Z_20] : ( multiply(identity,multiply(identity,multiply(multiply(Z_20,multiply(Z_20,Z_20)),multiply(multiply(Z_20,multiply(Z_20,Z_20)),multiply(Z_20,multiply(Z_20,Z_20)))))) = multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(identity,Z_20))) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_601]) ).
tff(c_6846,plain,
! [Z_82] : ( multiply(identity,multiply(identity,multiply(multiply(Z_82,multiply(Z_82,Z_82)),multiply(multiply(Z_82,multiply(Z_82,Z_82)),multiply(Z_82,multiply(Z_82,Z_82)))))) = multiply(identity,multiply(identity,multiply(identity,Z_82))) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_4,c_4,c_819]) ).
tff(c_701,plain,
! [Y_18,X_19,Z_20] : ( multiply(multiply(Y_18,Y_18),multiply(multiply(Y_18,multiply(multiply(Y_18,X_19),multiply(multiply(Z_20,multiply(Z_20,Z_20)),multiply(multiply(Z_20,multiply(Z_20,Z_20)),multiply(Z_20,multiply(Z_20,Z_20)))))),multiply(Z_20,multiply(Z_20,Z_20)))) = X_19 ),
inference(superposition,[status(thm),theory(equality)],[c_601,c_2]) ).
tff(c_6882,plain,
! [Z_82,Z_20] : ( multiply(multiply(identity,identity),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(identity,Z_82))),multiply(multiply(Z_20,multiply(Z_20,Z_20)),multiply(multiply(Z_20,multiply(Z_20,Z_20)),multiply(Z_20,multiply(Z_20,Z_20)))))),multiply(Z_20,multiply(Z_20,Z_20)))) = multiply(identity,multiply(multiply(Z_82,multiply(Z_82,Z_82)),multiply(multiply(Z_82,multiply(Z_82,Z_82)),multiply(Z_82,multiply(Z_82,Z_82))))) ),
inference(superposition,[status(thm),theory(equality)],[c_6846,c_701]) ).
tff(c_9924,plain,
! [Z_96] : ( multiply(identity,multiply(multiply(Z_96,multiply(Z_96,Z_96)),multiply(multiply(Z_96,multiply(Z_96,Z_96)),multiply(Z_96,multiply(Z_96,Z_96))))) = multiply(identity,multiply(identity,Z_96)) ),
inference(demodulation,[status(thm),theory(equality)],[c_278,c_1113,c_4,c_4,c_4,c_4,c_18,c_4,c_6882]) ).
tff(c_9984,plain,
! [Z_96,Z_20] : ( multiply(multiply(identity,identity),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,Z_96)),multiply(multiply(Z_20,multiply(Z_20,Z_20)),multiply(multiply(Z_20,multiply(Z_20,Z_20)),multiply(Z_20,multiply(Z_20,Z_20)))))),multiply(Z_20,multiply(Z_20,Z_20)))) = multiply(multiply(Z_96,multiply(Z_96,Z_96)),multiply(multiply(Z_96,multiply(Z_96,Z_96)),multiply(Z_96,multiply(Z_96,Z_96)))) ),
inference(superposition,[status(thm),theory(equality)],[c_9924,c_701]) ).
tff(c_10033,plain,
! [Z_96] : ( multiply(multiply(Z_96,multiply(Z_96,Z_96)),multiply(multiply(Z_96,multiply(Z_96,Z_96)),multiply(Z_96,multiply(Z_96,Z_96)))) = multiply(identity,Z_96) ),
inference(demodulation,[status(thm),theory(equality)],[c_278,c_1113,c_4,c_4,c_4,c_4,c_18,c_4,c_9984]) ).
tff(c_838,plain,
! [Y_18,X_19] : ( multiply(multiply(Y_18,Y_18),multiply(multiply(Y_18,multiply(multiply(Y_18,X_19),identity)),identity)) = X_19 ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_4,c_4,c_4,c_4,c_4,c_4,c_677]) ).
tff(c_106,plain,
! [X_10,Z_11] : ( multiply(identity,multiply(multiply(identity,X_10),multiply(multiply(Z_11,multiply(Z_11,Z_11)),multiply(multiply(Z_11,multiply(Z_11,Z_11)),multiply(Z_11,multiply(Z_11,Z_11)))))) = multiply(identity,multiply(identity,multiply(X_10,Z_11))) ),
inference(superposition,[status(thm),theory(equality)],[c_100,c_34]) ).
tff(c_10121,plain,
! [X_98,Z_99] : ( multiply(identity,multiply(multiply(identity,X_98),multiply(identity,Z_99))) = multiply(identity,multiply(identity,multiply(X_98,Z_99))) ),
inference(demodulation,[status(thm),theory(equality)],[c_10033,c_106]) ).
tff(c_10207,plain,
! [X_98,Z_99] : ( multiply(multiply(identity,identity),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X_98,Z_99))),identity)),identity)) = multiply(multiply(identity,X_98),multiply(identity,Z_99)) ),
inference(superposition,[status(thm),theory(equality)],[c_10121,c_838]) ).
tff(c_10371,plain,
! [X_98,Z_99] : ( multiply(multiply(identity,X_98),multiply(identity,Z_99)) = multiply(identity,multiply(X_98,Z_99)) ),
inference(demodulation,[status(thm),theory(equality)],[c_278,c_591,c_591,c_591,c_591,c_591,c_4,c_10207]) ).
tff(c_1097,plain,
! [Y_1,X_2,Z_3] : ( multiply(multiply(Y_1,multiply(multiply(Y_1,Y_1),multiply(X_2,Z_3))),multiply(Z_3,multiply(Z_3,Z_3))) = multiply(multiply(Y_1,Y_1),multiply(multiply(Y_1,multiply(X_2,identity)),identity)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1023]) ).
tff(c_1831,plain,
! [Y_1,X_2] : ( multiply(Y_1,multiply(multiply(Y_1,Y_1),multiply(multiply(Y_1,multiply(X_2,identity)),identity))) = X_2 ),
inference(demodulation,[status(thm),theory(equality)],[c_1097,c_2]) ).
tff(c_11371,plain,
! [X_103,Z_104] : ( multiply(multiply(identity,X_103),multiply(identity,Z_104)) = multiply(identity,multiply(X_103,Z_104)) ),
inference(demodulation,[status(thm),theory(equality)],[c_278,c_591,c_591,c_591,c_591,c_591,c_4,c_10207]) ).
tff(c_11764,plain,
! [X_2,Z_104] : ( multiply(identity,multiply(multiply(multiply(identity,identity),multiply(multiply(identity,multiply(X_2,identity)),identity)),Z_104)) = multiply(X_2,multiply(identity,Z_104)) ),
inference(superposition,[status(thm),theory(equality)],[c_1831,c_11371]) ).
tff(c_13680,plain,
! [X_112,Z_113] : ( multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(X_112,identity),identity))),Z_113)) = multiply(X_112,multiply(identity,Z_113)) ),
inference(demodulation,[status(thm),theory(equality)],[c_591,c_4,c_11764]) ).
tff(c_779,plain,
! [X_5,Z_20] : ( multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(multiply(identity,multiply(X_5,multiply(Z_20,multiply(Z_20,Z_20)))),Z_20))) = X_5 ),
inference(superposition,[status(thm),theory(equality)],[c_34,c_601]) ).
tff(c_1123,plain,
! [X_27,Z_28] : ( multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X_27,multiply(Z_28,multiply(Z_28,Z_28)))),Z_28))) = X_27 ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_4,c_4,c_779]) ).
tff(c_1132,plain,
! [X_27,Z_28] : ( multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(X_27,multiply(Z_28,multiply(Z_28,Z_28)))),Z_28)),identity)) = multiply(X_27,identity) ),
inference(superposition,[status(thm),theory(equality)],[c_1123,c_591]) ).
tff(c_4549,plain,
! [X_66,Z_67] : ( multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(X_66,multiply(Z_67,multiply(Z_67,Z_67)))),Z_67),identity))) = multiply(X_66,identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_591,c_1132]) ).
tff(c_573,plain,
! [X_5] : ( multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X_5,identity))),identity) = multiply(identity,multiply(identity,multiply(multiply(X_5,identity),identity))) ),
inference(superposition,[status(thm),theory(equality)],[c_44,c_508]) ).
tff(c_2327,plain,
! [X_44] : ( multiply(multiply(identity,multiply(identity,multiply(X_44,identity))),identity) = multiply(identity,multiply(identity,multiply(multiply(X_44,identity),identity))) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_573]) ).
tff(c_2394,plain,
! [X_17] : ( multiply(multiply(identity,multiply(identity,multiply(identity,multiply(X_17,identity)))),identity) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X_17),identity),identity))) ),
inference(superposition,[status(thm),theory(equality)],[c_591,c_2327]) ).
tff(c_2423,plain,
! [X_17] : ( multiply(multiply(identity,multiply(identity,multiply(identity,multiply(X_17,identity)))),identity) = X_17 ),
inference(demodulation,[status(thm),theory(equality)],[c_278,c_591,c_591,c_2394]) ).
tff(c_4588,plain,
! [X_66,Z_67] : ( multiply(multiply(identity,multiply(X_66,multiply(Z_67,multiply(Z_67,Z_67)))),Z_67) = multiply(multiply(identity,multiply(X_66,identity)),identity) ),
inference(superposition,[status(thm),theory(equality)],[c_4549,c_2423]) ).
tff(c_4672,plain,
! [X_66,Z_67] : ( multiply(multiply(identity,multiply(X_66,multiply(Z_67,multiply(Z_67,Z_67)))),Z_67) = multiply(identity,multiply(multiply(X_66,identity),identity)) ),
inference(demodulation,[status(thm),theory(equality)],[c_591,c_4588]) ).
tff(c_13793,plain,
! [X_112,Z_67] : ( multiply(multiply(X_112,multiply(identity,multiply(Z_67,multiply(Z_67,Z_67)))),Z_67) = multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(multiply(X_112,identity),identity))),identity),identity)) ),
inference(superposition,[status(thm),theory(equality)],[c_13680,c_4672]) ).
tff(c_14036,plain,
! [X_114,Z_115] : ( multiply(multiply(X_114,multiply(identity,multiply(Z_115,multiply(Z_115,Z_115)))),Z_115) = multiply(multiply(X_114,identity),identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_278,c_591,c_591,c_591,c_591,c_13793]) ).
tff(c_13992,plain,
! [X_112,Z_67] : ( multiply(multiply(X_112,multiply(identity,multiply(Z_67,multiply(Z_67,Z_67)))),Z_67) = multiply(multiply(X_112,identity),identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_278,c_591,c_591,c_591,c_591,c_13793]) ).
tff(c_14040,plain,
! [X_114,Z_67] : ( multiply(multiply(multiply(X_114,multiply(identity,multiply(multiply(identity,multiply(Z_67,multiply(Z_67,Z_67))),multiply(multiply(identity,multiply(Z_67,multiply(Z_67,Z_67))),multiply(identity,multiply(Z_67,multiply(Z_67,Z_67))))))),identity),identity) = multiply(multiply(multiply(X_114,identity),identity),Z_67) ),
inference(superposition,[status(thm),theory(equality)],[c_14036,c_13992]) ).
tff(c_21177,plain,
! [X_146,Z_147] : ( multiply(multiply(multiply(X_146,multiply(identity,multiply(identity,multiply(identity,Z_147)))),identity),identity) = multiply(multiply(multiply(X_146,identity),identity),Z_147) ),
inference(demodulation,[status(thm),theory(equality)],[c_10033,c_10371,c_10371,c_14040]) ).
tff(c_21668,plain,
! [X_146,X_9] : ( multiply(multiply(multiply(X_146,identity),identity),multiply(multiply(X_9,identity),identity)) = multiply(multiply(multiply(X_146,X_9),identity),identity) ),
inference(superposition,[status(thm),theory(equality)],[c_278,c_21177]) ).
tff(c_6620,plain,
! [X_80,Z_81] : ( multiply(multiply(identity,multiply(identity,multiply(X_80,Z_81))),multiply(Z_81,multiply(Z_81,Z_81))) = multiply(identity,multiply(identity,multiply(multiply(X_80,identity),identity))) ),
inference(demodulation,[status(thm),theory(equality)],[c_591,c_4,c_1082]) ).
tff(c_6801,plain,
! [X_9] : ( multiply(X_9,multiply(multiply(multiply(X_9,identity),identity),multiply(multiply(multiply(X_9,identity),identity),multiply(multiply(X_9,identity),identity)))) = multiply(identity,multiply(identity,multiply(multiply(identity,identity),identity))) ),
inference(superposition,[status(thm),theory(equality)],[c_278,c_6620]) ).
tff(c_6843,plain,
! [X_9] : ( multiply(X_9,multiply(multiply(multiply(X_9,identity),identity),multiply(multiply(multiply(X_9,identity),identity),multiply(multiply(X_9,identity),identity)))) = identity ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_4,c_4,c_6801]) ).
tff(c_22376,plain,
! [X_150] : ( multiply(X_150,multiply(multiply(multiply(X_150,multiply(X_150,X_150)),identity),identity)) = identity ),
inference(demodulation,[status(thm),theory(equality)],[c_21668,c_21668,c_6843]) ).
tff(c_22643,plain,
! [Z_96] : ( multiply(multiply(Z_96,multiply(Z_96,Z_96)),multiply(multiply(multiply(identity,Z_96),identity),identity)) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_10033,c_22376]) ).
tff(c_22723,plain,
! [Z_96] : ( multiply(multiply(Z_96,multiply(Z_96,Z_96)),multiply(identity,multiply(multiply(Z_96,identity),identity))) = identity ),
inference(demodulation,[status(thm),theory(equality)],[c_591,c_591,c_22643]) ).
tff(c_2427,plain,
! [X_45] : ( multiply(multiply(identity,multiply(identity,multiply(identity,multiply(X_45,identity)))),identity) = X_45 ),
inference(demodulation,[status(thm),theory(equality)],[c_278,c_591,c_591,c_2394]) ).
tff(c_2454,plain,
! [Y_1,X_45] : ( multiply(multiply(Y_1,Y_1),multiply(multiply(Y_1,multiply(multiply(identity,multiply(identity,multiply(identity,multiply(X_45,identity)))),identity)),identity)) = multiply(multiply(Y_1,multiply(multiply(Y_1,Y_1),X_45)),multiply(identity,multiply(identity,identity))) ),
inference(superposition,[status(thm),theory(equality)],[c_2427,c_1097]) ).
tff(c_2523,plain,
! [Y_1,X_45] : ( multiply(multiply(Y_1,multiply(multiply(Y_1,Y_1),X_45)),identity) = multiply(multiply(Y_1,Y_1),multiply(multiply(Y_1,X_45),identity)) ),
inference(demodulation,[status(thm),theory(equality)],[c_278,c_591,c_591,c_591,c_4,c_4,c_2454]) ).
tff(c_6870,plain,
! [Z_82] : ( multiply(multiply(identity,multiply(identity,multiply(identity,Z_82))),multiply(Z_82,multiply(Z_82,Z_82))) = multiply(identity,multiply(multiply(identity,identity),identity)) ),
inference(superposition,[status(thm),theory(equality)],[c_6846,c_4672]) ).
tff(c_6922,plain,
! [Z_82] : ( multiply(multiply(identity,multiply(identity,multiply(identity,Z_82))),multiply(Z_82,multiply(Z_82,Z_82))) = identity ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_4,c_6870]) ).
tff(c_37,plain,
! [Y_4] : ( multiply(Y_4,multiply(multiply(Y_4,multiply(multiply(Y_4,Y_4),identity)),multiply(identity,multiply(identity,identity)))) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_11]) ).
tff(c_43,plain,
! [Y_4] : ( multiply(Y_4,multiply(multiply(Y_4,multiply(multiply(Y_4,Y_4),identity)),identity)) = identity ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_37]) ).
tff(c_131,plain,
! [Y_4] : ( multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(multiply(multiply(Y_4,multiply(multiply(Y_4,Y_4),identity)),identity),multiply(multiply(multiply(Y_4,multiply(multiply(Y_4,Y_4),identity)),identity),multiply(multiply(Y_4,multiply(multiply(Y_4,Y_4),identity)),identity))))) = Y_4 ),
inference(superposition,[status(thm),theory(equality)],[c_43,c_100]) ).
tff(c_152,plain,
! [Y_4] : ( multiply(identity,multiply(identity,multiply(multiply(multiply(Y_4,multiply(multiply(Y_4,Y_4),identity)),identity),multiply(multiply(multiply(Y_4,multiply(multiply(Y_4,Y_4),identity)),identity),multiply(multiply(Y_4,multiply(multiply(Y_4,Y_4),identity)),identity))))) = Y_4 ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_131]) ).
tff(c_9608,plain,
! [Y_4] : ( multiply(identity,multiply(identity,multiply(multiply(multiply(Y_4,Y_4),multiply(multiply(Y_4,identity),identity)),multiply(multiply(multiply(Y_4,Y_4),multiply(multiply(Y_4,identity),identity)),multiply(multiply(Y_4,Y_4),multiply(multiply(Y_4,identity),identity)))))) = Y_4 ),
inference(demodulation,[status(thm),theory(equality)],[c_2523,c_2523,c_2523,c_152]) ).
tff(c_10047,plain,
! [Z_97] : ( multiply(multiply(Z_97,multiply(Z_97,Z_97)),multiply(multiply(Z_97,multiply(Z_97,Z_97)),multiply(Z_97,multiply(Z_97,Z_97)))) = multiply(identity,Z_97) ),
inference(demodulation,[status(thm),theory(equality)],[c_278,c_1113,c_4,c_4,c_4,c_4,c_18,c_4,c_9984]) ).
tff(c_10062,plain,
! [Z_97] : ( multiply(multiply(identity,multiply(identity,multiply(identity,multiply(Z_97,multiply(Z_97,Z_97))))),multiply(identity,Z_97)) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_10047,c_6922]) ).
tff(c_809,plain,
! [Y_1,X_2,Z_3,Z_20] : ( multiply(multiply(Y_1,Y_1),multiply(multiply(multiply(Y_1,Y_1),multiply(Y_1,Y_1)),multiply(multiply(multiply(Y_1,multiply(multiply(Y_1,Y_1),multiply(X_2,Z_3))),multiply(Z_3,multiply(Z_3,Z_3))),Z_20))) = multiply(Y_1,multiply(X_2,multiply(multiply(Z_20,multiply(Z_20,Z_20)),multiply(multiply(Z_20,multiply(Z_20,Z_20)),multiply(Z_20,multiply(Z_20,Z_20)))))) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_601]) ).
tff(c_23997,plain,
! [Y_155,X_156,Z_157] : ( multiply(multiply(Y_155,Y_155),multiply(multiply(multiply(Y_155,Y_155),multiply(Y_155,Y_155)),multiply(multiply(multiply(Y_155,Y_155),multiply(multiply(Y_155,multiply(X_156,identity)),identity)),Z_157))) = multiply(Y_155,multiply(X_156,multiply(identity,Z_157))) ),
inference(demodulation,[status(thm),theory(equality)],[c_10033,c_1097,c_809]) ).
tff(c_24088,plain,
! [Y_155,X_156,Z_157] : ( multiply(multiply(multiply(Y_155,Y_155),multiply(Y_155,Y_155)),multiply(multiply(multiply(Y_155,Y_155),multiply(multiply(multiply(Y_155,Y_155),multiply(multiply(Y_155,multiply(X_156,identity)),identity)),identity)),identity)) = multiply(multiply(Y_155,multiply(X_156,multiply(identity,Z_157))),multiply(Z_157,multiply(Z_157,Z_157))) ),
inference(superposition,[status(thm),theory(equality)],[c_23997,c_1097]) ).
tff(c_24582,plain,
! [Y_159,X_160,Z_161] : ( multiply(multiply(Y_159,multiply(X_160,multiply(identity,Z_161))),multiply(Z_161,multiply(Z_161,Z_161))) = multiply(multiply(Y_159,multiply(X_160,identity)),identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_838,c_24088]) ).
tff(c_24894,plain,
! [Y_159,Y_4] : ( multiply(multiply(Y_159,Y_4),multiply(multiply(multiply(multiply(Y_4,Y_4),multiply(multiply(Y_4,identity),identity)),multiply(multiply(multiply(Y_4,Y_4),multiply(multiply(Y_4,identity),identity)),multiply(multiply(Y_4,Y_4),multiply(multiply(Y_4,identity),identity)))),multiply(multiply(multiply(multiply(Y_4,Y_4),multiply(multiply(Y_4,identity),identity)),multiply(multiply(multiply(Y_4,Y_4),multiply(multiply(Y_4,identity),identity)),multiply(multiply(Y_4,Y_4),multiply(multiply(Y_4,identity),identity)))),multiply(multiply(multiply(Y_4,Y_4),multiply(multiply(Y_4,identity),identity)),multiply(multiply(multiply(Y_4,Y_4),multiply(multiply(Y_4,identity),identity)),multiply(multiply(Y_4,Y_4),multiply(multiply(Y_4,identity),identity))))))) = multiply(multiply(Y_159,multiply(identity,identity)),identity) ),
inference(superposition,[status(thm),theory(equality)],[c_9608,c_24582]) ).
tff(c_25083,plain,
! [Y_162,Y_163] : ( multiply(multiply(Y_162,Y_163),multiply(identity,multiply(multiply(Y_163,Y_163),multiply(multiply(Y_163,identity),identity)))) = multiply(multiply(Y_162,identity),identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_10033,c_4,c_24894]) ).
tff(c_25310,plain,
! [Z_97] : ( multiply(identity,multiply(identity,multiply(multiply(multiply(identity,Z_97),multiply(identity,Z_97)),multiply(multiply(multiply(identity,Z_97),identity),identity)))) = multiply(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(Z_97,multiply(Z_97,Z_97))))),identity),identity) ),
inference(superposition,[status(thm),theory(equality)],[c_10062,c_25083]) ).
tff(c_25880,plain,
! [Z_166] : ( multiply(identity,multiply(identity,multiply(identity,multiply(multiply(Z_166,Z_166),multiply(multiply(Z_166,identity),identity))))) = multiply(Z_166,multiply(Z_166,Z_166)) ),
inference(demodulation,[status(thm),theory(equality)],[c_10371,c_10371,c_278,c_591,c_591,c_591,c_591,c_591,c_591,c_591,c_591,c_25310]) ).
tff(c_24339,plain,
! [Y_155,X_156,Z_157] : ( multiply(multiply(Y_155,multiply(X_156,multiply(identity,Z_157))),multiply(Z_157,multiply(Z_157,Z_157))) = multiply(multiply(Y_155,multiply(X_156,identity)),identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_838,c_24088]) ).
tff(c_25889,plain,
! [Y_155,X_156,Z_166] : ( multiply(multiply(Y_155,multiply(X_156,multiply(Z_166,multiply(Z_166,Z_166)))),multiply(multiply(identity,multiply(identity,multiply(multiply(Z_166,Z_166),multiply(multiply(Z_166,identity),identity)))),multiply(multiply(identity,multiply(identity,multiply(multiply(Z_166,Z_166),multiply(multiply(Z_166,identity),identity)))),multiply(identity,multiply(identity,multiply(multiply(Z_166,Z_166),multiply(multiply(Z_166,identity),identity))))))) = multiply(multiply(Y_155,multiply(X_156,identity)),identity) ),
inference(superposition,[status(thm),theory(equality)],[c_25880,c_24339]) ).
tff(c_26224,plain,
! [Y_167,X_168,Z_169] : ( multiply(multiply(Y_167,multiply(X_168,multiply(Z_169,multiply(Z_169,Z_169)))),Z_169) = multiply(multiply(Y_167,multiply(X_168,identity)),identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_9608,c_10371,c_10371,c_10371,c_10371,c_25889]) ).
tff(c_26833,plain,
! [Y_167,Z_82] : ( multiply(multiply(Y_167,multiply(multiply(identity,multiply(identity,multiply(identity,Z_82))),identity)),identity) = multiply(multiply(Y_167,identity),Z_82) ),
inference(superposition,[status(thm),theory(equality)],[c_6922,c_26224]) ).
tff(c_27029,plain,
! [Y_170,Z_171] : ( multiply(multiply(Y_170,multiply(identity,multiply(identity,multiply(identity,multiply(Z_171,identity))))),identity) = multiply(multiply(Y_170,identity),Z_171) ),
inference(demodulation,[status(thm),theory(equality)],[c_591,c_591,c_591,c_26833]) ).
tff(c_27341,plain,
! [Y_170,X_112] : ( multiply(multiply(Y_170,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X_112,identity),identity))))),identity) = multiply(multiply(Y_170,identity),multiply(X_112,multiply(identity,multiply(identity,multiply(identity,identity))))) ),
inference(superposition,[status(thm),theory(equality)],[c_13992,c_27029]) ).
tff(c_27492,plain,
! [Y_170,X_112] : ( multiply(multiply(Y_170,identity),multiply(X_112,identity)) = multiply(multiply(Y_170,X_112),identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_278,c_4,c_4,c_4,c_27341]) ).
tff(c_27515,plain,
! [Y_172,X_173] : ( multiply(multiply(Y_172,identity),multiply(X_173,identity)) = multiply(multiply(Y_172,X_173),identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_278,c_4,c_4,c_4,c_27341]) ).
tff(c_28079,plain,
! [Y_172,X_19] : ( multiply(multiply(multiply(Y_172,identity),multiply(Y_172,identity)),multiply(multiply(multiply(Y_172,multiply(multiply(Y_172,identity),X_19)),identity),identity)) = X_19 ),
inference(superposition,[status(thm),theory(equality)],[c_27515,c_838]) ).
tff(c_29202,plain,
! [Y_178,X_179] : ( multiply(multiply(multiply(Y_178,Y_178),multiply(multiply(Y_178,multiply(multiply(Y_178,identity),X_179)),identity)),identity) = X_179 ),
inference(demodulation,[status(thm),theory(equality)],[c_27492,c_27492,c_28079]) ).
tff(c_861,plain,
! [X_21] : ( multiply(multiply(identity,X_21),identity) = multiply(identity,multiply(X_21,identity)) ),
inference(demodulation,[status(thm),theory(equality)],[c_278,c_151,c_532]) ).
tff(c_898,plain,
! [Y_1,X_21] : ( multiply(Y_1,multiply(multiply(Y_1,multiply(multiply(Y_1,Y_1),multiply(identity,multiply(X_21,identity)))),multiply(identity,multiply(identity,identity)))) = multiply(identity,X_21) ),
inference(superposition,[status(thm),theory(equality)],[c_861,c_2]) ).
tff(c_2654,plain,
! [Y_47,X_48] : ( multiply(Y_47,multiply(multiply(Y_47,multiply(multiply(Y_47,Y_47),multiply(identity,multiply(X_48,identity)))),identity)) = multiply(identity,X_48) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_898]) ).
tff(c_2765,plain,
! [X_5,Y_47] : ( multiply(identity,multiply(identity,multiply(multiply(identity,identity),multiply(X_5,identity)))) = multiply(Y_47,multiply(multiply(Y_47,multiply(multiply(Y_47,Y_47),X_5)),identity)) ),
inference(superposition,[status(thm),theory(equality)],[c_44,c_2654]) ).
tff(c_2792,plain,
! [Y_47,X_5] : ( multiply(Y_47,multiply(multiply(Y_47,multiply(multiply(Y_47,Y_47),X_5)),identity)) = multiply(identity,multiply(identity,multiply(identity,multiply(X_5,identity)))) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_2765]) ).
tff(c_5250,plain,
! [Y_47,X_5] : ( multiply(Y_47,multiply(multiply(Y_47,Y_47),multiply(multiply(Y_47,X_5),identity))) = multiply(identity,multiply(identity,multiply(identity,multiply(X_5,identity)))) ),
inference(demodulation,[status(thm),theory(equality)],[c_2523,c_2792]) ).
tff(c_29358,plain,
! [Y_178,X_179] : ( multiply(multiply(Y_178,Y_178),multiply(multiply(multiply(Y_178,Y_178),multiply(Y_178,Y_178)),X_179)) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(Y_178,multiply(multiply(Y_178,identity),X_179)),identity),identity)))) ),
inference(superposition,[status(thm),theory(equality)],[c_29202,c_5250]) ).
tff(c_29688,plain,
! [Y_178,X_179] : ( multiply(multiply(Y_178,Y_178),multiply(multiply(multiply(Y_178,Y_178),multiply(Y_178,Y_178)),X_179)) = multiply(Y_178,multiply(multiply(Y_178,identity),X_179)) ),
inference(demodulation,[status(thm),theory(equality)],[c_278,c_29358]) ).
tff(c_680,plain,
! [Y_1,Y_18,X_19,Z_20] : ( multiply(Y_1,multiply(multiply(Y_1,multiply(multiply(Y_1,Y_1),multiply(multiply(Y_18,Y_18),multiply(multiply(multiply(Y_18,Y_18),multiply(Y_18,Y_18)),multiply(X_19,Z_20))))),multiply(multiply(multiply(Y_18,X_19),multiply(multiply(Z_20,multiply(Z_20,Z_20)),multiply(multiply(Z_20,multiply(Z_20,Z_20)),multiply(Z_20,multiply(Z_20,Z_20))))),multiply(multiply(multiply(Y_18,X_19),multiply(multiply(Z_20,multiply(Z_20,Z_20)),multiply(multiply(Z_20,multiply(Z_20,Z_20)),multiply(Z_20,multiply(Z_20,Z_20))))),multiply(multiply(Y_18,X_19),multiply(multiply(Z_20,multiply(Z_20,Z_20)),multiply(multiply(Z_20,multiply(Z_20,Z_20)),multiply(Z_20,multiply(Z_20,Z_20))))))))) = Y_18 ),
inference(superposition,[status(thm),theory(equality)],[c_601,c_2]) ).
tff(c_67760,plain,
! [Y_270,Y_271,X_272,Z_273] : ( multiply(Y_270,multiply(multiply(Y_270,multiply(multiply(Y_270,Y_270),multiply(Y_271,multiply(multiply(Y_271,identity),multiply(X_272,Z_273))))),multiply(multiply(multiply(Y_271,X_272),multiply(identity,Z_273)),multiply(multiply(multiply(Y_271,X_272),multiply(identity,Z_273)),multiply(multiply(Y_271,X_272),multiply(identity,Z_273)))))) = Y_271 ),
inference(demodulation,[status(thm),theory(equality)],[c_29688,c_10033,c_10033,c_10033,c_680]) ).
tff(c_26151,plain,
! [Y_155,X_156,Z_166] : ( multiply(multiply(Y_155,multiply(X_156,multiply(Z_166,multiply(Z_166,Z_166)))),Z_166) = multiply(multiply(Y_155,multiply(X_156,identity)),identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_9608,c_10371,c_10371,c_10371,c_10371,c_25889]) ).
tff(c_67988,plain,
! [Y_270,Y_271,X_272,Z_273] : ( multiply(multiply(Y_270,multiply(multiply(Y_270,multiply(multiply(Y_270,Y_270),multiply(Y_271,multiply(multiply(Y_271,identity),multiply(X_272,Z_273))))),identity)),identity) = multiply(Y_271,multiply(multiply(Y_271,X_272),multiply(identity,Z_273))) ),
inference(superposition,[status(thm),theory(equality)],[c_67760,c_26151]) ).
tff(c_71495,plain,
! [Y_274,X_275,Z_276] : ( multiply(Y_274,multiply(multiply(Y_274,identity),multiply(X_275,Z_276))) = multiply(Y_274,multiply(multiply(Y_274,X_275),multiply(identity,Z_276))) ),
inference(demodulation,[status(thm),theory(equality)],[c_838,c_2523,c_2523,c_67988]) ).
tff(c_87227,plain,
! [Z_295] : ( multiply(Z_295,multiply(multiply(Z_295,identity),multiply(multiply(Z_295,Z_295),multiply(multiply(Z_295,identity),identity)))) = multiply(Z_295,identity) ),
inference(superposition,[status(thm),theory(equality)],[c_22723,c_71495]) ).
tff(c_87715,plain,
! [Z_295] : ( multiply(multiply(Z_295,identity),multiply(multiply(Z_295,Z_295),multiply(multiply(Z_295,identity),identity))) = multiply(multiply(Z_295,Z_295),multiply(multiply(Z_295,multiply(multiply(Z_295,identity),identity)),identity)) ),
inference(superposition,[status(thm),theory(equality)],[c_87227,c_838]) ).
tff(c_88059,plain,
! [Z_295] : ( multiply(multiply(Z_295,identity),multiply(multiply(Z_295,Z_295),multiply(multiply(Z_295,identity),identity))) = identity ),
inference(demodulation,[status(thm),theory(equality)],[c_838,c_87715]) ).
tff(c_22608,plain,
! [X_150] : ( multiply(X_150,multiply(multiply(X_150,X_150),multiply(identity,identity))) = multiply(multiply(X_150,multiply(X_150,X_150)),identity) ),
inference(superposition,[status(thm),theory(equality)],[c_22376,c_1831]) ).
tff(c_22713,plain,
! [X_150] : ( multiply(multiply(X_150,multiply(X_150,X_150)),identity) = multiply(X_150,multiply(multiply(X_150,X_150),identity)) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_22608]) ).
tff(c_22900,plain,
! [Z_152] : ( multiply(multiply(Z_152,multiply(Z_152,Z_152)),multiply(identity,multiply(multiply(Z_152,identity),identity))) = identity ),
inference(demodulation,[status(thm),theory(equality)],[c_591,c_591,c_22643]) ).
tff(c_10045,plain,
! [Y_18,X_19,Z_20] : ( multiply(multiply(Y_18,Y_18),multiply(multiply(Y_18,multiply(multiply(Y_18,X_19),multiply(identity,Z_20))),multiply(Z_20,multiply(Z_20,Z_20)))) = X_19 ),
inference(demodulation,[status(thm),theory(equality)],[c_10033,c_701]) ).
tff(c_22939,plain,
! [Z_152] : ( multiply(multiply(Z_152,Z_152),multiply(multiply(Z_152,identity),multiply(multiply(multiply(Z_152,identity),identity),multiply(multiply(multiply(Z_152,identity),identity),multiply(multiply(Z_152,identity),identity))))) = multiply(Z_152,Z_152) ),
inference(superposition,[status(thm),theory(equality)],[c_22900,c_10045]) ).
tff(c_23060,plain,
! [Z_152] : ( multiply(multiply(Z_152,Z_152),multiply(multiply(Z_152,identity),multiply(multiply(multiply(Z_152,multiply(Z_152,Z_152)),identity),identity))) = multiply(Z_152,Z_152) ),
inference(demodulation,[status(thm),theory(equality)],[c_21668,c_21668,c_22939]) ).
tff(c_46696,plain,
! [Z_152] : ( multiply(multiply(Z_152,Z_152),multiply(multiply(Z_152,identity),multiply(multiply(Z_152,Z_152),multiply(multiply(Z_152,identity),identity)))) = multiply(Z_152,Z_152) ),
inference(demodulation,[status(thm),theory(equality)],[c_2523,c_22713,c_23060]) ).
tff(c_88631,plain,
! [Z_297] : ( multiply(multiply(Z_297,Z_297),identity) = multiply(Z_297,Z_297) ),
inference(demodulation,[status(thm),theory(equality)],[c_88059,c_46696]) ).
tff(c_6937,plain,
! [Z_83] : ( multiply(multiply(identity,multiply(identity,multiply(identity,Z_83))),multiply(Z_83,multiply(Z_83,Z_83))) = identity ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_4,c_6870]) ).
tff(c_6968,plain,
! [Z_83] : ( multiply(multiply(multiply(identity,multiply(identity,multiply(identity,Z_83))),multiply(identity,multiply(identity,multiply(identity,Z_83)))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,Z_83))),multiply(identity,identity)),identity)) = multiply(Z_83,multiply(Z_83,Z_83)) ),
inference(superposition,[status(thm),theory(equality)],[c_6937,c_838]) ).
tff(c_7057,plain,
! [Z_83] : ( multiply(multiply(multiply(identity,multiply(identity,multiply(identity,Z_83))),multiply(identity,multiply(identity,multiply(identity,Z_83)))),Z_83) = multiply(Z_83,multiply(Z_83,Z_83)) ),
inference(demodulation,[status(thm),theory(equality)],[c_278,c_591,c_591,c_591,c_591,c_591,c_591,c_4,c_6968]) ).
tff(c_12063,plain,
! [Z_106] : ( multiply(multiply(identity,multiply(identity,multiply(identity,multiply(Z_106,Z_106)))),Z_106) = multiply(Z_106,multiply(Z_106,Z_106)) ),
inference(demodulation,[status(thm),theory(equality)],[c_10371,c_10371,c_10371,c_7057]) ).
tff(c_12181,plain,
! [Z_67] : ( multiply(multiply(identity,multiply(multiply(Z_67,multiply(Z_67,Z_67)),multiply(multiply(Z_67,multiply(Z_67,Z_67)),multiply(Z_67,multiply(Z_67,Z_67))))),Z_67) = multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(Z_67,multiply(Z_67,Z_67)),multiply(Z_67,multiply(Z_67,Z_67)))))),identity),identity)) ),
inference(superposition,[status(thm),theory(equality)],[c_12063,c_4672]) ).
tff(c_12356,plain,
! [Z_67] : ( multiply(identity,multiply(multiply(Z_67,multiply(Z_67,Z_67)),multiply(Z_67,multiply(Z_67,Z_67)))) = multiply(multiply(identity,multiply(identity,Z_67)),Z_67) ),
inference(demodulation,[status(thm),theory(equality)],[c_10033,c_278,c_591,c_591,c_591,c_591,c_591,c_591,c_12181]) ).
tff(c_11768,plain,
! [X_103,X_2] : ( multiply(identity,multiply(X_103,multiply(multiply(identity,identity),multiply(multiply(identity,multiply(X_2,identity)),identity)))) = multiply(multiply(identity,X_103),X_2) ),
inference(superposition,[status(thm),theory(equality)],[c_1831,c_11371]) ).
tff(c_13433,plain,
! [X_110,X_111] : ( multiply(identity,multiply(X_110,multiply(identity,multiply(identity,multiply(multiply(X_111,identity),identity))))) = multiply(multiply(identity,X_110),X_111) ),
inference(demodulation,[status(thm),theory(equality)],[c_591,c_4,c_11768]) ).
tff(c_13589,plain,
! [X_98,X_111] : ( multiply(identity,multiply(identity,multiply(X_98,multiply(identity,multiply(multiply(X_111,identity),identity))))) = multiply(multiply(identity,multiply(identity,X_98)),X_111) ),
inference(superposition,[status(thm),theory(equality)],[c_10371,c_13433]) ).
tff(c_22908,plain,
! [Z_152] : ( multiply(multiply(identity,multiply(identity,multiply(Z_152,multiply(Z_152,Z_152)))),Z_152) = multiply(identity,multiply(identity,identity)) ),
inference(superposition,[status(thm),theory(equality)],[c_22900,c_13589]) ).
tff(c_23092,plain,
! [Z_153] : ( multiply(multiply(identity,multiply(identity,multiply(Z_153,multiply(Z_153,Z_153)))),Z_153) = identity ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_22908]) ).
tff(c_1048,plain,
! [Y_1,X_26,Y_25] : ( multiply(Y_1,multiply(multiply(Y_1,multiply(multiply(Y_1,Y_1),X_26)),multiply(multiply(multiply(Y_25,multiply(multiply(Y_25,X_26),identity)),identity),multiply(multiply(multiply(Y_25,multiply(multiply(Y_25,X_26),identity)),identity),multiply(multiply(Y_25,multiply(multiply(Y_25,X_26),identity)),identity))))) = multiply(Y_25,Y_25) ),
inference(superposition,[status(thm),theory(equality)],[c_1023,c_2]) ).
tff(c_23295,plain,
! [Y_1,Z_153] : ( multiply(Y_1,multiply(multiply(Y_1,multiply(multiply(Y_1,Y_1),Z_153)),multiply(multiply(multiply(multiply(identity,multiply(identity,multiply(Z_153,multiply(Z_153,Z_153)))),multiply(multiply(multiply(identity,multiply(identity,multiply(Z_153,multiply(Z_153,Z_153)))),Z_153),identity)),identity),multiply(multiply(multiply(multiply(identity,multiply(identity,multiply(Z_153,multiply(Z_153,Z_153)))),multiply(multiply(multiply(identity,multiply(identity,multiply(Z_153,multiply(Z_153,Z_153)))),Z_153),identity)),identity),multiply(multiply(multiply(identity,multiply(identity,multiply(Z_153,multiply(Z_153,Z_153)))),multiply(identity,identity)),identity))))) = multiply(multiply(identity,multiply(identity,multiply(Z_153,multiply(Z_153,Z_153)))),multiply(identity,multiply(identity,multiply(Z_153,multiply(Z_153,Z_153))))) ),
inference(superposition,[status(thm),theory(equality)],[c_23092,c_1048]) ).
tff(c_23584,plain,
! [Y_1,Z_153] : ( multiply(Y_1,multiply(multiply(Y_1,multiply(multiply(Y_1,Y_1),Z_153)),Z_153)) = multiply(identity,multiply(multiply(identity,multiply(identity,Z_153)),Z_153)) ),
inference(demodulation,[status(thm),theory(equality)],[c_278,c_591,c_591,c_10033,c_21668,c_21668,c_12356,c_10371,c_10371,c_10371,c_10371,c_10371,c_10371,c_591,c_591,c_591,c_591,c_4,c_4,c_4,c_4,c_4672,c_591,c_591,c_591,c_591,c_4,c_4,c_4,c_4,c_4672,c_591,c_591,c_591,c_591,c_4,c_23295]) ).
tff(c_88845,plain,
! [Z_297] : ( multiply(identity,multiply(multiply(identity,multiply(identity,identity)),identity)) = multiply(Z_297,multiply(multiply(Z_297,multiply(Z_297,Z_297)),identity)) ),
inference(superposition,[status(thm),theory(equality)],[c_88631,c_23584]) ).
tff(c_93121,plain,
! [Z_303] : ( multiply(Z_303,multiply(multiply(Z_303,multiply(Z_303,Z_303)),identity)) = identity ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_4,c_4,c_88845]) ).
tff(c_28107,plain,
! [X_150,X_173] : ( multiply(multiply(X_150,multiply(multiply(X_150,X_150),identity)),multiply(X_173,identity)) = multiply(multiply(multiply(X_150,multiply(X_150,X_150)),X_173),identity) ),
inference(superposition,[status(thm),theory(equality)],[c_22713,c_27515]) ).
tff(c_1091,plain,
! [Y_4] : ( multiply(multiply(Y_4,Y_4),multiply(multiply(Y_4,multiply(identity,identity)),identity)) = multiply(multiply(Y_4,multiply(multiply(Y_4,Y_4),identity)),identity) ),
inference(superposition,[status(thm),theory(equality)],[c_43,c_1023]) ).
tff(c_1638,plain,
! [Y_33] : ( multiply(multiply(Y_33,multiply(multiply(Y_33,Y_33),identity)),identity) = multiply(multiply(Y_33,Y_33),multiply(multiply(Y_33,identity),identity)) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_1091]) ).
tff(c_2048,plain,
! [Y_40] : ( multiply(multiply(Y_40,Y_40),multiply(multiply(Y_40,Y_40),multiply(multiply(Y_40,identity),identity))) = Y_40 ),
inference(superposition,[status(thm),theory(equality)],[c_1638,c_838]) ).
tff(c_2057,plain,
! [Y_40] : ( multiply(multiply(Y_40,Y_40),multiply(multiply(multiply(Y_40,identity),identity),multiply(multiply(multiply(Y_40,identity),identity),multiply(multiply(Y_40,identity),identity)))) = multiply(multiply(Y_40,Y_40),multiply(multiply(Y_40,multiply(multiply(Y_40,Y_40),identity)),identity)) ),
inference(superposition,[status(thm),theory(equality)],[c_2048,c_1097]) ).
tff(c_7801,plain,
! [Y_88] : ( multiply(multiply(Y_88,Y_88),multiply(multiply(multiply(Y_88,identity),identity),multiply(multiply(multiply(Y_88,identity),identity),multiply(multiply(Y_88,identity),identity)))) = Y_88 ),
inference(demodulation,[status(thm),theory(equality)],[c_838,c_2057]) ).
tff(c_7816,plain,
! [Y_88] : ( multiply(multiply(identity,Y_88),multiply(multiply(Y_88,identity),identity)) = multiply(identity,multiply(multiply(multiply(Y_88,Y_88),identity),identity)) ),
inference(superposition,[status(thm),theory(equality)],[c_7801,c_4672]) ).
tff(c_18489,plain,
! [Z_134,X_135] : ( multiply(multiply(identity,Z_134),multiply(multiply(identity,multiply(Z_134,Z_134)),multiply(multiply(multiply(identity,Z_134),multiply(X_135,identity)),identity))) = X_135 ),
inference(superposition,[status(thm),theory(equality)],[c_11371,c_1831]) ).
tff(c_18668,plain,
! [Y_88] : ( multiply(multiply(identity,Y_88),multiply(multiply(identity,multiply(Y_88,Y_88)),multiply(multiply(identity,multiply(multiply(multiply(Y_88,Y_88),identity),identity)),identity))) = multiply(Y_88,identity) ),
inference(superposition,[status(thm),theory(equality)],[c_7816,c_18489]) ).
tff(c_18854,plain,
! [Y_88] : ( multiply(identity,multiply(Y_88,multiply(multiply(Y_88,Y_88),multiply(multiply(multiply(multiply(Y_88,Y_88),identity),identity),identity)))) = multiply(Y_88,identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_10371,c_10371,c_591,c_18668]) ).
tff(c_27229,plain,
! [Z_171,Y_170] : ( multiply(identity,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(identity,multiply(Z_171,identity)))),identity)))) = multiply(Y_170,multiply(multiply(Y_170,Y_170),multiply(multiply(Y_170,identity),Z_171))) ),
inference(superposition,[status(thm),theory(equality)],[c_27029,c_5250]) ).
tff(c_27474,plain,
! [Y_170,Z_171] : ( multiply(Y_170,multiply(multiply(Y_170,Y_170),multiply(multiply(Y_170,identity),Z_171))) = multiply(identity,multiply(identity,multiply(identity,Z_171))) ),
inference(demodulation,[status(thm),theory(equality)],[c_278,c_591,c_591,c_591,c_27229]) ).
tff(c_47109,plain,
! [Y_221,Z_222] : ( multiply(Y_221,multiply(multiply(Y_221,multiply(multiply(Y_221,Y_221),Z_222)),Z_222)) = multiply(identity,multiply(multiply(identity,multiply(identity,Z_222)),Z_222)) ),
inference(demodulation,[status(thm),theory(equality)],[c_278,c_591,c_591,c_10033,c_21668,c_21668,c_12356,c_10371,c_10371,c_10371,c_10371,c_10371,c_10371,c_591,c_591,c_591,c_591,c_4,c_4,c_4,c_4,c_4672,c_591,c_591,c_591,c_591,c_4,c_4,c_4,c_4,c_4672,c_591,c_591,c_591,c_591,c_4,c_23295]) ).
tff(c_23996,plain,
! [Y_1,X_2,Z_20] : ( multiply(multiply(Y_1,Y_1),multiply(multiply(multiply(Y_1,Y_1),multiply(Y_1,Y_1)),multiply(multiply(multiply(Y_1,Y_1),multiply(multiply(Y_1,multiply(X_2,identity)),identity)),Z_20))) = multiply(Y_1,multiply(X_2,multiply(identity,Z_20))) ),
inference(demodulation,[status(thm),theory(equality)],[c_10033,c_1097,c_809]) ).
tff(c_47321,plain,
! [Y_221,Z_20] : ( multiply(multiply(Y_221,Y_221),multiply(multiply(multiply(Y_221,Y_221),multiply(Y_221,Y_221)),multiply(multiply(multiply(Y_221,Y_221),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,identity)),identity)),identity)),Z_20))) = multiply(Y_221,multiply(multiply(Y_221,multiply(multiply(Y_221,Y_221),identity)),multiply(identity,Z_20))) ),
inference(superposition,[status(thm),theory(equality)],[c_47109,c_23996]) ).
tff(c_64784,plain,
! [Y_264,Z_265] : ( multiply(Y_264,multiply(multiply(Y_264,multiply(multiply(Y_264,Y_264),identity)),multiply(identity,Z_265))) = multiply(identity,multiply(identity,multiply(identity,Z_265))) ),
inference(demodulation,[status(thm),theory(equality)],[c_27474,c_4,c_4,c_4,c_4,c_4,c_47321]) ).
tff(c_65348,plain,
! [Y_88,Y_264] : ( multiply(identity,multiply(identity,multiply(identity,multiply(Y_88,multiply(multiply(Y_88,Y_88),multiply(multiply(multiply(multiply(Y_88,Y_88),identity),identity),identity)))))) = multiply(Y_264,multiply(multiply(Y_264,multiply(multiply(Y_264,Y_264),identity)),multiply(Y_88,identity))) ),
inference(superposition,[status(thm),theory(equality)],[c_18854,c_64784]) ).
tff(c_65566,plain,
! [Y_264,Y_88] : ( multiply(Y_264,multiply(multiply(multiply(Y_264,multiply(Y_264,Y_264)),Y_88),identity)) = multiply(identity,multiply(identity,multiply(Y_88,identity))) ),
inference(demodulation,[status(thm),theory(equality)],[c_28107,c_18854,c_65348]) ).
tff(c_93265,plain,
! [Y_264] : ( multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(Y_264,multiply(Y_264,Y_264)),multiply(multiply(Y_264,multiply(Y_264,Y_264)),multiply(Y_264,multiply(Y_264,Y_264)))),identity),identity))) = multiply(Y_264,multiply(identity,identity)) ),
inference(superposition,[status(thm),theory(equality)],[c_93121,c_65566]) ).
tff(c_93788,plain,
! [Y_264] : ( multiply(Y_264,identity) = Y_264 ),
inference(demodulation,[status(thm),theory(equality)],[c_278,c_591,c_591,c_10033,c_4,c_93265]) ).
tff(c_6,plain,
multiply(a,identity) != a,
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_94008,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_93788,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP121-1 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 22:44:09 EDT 2023
% 0.13/0.34 % CPUTime :
% 123.18/78.88 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 123.18/78.90
% 123.18/78.90 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 123.18/78.96
% 123.18/78.96 Inference rules
% 123.18/78.96 ----------------------
% 123.18/78.96 #Ref : 0
% 123.18/78.96 #Sup : 21970
% 123.18/78.96 #Fact : 0
% 123.18/78.96 #Define : 0
% 123.18/78.96 #Split : 0
% 123.18/78.96 #Chain : 0
% 123.18/78.96 #Close : 0
% 123.18/78.96
% 123.18/78.96 Ordering : KBO
% 123.18/78.96
% 123.18/78.96 Simplification rules
% 123.18/78.96 ----------------------
% 123.18/78.96 #Subsume : 55
% 123.18/78.96 #Demod : 161918
% 123.18/78.96 #Tautology : 7994
% 123.18/78.96 #SimpNegUnit : 0
% 123.18/78.96 #BackRed : 136
% 123.18/78.96
% 123.18/78.96 #Partial instantiations: 0
% 123.18/78.96 #Strategies tried : 1
% 123.18/78.96
% 123.18/78.96 Timing (in seconds)
% 123.18/78.96 ----------------------
% 123.18/78.97 Preprocessing : 0.37
% 123.18/78.97 Parsing : 0.20
% 123.18/78.97 CNF conversion : 0.02
% 123.18/78.97 Main loop : 77.48
% 123.18/78.97 Inferencing : 3.65
% 123.18/78.97 Reduction : 70.92
% 123.18/78.97 Demodulation : 69.99
% 123.18/78.97 BG Simplification : 0.55
% 123.18/78.97 Subsumption : 1.86
% 123.18/78.97 Abstraction : 1.59
% 123.18/78.97 MUC search : 0.00
% 123.18/78.97 Cooper : 0.00
% 123.18/78.97 Total : 77.95
% 123.18/78.97 Index Insertion : 0.00
% 123.18/78.97 Index Deletion : 0.00
% 123.18/78.97 Index Matching : 0.00
% 123.18/78.97 BG Taut test : 0.00
%------------------------------------------------------------------------------