TSTP Solution File: GRP344-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP344-1 : 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/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 : n012.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 10:41:00 EDT 2023
% Result : Unsatisfiable 35.33s 24.44s
% Output : CNFRefutation 35.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 29
% Syntax : Number of formulae : 315 ( 257 unt; 10 typ; 0 def)
% Number of atoms : 417 ( 402 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 241 ( 129 ~; 112 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 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 : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 163 (; 163 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > sk_c7 > 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_c7,type,
sk_c7: $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_63,axiom,
multiply(sk_c6,sk_c7) = sk_c5,
file(unknown,unknown) ).
tff(f_53,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_105,axiom,
( ( multiply(sk_c2,sk_c5) = sk_c6 )
| ( inverse(sk_c3) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_93,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( 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_81,axiom,
( ( multiply(sk_c1,sk_c6) = sk_c7 )
| ( inverse(sk_c3) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_69,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c3) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_138,axiom,
! [X3,X4,X1,X2] :
( ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( inverse(X3) != sk_c7 )
| ( multiply(X3,sk_c6) != sk_c7 )
| ( inverse(X4) != sk_c6 )
| ( multiply(X4,sk_c5) != sk_c6 )
| ( multiply(X1,sk_c6) != sk_c7 )
| ( inverse(X1) != sk_c6 )
| ( inverse(X2) != sk_c5 )
| ( multiply(X2,sk_c6) != sk_c5 ) ),
file(unknown,unknown) ).
tff(f_78,axiom,
( ( multiply(sk_c1,sk_c6) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_102,axiom,
( ( multiply(sk_c2,sk_c5) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_84,axiom,
( ( multiply(sk_c1,sk_c6) = sk_c7 )
| ( inverse(sk_c4) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_87,axiom,
( ( multiply(sk_c1,sk_c6) = sk_c7 )
| ( multiply(sk_c4,sk_c6) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_66,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_75,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c6) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_72,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c4) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_90,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_99,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c4,sk_c6) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_96,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c4) = sk_c5 ) ),
file(unknown,unknown) ).
tff(c_4,plain,
! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_8,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_2,plain,
! [X_1] : ( multiply(identity,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_36,plain,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(sk_c2,sk_c5) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_94,plain,
multiply(sk_c2,sk_c5) = sk_c6,
inference(splitLeft,[status(thm)],[c_36]) ).
tff(c_28,plain,
( ( inverse(sk_c3) = sk_c6 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_65,plain,
inverse(sk_c2) = sk_c6,
inference(splitLeft,[status(thm)],[c_28]) ).
tff(c_69,plain,
multiply(sk_c6,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_65,c_4]) ).
tff(c_111,plain,
! [X_12,Y_13,Z_14] : ( multiply(multiply(X_12,Y_13),Z_14) = multiply(X_12,multiply(Y_13,Z_14)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_135,plain,
! [Z_14] : ( multiply(sk_c6,multiply(sk_c2,Z_14)) = multiply(identity,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_69,c_111]) ).
tff(c_176,plain,
! [Z_16] : ( multiply(sk_c6,multiply(sk_c2,Z_16)) = Z_16 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_135]) ).
tff(c_188,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_94,c_176]) ).
tff(c_20,plain,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_99,plain,
multiply(sk_c1,sk_c6) = sk_c7,
inference(splitLeft,[status(thm)],[c_20]) ).
tff(c_12,plain,
( ( inverse(sk_c3) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_73,plain,
inverse(sk_c1) = sk_c7,
inference(splitLeft,[status(thm)],[c_12]) ).
tff(c_77,plain,
multiply(sk_c7,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_73,c_4]) ).
tff(c_132,plain,
! [Z_14] : ( multiply(sk_c7,multiply(sk_c1,Z_14)) = multiply(identity,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_77,c_111]) ).
tff(c_153,plain,
! [Z_15] : ( multiply(sk_c7,multiply(sk_c1,Z_15)) = Z_15 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_132]) ).
tff(c_165,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_99,c_153]) ).
tff(c_192,plain,
! [Z_17] : ( multiply(sk_c6,multiply(sk_c7,Z_17)) = multiply(sk_c5,Z_17) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_111]) ).
tff(c_204,plain,
multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7),
inference(superposition,[status(thm),theory(equality)],[c_165,c_192]) ).
tff(c_229,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_188,c_204]) ).
tff(c_138,plain,
! [X_2,Z_14] : ( multiply(inverse(X_2),multiply(X_2,Z_14)) = multiply(identity,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_111]) ).
tff(c_237,plain,
! [X_18,Z_19] : ( multiply(inverse(X_18),multiply(X_18,Z_19)) = Z_19 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_138]) ).
tff(c_255,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_229,c_237]) ).
tff(c_307,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_255]) ).
tff(c_314,plain,
multiply(identity,identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_307,c_307,c_165]) ).
tff(c_321,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_314]) ).
tff(c_765,plain,
multiply(identity,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_321,c_321,c_188]) ).
tff(c_772,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_765]) ).
tff(c_151,plain,
! [X_2,Z_14] : ( multiply(inverse(X_2),multiply(X_2,Z_14)) = Z_14 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_138]) ).
tff(c_935,plain,
! [X_31,Z_32] : ( multiply(inverse(inverse(X_31)),Z_32) = multiply(X_31,Z_32) ),
inference(superposition,[status(thm),theory(equality)],[c_237,c_151]) ).
tff(c_297,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_237]) ).
tff(c_942,plain,
! [X_31] : ( multiply(X_31,identity) = X_31 ),
inference(superposition,[status(thm),theory(equality)],[c_935,c_297]) ).
tff(c_466,plain,
! [X_21,Z_22] : ( multiply(inverse(inverse(X_21)),Z_22) = multiply(X_21,Z_22) ),
inference(superposition,[status(thm),theory(equality)],[c_151,c_237]) ).
tff(c_473,plain,
! [X_21] : ( multiply(X_21,identity) = X_21 ),
inference(superposition,[status(thm),theory(equality)],[c_466,c_297]) ).
tff(c_42,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c6) != sk_c5 )
| ( inverse(X2_9) != sk_c5 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( multiply(X4_7,sk_c5) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X3_6,sk_c6) != sk_c7 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_138]) ).
tff(c_44,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c6) != sk_c5 )
| ( inverse(X2_9) != sk_c5 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( multiply(X4_7,sk_c5) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X3_6,sk_c6) != sk_c7 )
| ( inverse(X3_6) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_42]) ).
tff(c_326,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c6) != sk_c5 )
| ( inverse(X2_9) != sk_c5 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(X1_8,sk_c6) != identity )
| ( multiply(X4_7,sk_c5) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X3_6,sk_c6) != identity )
| ( inverse(X3_6) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_307,c_307,c_307,c_44]) ).
tff(c_327,plain,
! [X3_6] :
( ( multiply(X3_6,sk_c6) != identity )
| ( inverse(X3_6) != identity ) ),
inference(splitLeft,[status(thm)],[c_326]) ).
tff(c_739,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_473,c_321,c_327]) ).
tff(c_317,plain,
multiply(identity,sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_307,c_77]) ).
tff(c_368,plain,
multiply(inverse(identity),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_317,c_151]) ).
tff(c_380,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_368]) ).
tff(c_318,plain,
inverse(sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_307,c_73]) ).
tff(c_384,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_380,c_318]) ).
tff(c_741,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_739,c_384]) ).
tff(c_742,plain,
! [X4_7,X1_8,X2_9] :
( ( multiply(X4_7,sk_c5) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(X1_8,sk_c6) != identity )
| ( multiply(X2_9,sk_c6) != sk_c5 )
| ( inverse(X2_9) != sk_c5 ) ),
inference(splitRight,[status(thm)],[c_326]) ).
tff(c_150538,plain,
! [X4_7,X1_8,X2_9] :
( ( identity != X4_7 )
| ( inverse(X4_7) != identity )
| ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( identity != X2_9 )
| ( inverse(X2_9) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_772,c_942,c_772,c_321,c_942,c_321,c_321,c_321,c_942,c_772,c_321,c_742]) ).
tff(c_150540,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_150538]) ).
tff(c_768,plain,
multiply(identity,sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_321,c_69]) ).
tff(c_819,plain,
multiply(inverse(identity),identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_768,c_151]) ).
tff(c_831,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_819]) ).
tff(c_769,plain,
inverse(sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_321,c_65]) ).
tff(c_835,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_831,c_769]) ).
tff(c_150542,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_150540,c_835]) ).
tff(c_150543,plain,
! [X1_8,X4_7] :
( ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( identity != X4_7 )
| ( inverse(X4_7) != identity ) ),
inference(splitRight,[status(thm)],[c_150538]) ).
tff(c_150545,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_150543]) ).
tff(c_150547,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_150545,c_835]) ).
tff(c_153315,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_150543]) ).
tff(c_153317,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_153315,c_835]) ).
tff(c_153319,plain,
multiply(sk_c1,sk_c6) != sk_c7,
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_18,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_153351,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_153319,c_18]) ).
tff(c_153318,plain,
inverse(sk_c3) = sk_c6,
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_153323,plain,
multiply(sk_c6,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_153318,c_4]) ).
tff(c_153357,plain,
! [X_516,Y_517,Z_518] : ( multiply(multiply(X_516,Y_517),Z_518) = multiply(X_516,multiply(Y_517,Z_518)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_153381,plain,
! [Z_518] : ( multiply(sk_c6,multiply(sk_c3,Z_518)) = multiply(identity,Z_518) ),
inference(superposition,[status(thm),theory(equality)],[c_153323,c_153357]) ).
tff(c_153730,plain,
! [Z_526] : ( multiply(sk_c6,multiply(sk_c3,Z_526)) = Z_526 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_153381]) ).
tff(c_153742,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_153351,c_153730]) ).
tff(c_153746,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_153742]) ).
tff(c_153758,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_153746,c_8]) ).
tff(c_153393,plain,
! [X_2,Z_518] : ( multiply(inverse(X_2),multiply(X_2,Z_518)) = multiply(identity,Z_518) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_153357]) ).
tff(c_153824,plain,
! [X_527,Z_528] : ( multiply(inverse(X_527),multiply(X_527,Z_528)) = Z_528 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_153393]) ).
tff(c_153857,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_153758,c_153824]) ).
tff(c_153894,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_153857]) ).
tff(c_153914,plain,
multiply(identity,sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_153894,c_77]) ).
tff(c_153408,plain,
! [X_2,Z_518] : ( multiply(inverse(X_2),multiply(X_2,Z_518)) = Z_518 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_153393]) ).
tff(c_154017,plain,
multiply(inverse(identity),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_153914,c_153408]) ).
tff(c_154029,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_154017]) ).
tff(c_153390,plain,
! [Z_518] : ( multiply(sk_c6,multiply(sk_c2,Z_518)) = multiply(identity,Z_518) ),
inference(superposition,[status(thm),theory(equality)],[c_69,c_153357]) ).
tff(c_153423,plain,
! [Z_520] : ( multiply(sk_c6,multiply(sk_c2,Z_520)) = Z_520 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_153390]) ).
tff(c_153435,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_94,c_153423]) ).
tff(c_153748,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_153746,c_153746,c_153435]) ).
tff(c_153845,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_153748,c_153824]) ).
tff(c_153892,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_153845]) ).
tff(c_153753,plain,
multiply(sk_c1,sk_c5) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_153746,c_153319]) ).
tff(c_153899,plain,
multiply(sk_c1,identity) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_153892,c_153753]) ).
tff(c_154077,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_154029,c_153894,c_153899]) ).
tff(c_154079,plain,
multiply(sk_c2,sk_c5) != sk_c6,
inference(splitRight,[status(thm)],[c_36]) ).
tff(c_34,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c2,sk_c5) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_154117,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_154079,c_34]) ).
tff(c_154078,plain,
inverse(sk_c3) = sk_c6,
inference(splitRight,[status(thm)],[c_36]) ).
tff(c_154083,plain,
multiply(sk_c6,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_154078,c_4]) ).
tff(c_154122,plain,
! [X_529,Y_530,Z_531] : ( multiply(multiply(X_529,Y_530),Z_531) = multiply(X_529,multiply(Y_530,Z_531)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_154149,plain,
! [Z_531] : ( multiply(sk_c6,multiply(sk_c3,Z_531)) = multiply(identity,Z_531) ),
inference(superposition,[status(thm),theory(equality)],[c_154083,c_154122]) ).
tff(c_154241,plain,
! [Z_535] : ( multiply(sk_c6,multiply(sk_c3,Z_535)) = Z_535 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_154149]) ).
tff(c_154253,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_154117,c_154241]) ).
tff(c_154257,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_154253]) ).
tff(c_154271,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_154257,c_8]) ).
tff(c_154158,plain,
! [X_2,Z_531] : ( multiply(inverse(X_2),multiply(X_2,Z_531)) = multiply(identity,Z_531) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_154122]) ).
tff(c_154337,plain,
! [X_536,Z_537] : ( multiply(inverse(X_536),multiply(X_536,Z_537)) = Z_537 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_154158]) ).
tff(c_154370,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_154271,c_154337]) ).
tff(c_154406,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_154370]) ).
tff(c_22,plain,
( ( inverse(sk_c4) = sk_c5 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_154093,plain,
multiply(sk_c1,sk_c6) = sk_c7,
inference(splitLeft,[status(thm)],[c_22]) ).
tff(c_154152,plain,
! [Z_531] : ( multiply(sk_c7,multiply(sk_c1,Z_531)) = multiply(identity,Z_531) ),
inference(superposition,[status(thm),theory(equality)],[c_77,c_154122]) ).
tff(c_154175,plain,
! [Z_532] : ( multiply(sk_c7,multiply(sk_c1,Z_532)) = Z_532 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_154152]) ).
tff(c_154187,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_154093,c_154175]) ).
tff(c_154262,plain,
multiply(sk_c7,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_154257,c_154187]) ).
tff(c_154408,plain,
multiply(identity,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_154406,c_154406,c_154262]) ).
tff(c_154414,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_154408]) ).
tff(c_154270,plain,
inverse(sk_c2) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_154257,c_65]) ).
tff(c_154288,plain,
multiply(sk_c5,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_154270,c_4]) ).
tff(c_154436,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_154414,c_154288]) ).
tff(c_154267,plain,
multiply(sk_c2,sk_c5) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_154257,c_154079]) ).
tff(c_154420,plain,
multiply(sk_c2,identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_154414,c_154414,c_154267]) ).
tff(c_154612,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_154436,c_154420]) ).
tff(c_154613,plain,
inverse(sk_c4) = sk_c5,
inference(splitRight,[status(thm)],[c_22]) ).
tff(c_154628,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_154079,c_34]) ).
tff(c_154642,plain,
! [X_540,Y_541,Z_542] : ( multiply(multiply(X_540,Y_541),Z_542) = multiply(X_540,multiply(Y_541,Z_542)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_154666,plain,
! [Z_542] : ( multiply(sk_c6,multiply(sk_c3,Z_542)) = multiply(identity,Z_542) ),
inference(superposition,[status(thm),theory(equality)],[c_154083,c_154642]) ).
tff(c_154718,plain,
! [Z_545] : ( multiply(sk_c6,multiply(sk_c3,Z_545)) = Z_545 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_154666]) ).
tff(c_154730,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_154628,c_154718]) ).
tff(c_154734,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_154730]) ).
tff(c_154614,plain,
multiply(sk_c1,sk_c6) != sk_c7,
inference(splitRight,[status(thm)],[c_22]) ).
tff(c_24,plain,
( ( multiply(sk_c4,sk_c6) = sk_c5 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_154633,plain,
multiply(sk_c4,sk_c6) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_154614,c_24]) ).
tff(c_154737,plain,
multiply(sk_c4,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_154734,c_154633]) ).
tff(c_154675,plain,
! [X_2,Z_542] : ( multiply(inverse(X_2),multiply(X_2,Z_542)) = multiply(identity,Z_542) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_154642]) ).
tff(c_154804,plain,
! [X_546,Z_547] : ( multiply(inverse(X_546),multiply(X_546,Z_547)) = Z_547 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_154675]) ).
tff(c_154825,plain,
multiply(inverse(sk_c4),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_154737,c_154804]) ).
tff(c_154868,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_154613,c_154825]) ).
tff(c_154690,plain,
! [X_2,Z_542] : ( multiply(inverse(X_2),multiply(X_2,Z_542)) = Z_542 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_154675]) ).
tff(c_154935,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_154868,c_154690]) ).
tff(c_154941,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_154935]) ).
tff(c_154745,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_154734,c_8]) ).
tff(c_154828,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_154745,c_154804]) ).
tff(c_154869,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_154828]) ).
tff(c_154877,plain,
inverse(sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_154869,c_73]) ).
tff(c_154888,plain,
multiply(identity,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_154877,c_4]) ).
tff(c_154896,plain,
multiply(inverse(identity),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_154888,c_154690]) ).
tff(c_154908,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_154896]) ).
tff(c_154739,plain,
multiply(sk_c1,sk_c5) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_154734,c_154614]) ).
tff(c_154872,plain,
multiply(sk_c1,sk_c5) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_154869,c_154739]) ).
tff(c_155040,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_154941,c_2,c_154908,c_154872]) ).
tff(c_155042,plain,
inverse(sk_c1) != sk_c7,
inference(splitRight,[status(thm)],[c_12]) ).
tff(c_10,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_155081,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_155042,c_10]) ).
tff(c_155041,plain,
inverse(sk_c3) = sk_c6,
inference(splitRight,[status(thm)],[c_12]) ).
tff(c_155046,plain,
multiply(sk_c6,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_155041,c_4]) ).
tff(c_155091,plain,
! [X_549,Y_550,Z_551] : ( multiply(multiply(X_549,Y_550),Z_551) = multiply(X_549,multiply(Y_550,Z_551)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_155115,plain,
! [Z_551] : ( multiply(sk_c6,multiply(sk_c3,Z_551)) = multiply(identity,Z_551) ),
inference(superposition,[status(thm),theory(equality)],[c_155046,c_155091]) ).
tff(c_155173,plain,
! [Z_554] : ( multiply(sk_c6,multiply(sk_c3,Z_554)) = Z_554 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_155115]) ).
tff(c_155185,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_155081,c_155173]) ).
tff(c_155189,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_155185]) ).
tff(c_16,plain,
( ( multiply(sk_c4,sk_c6) = sk_c5 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_155072,plain,
multiply(sk_c4,sk_c6) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_155042,c_16]) ).
tff(c_14,plain,
( ( inverse(sk_c4) = sk_c5 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_155059,plain,
inverse(sk_c4) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_155042,c_14]) ).
tff(c_155063,plain,
multiply(sk_c5,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_155059,c_4]) ).
tff(c_155112,plain,
! [Z_551] : ( multiply(sk_c5,multiply(sk_c4,Z_551)) = multiply(identity,Z_551) ),
inference(superposition,[status(thm),theory(equality)],[c_155063,c_155091]) ).
tff(c_155137,plain,
! [Z_552] : ( multiply(sk_c5,multiply(sk_c4,Z_552)) = Z_552 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_155112]) ).
tff(c_155149,plain,
multiply(sk_c5,sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_155072,c_155137]) ).
tff(c_155192,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_155189,c_155149]) ).
tff(c_155121,plain,
! [X_2,Z_551] : ( multiply(inverse(X_2),multiply(X_2,Z_551)) = multiply(identity,Z_551) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_155091]) ).
tff(c_156080,plain,
! [X_573,Z_574] : ( multiply(inverse(X_573),multiply(X_573,Z_574)) = Z_574 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_155121]) ).
tff(c_156098,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_155192,c_156080]) ).
tff(c_156141,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_156098]) ).
tff(c_155135,plain,
! [X_2,Z_551] : ( multiply(inverse(X_2),multiply(X_2,Z_551)) = Z_551 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_155121]) ).
tff(c_156391,plain,
! [X_578,Z_579] : ( multiply(inverse(inverse(X_578)),Z_579) = multiply(X_578,Z_579) ),
inference(superposition,[status(thm),theory(equality)],[c_156080,c_155135]) ).
tff(c_156134,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_156080]) ).
tff(c_156398,plain,
! [X_578] : ( multiply(X_578,identity) = X_578 ),
inference(superposition,[status(thm),theory(equality)],[c_156391,c_156134]) ).
tff(c_155199,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_155189,c_8]) ).
tff(c_156110,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_155199,c_156080]) ).
tff(c_156143,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_156110]) ).
tff(c_155301,plain,
! [X_557,Z_558] : ( multiply(inverse(X_557),multiply(X_557,Z_558)) = Z_558 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_155121]) ).
tff(c_155337,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_155199,c_155301]) ).
tff(c_155370,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_155337]) ).
tff(c_155653,plain,
! [X_563,Z_564] : ( multiply(inverse(inverse(X_563)),Z_564) = multiply(X_563,Z_564) ),
inference(superposition,[status(thm),theory(equality)],[c_155301,c_155135]) ).
tff(c_155361,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_155301]) ).
tff(c_155660,plain,
! [X_563] : ( multiply(X_563,identity) = X_563 ),
inference(superposition,[status(thm),theory(equality)],[c_155653,c_155361]) ).
tff(c_155334,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_155192,c_155301]) ).
tff(c_155369,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_155334]) ).
tff(c_155225,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c5) != sk_c5 )
| ( inverse(X2_9) != sk_c5 )
| ( inverse(X1_8) != sk_c5 )
| ( multiply(X1_8,sk_c5) != sk_c7 )
| ( multiply(X4_7,sk_c5) != sk_c5 )
| ( inverse(X4_7) != sk_c5 )
| ( multiply(X3_6,sk_c5) != sk_c7 )
| ( inverse(X3_6) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_155189,c_155189,c_155189,c_155189,c_155189,c_155189,c_44]) ).
tff(c_155226,plain,
! [X3_6] :
( ( multiply(X3_6,sk_c5) != sk_c7 )
| ( inverse(X3_6) != sk_c7 ) ),
inference(splitLeft,[status(thm)],[c_155225]) ).
tff(c_156034,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_155370,c_155660,c_155370,c_155369,c_155226]) ).
tff(c_155196,plain,
multiply(sk_c5,sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_155189,c_69]) ).
tff(c_155379,plain,
multiply(identity,sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_155369,c_155196]) ).
tff(c_155472,plain,
multiply(inverse(identity),identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_155379,c_155135]) ).
tff(c_155484,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_155472]) ).
tff(c_155198,plain,
inverse(sk_c2) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_155189,c_65]) ).
tff(c_155383,plain,
inverse(sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_155369,c_155198]) ).
tff(c_155506,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_155484,c_155383]) ).
tff(c_156036,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_156034,c_155506]) ).
tff(c_156037,plain,
! [X4_7,X1_8,X2_9] :
( ( multiply(X4_7,sk_c5) != sk_c5 )
| ( inverse(X4_7) != sk_c5 )
| ( inverse(X1_8) != sk_c5 )
| ( multiply(X1_8,sk_c5) != sk_c7 )
| ( multiply(X2_9,sk_c5) != sk_c5 )
| ( inverse(X2_9) != sk_c5 ) ),
inference(splitRight,[status(thm)],[c_155225]) ).
tff(c_163859,plain,
! [X4_7,X1_8,X2_9] :
( ( identity != X4_7 )
| ( inverse(X4_7) != identity )
| ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( identity != X2_9 )
| ( inverse(X2_9) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_156141,c_156398,c_156141,c_156141,c_156398,c_156143,c_156141,c_156141,c_156141,c_156398,c_156141,c_156141,c_156037]) ).
tff(c_163861,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_163859]) ).
tff(c_156156,plain,
multiply(identity,sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_156141,c_155063]) ).
tff(c_156260,plain,
multiply(inverse(identity),identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_156156,c_155135]) ).
tff(c_156272,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_156260]) ).
tff(c_156157,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_156141,c_155059]) ).
tff(c_156276,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_156272,c_156157]) ).
tff(c_163863,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_163861,c_156276]) ).
tff(c_163864,plain,
! [X1_8,X4_7] :
( ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( identity != X4_7 )
| ( inverse(X4_7) != identity ) ),
inference(splitRight,[status(thm)],[c_163859]) ).
tff(c_163866,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_163864]) ).
tff(c_163868,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_163866,c_156276]) ).
tff(c_163871,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_163864]) ).
tff(c_163873,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_163871,c_156276]) ).
tff(c_163875,plain,
inverse(sk_c2) != sk_c6,
inference(splitRight,[status(thm)],[c_28]) ).
tff(c_26,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_163918,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_163875,c_26]) ).
tff(c_163874,plain,
inverse(sk_c3) = sk_c6,
inference(splitRight,[status(thm)],[c_28]) ).
tff(c_163879,plain,
multiply(sk_c6,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_163874,c_4]) ).
tff(c_163932,plain,
! [X_664,Y_665,Z_666] : ( multiply(multiply(X_664,Y_665),Z_666) = multiply(X_664,multiply(Y_665,Z_666)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_163959,plain,
! [Z_666] : ( multiply(sk_c6,multiply(sk_c3,Z_666)) = multiply(identity,Z_666) ),
inference(superposition,[status(thm),theory(equality)],[c_163879,c_163932]) ).
tff(c_164280,plain,
! [Z_675] : ( multiply(sk_c6,multiply(sk_c3,Z_675)) = Z_675 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_163959]) ).
tff(c_164292,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_163918,c_164280]) ).
tff(c_164296,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_164292]) ).
tff(c_32,plain,
( ( multiply(sk_c4,sk_c6) = sk_c5 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_163923,plain,
multiply(sk_c4,sk_c6) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_163875,c_32]) ).
tff(c_30,plain,
( ( inverse(sk_c4) = sk_c5 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_163888,plain,
inverse(sk_c4) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_163875,c_30]) ).
tff(c_163892,plain,
multiply(sk_c5,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_163888,c_4]) ).
tff(c_163956,plain,
! [Z_666] : ( multiply(sk_c5,multiply(sk_c4,Z_666)) = multiply(identity,Z_666) ),
inference(superposition,[status(thm),theory(equality)],[c_163892,c_163932]) ).
tff(c_163978,plain,
! [Z_667] : ( multiply(sk_c5,multiply(sk_c4,Z_667)) = Z_667 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_163956]) ).
tff(c_163990,plain,
multiply(sk_c5,sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_163923,c_163978]) ).
tff(c_164298,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_164296,c_163990]) ).
tff(c_163962,plain,
! [X_2,Z_666] : ( multiply(inverse(X_2),multiply(X_2,Z_666)) = multiply(identity,Z_666) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_163932]) ).
tff(c_165144,plain,
! [X_693,Z_694] : ( multiply(inverse(X_693),multiply(X_693,Z_694)) = Z_694 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_163962]) ).
tff(c_165168,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_164298,c_165144]) ).
tff(c_165203,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_165168]) ).
tff(c_163976,plain,
! [X_2,Z_666] : ( multiply(inverse(X_2),multiply(X_2,Z_666)) = Z_666 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_163962]) ).
tff(c_165386,plain,
! [X_697,Z_698] : ( multiply(inverse(inverse(X_697)),Z_698) = multiply(X_697,Z_698) ),
inference(superposition,[status(thm),theory(equality)],[c_165144,c_163976]) ).
tff(c_165195,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_165144]) ).
tff(c_165393,plain,
! [X_697] : ( multiply(X_697,identity) = X_697 ),
inference(superposition,[status(thm),theory(equality)],[c_165386,c_165195]) ).
tff(c_164304,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_164296,c_8]) ).
tff(c_165162,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_164304,c_165144]) ).
tff(c_165202,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_165162]) ).
tff(c_164389,plain,
! [X_678,Z_679] : ( multiply(inverse(X_678),multiply(X_678,Z_679)) = Z_679 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_163962]) ).
tff(c_164422,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_164298,c_164389]) ).
tff(c_164458,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_164422]) ).
tff(c_164724,plain,
! [X_683,Z_684] : ( multiply(inverse(inverse(X_683)),Z_684) = multiply(X_683,Z_684) ),
inference(superposition,[status(thm),theory(equality)],[c_163976,c_164389]) ).
tff(c_164449,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_164389]) ).
tff(c_164731,plain,
! [X_683] : ( multiply(X_683,identity) = X_683 ),
inference(superposition,[status(thm),theory(equality)],[c_164724,c_164449]) ).
tff(c_164002,plain,
! [Z_668] : ( multiply(sk_c6,multiply(sk_c3,Z_668)) = Z_668 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_163959]) ).
tff(c_164014,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_163918,c_164002]) ).
tff(c_164018,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_164014]) ).
tff(c_164026,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_164018,c_8]) ).
tff(c_164137,plain,
! [X_672,Z_673] : ( multiply(inverse(X_672),multiply(X_672,Z_673)) = Z_673 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_163962]) ).
tff(c_164176,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_164026,c_164137]) ).
tff(c_164208,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_164176]) ).
tff(c_164020,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_164018,c_163990]) ).
tff(c_164170,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_164020,c_164137]) ).
tff(c_164206,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_164170]) ).
tff(c_164025,plain,
inverse(sk_c3) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_164018,c_163874]) ).
tff(c_164022,plain,
multiply(sk_c3,sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_164018,c_163918]) ).
tff(c_164001,plain,
! [X3_6] :
( ( multiply(X3_6,sk_c6) != sk_c7 )
| ( inverse(X3_6) != sk_c7 ) ),
inference(splitLeft,[status(thm)],[c_44]) ).
tff(c_164079,plain,
! [X3_669] :
( ( multiply(X3_669,sk_c5) != sk_c7 )
| ( inverse(X3_669) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_164018,c_164001]) ).
tff(c_164085,plain,
inverse(sk_c3) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_164022,c_164079]) ).
tff(c_164103,plain,
sk_c7 != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_164025,c_164085]) ).
tff(c_164212,plain,
sk_c7 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_164206,c_164103]) ).
tff(c_164278,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_164208,c_164212]) ).
tff(c_164279,plain,
! [X4_7,X1_8,X2_9] :
( ( multiply(X4_7,sk_c5) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( multiply(X2_9,sk_c6) != sk_c5 )
| ( inverse(X2_9) != sk_c5 ) ),
inference(splitRight,[status(thm)],[c_44]) ).
tff(c_164316,plain,
! [X4_7,X1_8,X2_9] :
( ( multiply(X4_7,sk_c5) != sk_c5 )
| ( inverse(X4_7) != sk_c5 )
| ( inverse(X1_8) != sk_c5 )
| ( multiply(X1_8,sk_c5) != sk_c7 )
| ( multiply(X2_9,sk_c5) != sk_c5 )
| ( inverse(X2_9) != sk_c5 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_164296,c_164296,c_164296,c_164296,c_164296,c_164279]) ).
tff(c_164317,plain,
! [X2_9] :
( ( multiply(X2_9,sk_c5) != sk_c5 )
| ( inverse(X2_9) != sk_c5 ) ),
inference(splitLeft,[status(thm)],[c_164316]) ).
tff(c_165108,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_164458,c_164731,c_164458,c_164458,c_164317]) ).
tff(c_164301,plain,
multiply(sk_c5,sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_164296,c_163879]) ).
tff(c_164473,plain,
multiply(identity,sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_164458,c_164301]) ).
tff(c_164591,plain,
multiply(inverse(identity),identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_164473,c_163976]) ).
tff(c_164603,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_164591]) ).
tff(c_164303,plain,
inverse(sk_c3) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_164296,c_163874]) ).
tff(c_164476,plain,
inverse(sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_164458,c_164303]) ).
tff(c_164608,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_164603,c_164476]) ).
tff(c_165110,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_165108,c_164608]) ).
tff(c_165111,plain,
! [X1_8,X4_7] :
( ( inverse(X1_8) != sk_c5 )
| ( multiply(X1_8,sk_c5) != sk_c7 )
| ( multiply(X4_7,sk_c5) != sk_c5 )
| ( inverse(X4_7) != sk_c5 ) ),
inference(splitRight,[status(thm)],[c_164316]) ).
tff(c_168592,plain,
! [X1_8,X4_7] :
( ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( identity != X4_7 )
| ( inverse(X4_7) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_165203,c_165393,c_165203,c_165203,c_165393,c_165203,c_165202,c_165203,c_165111]) ).
tff(c_168594,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_168592]) ).
tff(c_164312,plain,
multiply(sk_c5,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_164303,c_4]) ).
tff(c_165231,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_165203,c_164312]) ).
tff(c_165216,plain,
inverse(sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_165203,c_164303]) ).
tff(c_165236,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_165231,c_165216]) ).
tff(c_168596,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_168594,c_165236]) ).
tff(c_168598,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_168592]) ).
tff(c_168600,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_168598,c_165236]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP344-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 21:48:22 EDT 2023
% 0.14/0.35 % CPUTime :
% 35.33/24.44 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 35.33/24.48
% 35.33/24.48 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 35.88/24.54
% 35.88/24.54 Inference rules
% 35.88/24.54 ----------------------
% 35.88/24.54 #Ref : 0
% 35.88/24.54 #Sup : 40262
% 35.88/24.54 #Fact : 0
% 35.88/24.54 #Define : 0
% 35.88/24.54 #Split : 20
% 35.88/24.54 #Chain : 0
% 35.88/24.54 #Close : 0
% 35.88/24.54
% 35.88/24.54 Ordering : KBO
% 35.88/24.54
% 35.88/24.54 Simplification rules
% 35.88/24.54 ----------------------
% 35.88/24.54 #Subsume : 6
% 35.88/24.54 #Demod : 211842
% 35.88/24.54 #Tautology : 32997
% 35.88/24.54 #SimpNegUnit : 28
% 35.88/24.54 #BackRed : 329
% 35.88/24.54
% 35.88/24.54 #Partial instantiations: 0
% 35.88/24.54 #Strategies tried : 1
% 35.88/24.54
% 35.88/24.54 Timing (in seconds)
% 35.88/24.54 ----------------------
% 35.88/24.54 Preprocessing : 0.46
% 35.88/24.54 Parsing : 0.21
% 35.88/24.54 CNF conversion : 0.02
% 35.88/24.54 Main loop : 22.96
% 35.88/24.54 Inferencing : 4.48
% 35.88/24.54 Reduction : 15.95
% 35.88/24.54 Demodulation : 15.39
% 35.88/24.54 BG Simplification : 0.30
% 35.88/24.54 Subsumption : 1.65
% 35.88/24.54 Abstraction : 1.31
% 35.88/24.54 MUC search : 0.00
% 35.88/24.54 Cooper : 0.00
% 35.88/24.54 Total : 23.53
% 35.88/24.54 Index Insertion : 0.00
% 35.88/24.54 Index Deletion : 0.00
% 35.88/24.54 Index Matching : 0.00
% 35.88/24.54 BG Taut test : 0.00
%------------------------------------------------------------------------------