TSTP Solution File: GRP129-2.004 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP129-2.004 : 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 : n009.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 10:40:12 EDT 2023
% Result : Unsatisfiable 14.63s 6.32s
% Output : CNFRefutation 15.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 34
% Syntax : Number of formulae : 555 ( 281 unt; 9 typ; 0 def)
% Number of atoms : 1355 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 1194 ( 385 ~; 809 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 5 >; 5 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 238 (; 238 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > next > greater > equalish > group_element > #nlpp > e_4 > e_3 > e_2 > e_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(group_element,type,
group_element: $i > $o ).
tff(greater,type,
greater: ( $i * $i ) > $o ).
tff(e_2,type,
e_2: $i ).
tff(product,type,
product: ( $i * $i * $i ) > $o ).
tff(next,type,
next: ( $i * $i ) > $o ).
tff(e_4,type,
e_4: $i ).
tff(e_3,type,
e_3: $i ).
tff(equalish,type,
equalish: ( $i * $i ) > $o ).
tff(e_1,type,
e_1: $i ).
tff(f_65,axiom,
~ equalish(e_3,e_1),
file(unknown,unknown) ).
tff(f_59,axiom,
~ equalish(e_2,e_1),
file(unknown,unknown) ).
tff(f_31,axiom,
next(e_2,e_3),
file(unknown,unknown) ).
tff(f_48,axiom,
group_element(e_1),
file(unknown,unknown) ).
tff(f_50,axiom,
group_element(e_3),
file(unknown,unknown) ).
tff(f_89,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(X,Y,e_1)
| product(X,Y,e_2)
| product(X,Y,e_3)
| product(X,Y,e_4) ),
file(unknown,unknown) ).
tff(f_38,axiom,
greater(e_4,e_3),
file(unknown,unknown) ).
tff(f_47,axiom,
! [X,Y,X1] :
( ~ product(X,e_1,Y)
| ~ next(X,X1)
| ~ greater(Y,X1) ),
file(unknown,unknown) ).
tff(f_121,axiom,
! [Y,X,Z1,Z2] :
( ~ product(Y,X,Z1)
| ~ product(X,Z1,Z2)
| product(Z1,Y,Z2) ),
file(unknown,unknown) ).
tff(f_30,axiom,
next(e_1,e_2),
file(unknown,unknown) ).
tff(f_37,axiom,
greater(e_4,e_2),
file(unknown,unknown) ).
tff(f_36,axiom,
greater(e_3,e_2),
file(unknown,unknown) ).
tff(f_113,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_105,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_61,axiom,
~ equalish(e_2,e_3),
file(unknown,unknown) ).
tff(f_49,axiom,
group_element(e_2),
file(unknown,unknown) ).
tff(f_67,axiom,
~ equalish(e_3,e_2),
file(unknown,unknown) ).
tff(f_55,axiom,
~ equalish(e_1,e_3),
file(unknown,unknown) ).
tff(f_75,axiom,
~ equalish(e_4,e_3),
file(unknown,unknown) ).
tff(f_69,axiom,
~ equalish(e_3,e_4),
file(unknown,unknown) ).
tff(f_71,axiom,
~ equalish(e_4,e_1),
file(unknown,unknown) ).
tff(f_51,axiom,
group_element(e_4),
file(unknown,unknown) ).
tff(f_73,axiom,
~ equalish(e_4,e_2),
file(unknown,unknown) ).
tff(f_97,axiom,
! [X,Y,W,Z] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_53,axiom,
~ equalish(e_1,e_2),
file(unknown,unknown) ).
tff(c_42,plain,
~ equalish(e_3,e_1),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_36,plain,
~ equalish(e_2,e_1),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_4,plain,
next(e_2,e_3),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_22,plain,
group_element(e_1),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_26,plain,
group_element(e_3),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_92,plain,
! [X_47,Y_48] :
( product(X_47,Y_48,e_4)
| product(X_47,Y_48,e_3)
| product(X_47,Y_48,e_2)
| product(X_47,Y_48,e_1)
| ~ group_element(Y_48)
| ~ group_element(X_47) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_18,plain,
greater(e_4,e_3),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_63,plain,
! [Y_22,X1_23,X_24] :
( ~ greater(Y_22,X1_23)
| ~ next(X_24,X1_23)
| ~ product(X_24,e_1,Y_22) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_79,plain,
! [X_24] :
( ~ next(X_24,e_3)
| ~ product(X_24,e_1,e_4) ),
inference(resolution,[status(thm)],[c_18,c_63]) ).
tff(c_106,plain,
! [X_47] :
( ~ next(X_47,e_3)
| product(X_47,e_1,e_3)
| product(X_47,e_1,e_2)
| product(X_47,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X_47) ),
inference(resolution,[status(thm)],[c_92,c_79]) ).
tff(c_121,plain,
! [X_47] :
( ~ next(X_47,e_3)
| product(X_47,e_1,e_3)
| product(X_47,e_1,e_2)
| product(X_47,e_1,e_1)
| ~ group_element(X_47) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_106]) ).
tff(c_62,plain,
! [Z1_20,Y_18,Z2_21,X_19] :
( product(Z1_20,Y_18,Z2_21)
| ~ product(X_19,Z1_20,Z2_21)
| ~ product(Y_18,X_19,Z1_20) ),
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_338,plain,
! [Y_80,Y_81,X_82] :
( product(Y_80,Y_81,e_4)
| ~ product(Y_81,X_82,Y_80)
| product(X_82,Y_80,e_3)
| product(X_82,Y_80,e_2)
| product(X_82,Y_80,e_1)
| ~ group_element(Y_80)
| ~ group_element(X_82) ),
inference(resolution,[status(thm)],[c_92,c_62]) ).
tff(c_342,plain,
! [X_47] :
( product(e_3,X_47,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_1)
| ~ next(X_47,e_3)
| product(X_47,e_1,e_2)
| product(X_47,e_1,e_1)
| ~ group_element(X_47) ),
inference(resolution,[status(thm)],[c_121,c_338]) ).
tff(c_350,plain,
! [X_47] :
( product(e_3,X_47,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| ~ next(X_47,e_3)
| product(X_47,e_1,e_2)
| product(X_47,e_1,e_1)
| ~ group_element(X_47) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_26,c_342]) ).
tff(c_3369,plain,
product(e_1,e_3,e_1),
inference(splitLeft,[status(thm)],[c_350]) ).
tff(c_2,plain,
next(e_1,e_2),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_16,plain,
greater(e_4,e_2),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_76,plain,
! [X_24] :
( ~ next(X_24,e_2)
| ~ product(X_24,e_1,e_4) ),
inference(resolution,[status(thm)],[c_16,c_63]) ).
tff(c_112,plain,
! [X_47] :
( ~ next(X_47,e_2)
| product(X_47,e_1,e_3)
| product(X_47,e_1,e_2)
| product(X_47,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X_47) ),
inference(resolution,[status(thm)],[c_92,c_76]) ).
tff(c_237,plain,
! [X_62] :
( ~ next(X_62,e_2)
| product(X_62,e_1,e_3)
| product(X_62,e_1,e_2)
| product(X_62,e_1,e_1)
| ~ group_element(X_62) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_112]) ).
tff(c_14,plain,
greater(e_3,e_2),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_80,plain,
! [X_24] :
( ~ next(X_24,e_2)
| ~ product(X_24,e_1,e_3) ),
inference(resolution,[status(thm)],[c_14,c_63]) ).
tff(c_255,plain,
! [X_62] :
( ~ next(X_62,e_2)
| product(X_62,e_1,e_2)
| product(X_62,e_1,e_1)
| ~ group_element(X_62) ),
inference(resolution,[status(thm)],[c_237,c_80]) ).
tff(c_262,plain,
! [X_66] :
( ~ next(X_66,e_2)
| product(X_66,e_1,e_2)
| product(X_66,e_1,e_1)
| ~ group_element(X_66) ),
inference(resolution,[status(thm)],[c_237,c_80]) ).
tff(c_60,plain,
! [W_14,Z_17,Y_15,X_16] :
( equalish(W_14,Z_17)
| ~ product(Z_17,Y_15,X_16)
| ~ product(W_14,Y_15,X_16) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_284,plain,
! [W_69,X_70] :
( equalish(W_69,X_70)
| ~ product(W_69,e_1,e_2)
| ~ next(X_70,e_2)
| product(X_70,e_1,e_1)
| ~ group_element(X_70) ),
inference(resolution,[status(thm)],[c_262,c_60]) ).
tff(c_287,plain,
! [X_62,X_70] :
( equalish(X_62,X_70)
| ~ next(X_70,e_2)
| product(X_70,e_1,e_1)
| ~ group_element(X_70)
| ~ next(X_62,e_2)
| product(X_62,e_1,e_1)
| ~ group_element(X_62) ),
inference(resolution,[status(thm)],[c_255,c_284]) ).
tff(c_825,plain,
! [X_98] :
( equalish(X_98,X_98)
| ~ next(X_98,e_2)
| ~ group_element(X_98)
| product(X_98,e_1,e_1) ),
inference(factorization,[status(thm),theory(equality)],[c_287]) ).
tff(c_274,plain,
! [Y_18,X_66] :
( product(e_1,Y_18,e_2)
| ~ product(Y_18,X_66,e_1)
| ~ next(X_66,e_2)
| product(X_66,e_1,e_1)
| ~ group_element(X_66) ),
inference(resolution,[status(thm)],[c_262,c_62]) ).
tff(c_833,plain,
! [X_98] :
( product(e_1,X_98,e_2)
| ~ next(e_1,e_2)
| product(e_1,e_1,e_1)
| ~ group_element(e_1)
| equalish(X_98,X_98)
| ~ next(X_98,e_2)
| ~ group_element(X_98) ),
inference(resolution,[status(thm)],[c_825,c_274]) ).
tff(c_856,plain,
! [X_98] :
( product(e_1,X_98,e_2)
| product(e_1,e_1,e_1)
| equalish(X_98,X_98)
| ~ next(X_98,e_2)
| ~ group_element(X_98) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_2,c_833]) ).
tff(c_1124,plain,
product(e_1,e_1,e_1),
inference(splitLeft,[status(thm)],[c_856]) ).
tff(c_58,plain,
! [W_11,Z_13,X_10,Y_12] :
( equalish(W_11,Z_13)
| ~ product(X_10,Z_13,Y_12)
| ~ product(X_10,W_11,Y_12) ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_1185,plain,
! [W_11] :
( equalish(W_11,e_1)
| ~ product(e_1,W_11,e_1) ),
inference(resolution,[status(thm)],[c_1124,c_58]) ).
tff(c_3386,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_3369,c_1185]) ).
tff(c_3431,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_42,c_3386]) ).
tff(c_3433,plain,
~ product(e_1,e_3,e_1),
inference(splitRight,[status(thm)],[c_350]) ).
tff(c_38,plain,
~ equalish(e_2,e_3),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_24,plain,
group_element(e_2),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_44,plain,
~ equalish(e_3,e_2),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_32,plain,
~ equalish(e_1,e_3),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_3432,plain,
! [X_47] :
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_3,X_47,e_4)
| ~ next(X_47,e_3)
| product(X_47,e_1,e_2)
| product(X_47,e_1,e_1)
| ~ group_element(X_47) ),
inference(splitRight,[status(thm)],[c_350]) ).
tff(c_3538,plain,
product(e_1,e_3,e_3),
inference(splitLeft,[status(thm)],[c_3432]) ).
tff(c_52,plain,
~ equalish(e_4,e_3),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_46,plain,
~ equalish(e_3,e_4),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_48,plain,
~ equalish(e_4,e_1),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_28,plain,
group_element(e_4),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_113,plain,
! [Y_48,Y_18,X_47] :
( product(Y_48,Y_18,e_4)
| ~ product(Y_18,X_47,Y_48)
| product(X_47,Y_48,e_3)
| product(X_47,Y_48,e_2)
| product(X_47,Y_48,e_1)
| ~ group_element(Y_48)
| ~ group_element(X_47) ),
inference(resolution,[status(thm)],[c_92,c_62]) ).
tff(c_3560,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_3538,c_113]) ).
tff(c_3607,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_3560]) ).
tff(c_3902,plain,
product(e_3,e_3,e_1),
inference(splitLeft,[status(thm)],[c_3607]) ).
tff(c_4155,plain,
! [Y_179] :
( product(e_3,Y_179,e_1)
| ~ product(Y_179,e_3,e_3) ),
inference(resolution,[status(thm)],[c_3902,c_62]) ).
tff(c_4179,plain,
product(e_3,e_1,e_1),
inference(resolution,[status(thm)],[c_3538,c_4155]) ).
tff(c_3979,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product(e_3,W_11,e_1) ),
inference(resolution,[status(thm)],[c_3902,c_58]) ).
tff(c_4203,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_4179,c_3979]) ).
tff(c_4254,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_4203]) ).
tff(c_4255,plain,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_3)
| product(e_3,e_1,e_4) ),
inference(splitRight,[status(thm)],[c_3607]) ).
tff(c_4257,plain,
product(e_3,e_1,e_4),
inference(splitLeft,[status(thm)],[c_4255]) ).
tff(c_4271,plain,
( product(e_4,e_3,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_4257,c_113]) ).
tff(c_4322,plain,
( product(e_4,e_3,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_28,c_4271]) ).
tff(c_4726,plain,
product(e_1,e_4,e_1),
inference(splitLeft,[status(thm)],[c_4322]) ).
tff(c_4745,plain,
equalish(e_4,e_1),
inference(resolution,[status(thm)],[c_4726,c_1185]) ).
tff(c_4794,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_48,c_4745]) ).
tff(c_4795,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_4,e_3,e_4) ),
inference(splitRight,[status(thm)],[c_4322]) ).
tff(c_4997,plain,
product(e_4,e_3,e_4),
inference(splitLeft,[status(thm)],[c_4795]) ).
tff(c_5007,plain,
( product(e_4,e_4,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_4997,c_113]) ).
tff(c_5038,plain,
( product(e_4,e_4,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_28,c_5007]) ).
tff(c_5486,plain,
product(e_3,e_4,e_1),
inference(splitLeft,[status(thm)],[c_5038]) ).
tff(c_5773,plain,
! [Y_205] :
( product(e_4,Y_205,e_1)
| ~ product(Y_205,e_3,e_4) ),
inference(resolution,[status(thm)],[c_5486,c_62]) ).
tff(c_5782,plain,
product(e_4,e_4,e_1),
inference(resolution,[status(thm)],[c_4997,c_5773]) ).
tff(c_5564,plain,
! [W_14] :
( equalish(W_14,e_3)
| ~ product(W_14,e_4,e_1) ),
inference(resolution,[status(thm)],[c_5486,c_60]) ).
tff(c_5791,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_5782,c_5564]) ).
tff(c_5827,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_5791]) ).
tff(c_5828,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_4,e_3)
| product(e_4,e_4,e_4) ),
inference(splitRight,[status(thm)],[c_5038]) ).
tff(c_5977,plain,
product(e_4,e_4,e_4),
inference(splitLeft,[status(thm)],[c_5828]) ).
tff(c_5049,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product(e_4,W_11,e_4) ),
inference(resolution,[status(thm)],[c_4997,c_58]) ).
tff(c_5980,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_5977,c_5049]) ).
tff(c_6008,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_5980]) ).
tff(c_6009,plain,
( product(e_3,e_4,e_3)
| product(e_3,e_4,e_2) ),
inference(splitRight,[status(thm)],[c_5828]) ).
tff(c_6023,plain,
product(e_3,e_4,e_2),
inference(splitLeft,[status(thm)],[c_6009]) ).
tff(c_6329,plain,
! [Y_214] :
( product(e_4,Y_214,e_2)
| ~ product(Y_214,e_3,e_4) ),
inference(resolution,[status(thm)],[c_6023,c_62]) ).
tff(c_6338,plain,
product(e_4,e_4,e_2),
inference(resolution,[status(thm)],[c_4997,c_6329]) ).
tff(c_6209,plain,
! [W_14] :
( equalish(W_14,e_3)
| ~ product(W_14,e_4,e_2) ),
inference(resolution,[status(thm)],[c_6023,c_60]) ).
tff(c_6347,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_6338,c_6209]) ).
tff(c_6377,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_6347]) ).
tff(c_6378,plain,
product(e_3,e_4,e_3),
inference(splitRight,[status(thm)],[c_6009]) ).
tff(c_5048,plain,
! [Y_18] :
( product(e_3,Y_18,e_4)
| ~ product(Y_18,e_4,e_3) ),
inference(resolution,[status(thm)],[c_4997,c_62]) ).
tff(c_6414,plain,
product(e_3,e_3,e_4),
inference(resolution,[status(thm)],[c_6378,c_5048]) ).
tff(c_5050,plain,
! [W_14] :
( equalish(W_14,e_4)
| ~ product(W_14,e_3,e_4) ),
inference(resolution,[status(thm)],[c_4997,c_60]) ).
tff(c_6461,plain,
equalish(e_3,e_4),
inference(resolution,[status(thm)],[c_6414,c_5050]) ).
tff(c_6496,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_6461]) ).
tff(c_6497,plain,
( product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(splitRight,[status(thm)],[c_4795]) ).
tff(c_6557,plain,
product(e_1,e_4,e_2),
inference(splitLeft,[status(thm)],[c_6497]) ).
tff(c_6571,plain,
( product(e_2,e_1,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_6557,c_113]) ).
tff(c_6608,plain,
( product(e_2,e_1,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_24,c_6571]) ).
tff(c_8620,plain,
product(e_4,e_2,e_1),
inference(splitLeft,[status(thm)],[c_6608]) ).
tff(c_9148,plain,
! [Y_252] :
( product(e_2,Y_252,e_1)
| ~ product(Y_252,e_4,e_2) ),
inference(resolution,[status(thm)],[c_8620,c_62]) ).
tff(c_9161,plain,
product(e_2,e_1,e_1),
inference(resolution,[status(thm)],[c_6557,c_9148]) ).
tff(c_1186,plain,
! [W_14] :
( equalish(W_14,e_1)
| ~ product(W_14,e_1,e_1) ),
inference(resolution,[status(thm)],[c_1124,c_60]) ).
tff(c_9188,plain,
equalish(e_2,e_1),
inference(resolution,[status(thm)],[c_9161,c_1186]) ).
tff(c_9253,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_36,c_9188]) ).
tff(c_9254,plain,
( product(e_4,e_2,e_2)
| product(e_4,e_2,e_3)
| product(e_2,e_1,e_4) ),
inference(splitRight,[status(thm)],[c_6608]) ).
tff(c_9256,plain,
product(e_2,e_1,e_4),
inference(splitLeft,[status(thm)],[c_9254]) ).
tff(c_4342,plain,
! [W_14] :
( equalish(W_14,e_3)
| ~ product(W_14,e_1,e_4) ),
inference(resolution,[status(thm)],[c_4257,c_60]) ).
tff(c_9261,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_9256,c_4342]) ).
tff(c_9307,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_38,c_9261]) ).
tff(c_9308,plain,
( product(e_4,e_2,e_3)
| product(e_4,e_2,e_2) ),
inference(splitRight,[status(thm)],[c_9254]) ).
tff(c_9534,plain,
product(e_4,e_2,e_2),
inference(splitLeft,[status(thm)],[c_9308]) ).
tff(c_6791,plain,
! [Y_221] :
( product(e_4,Y_221,e_2)
| ~ product(Y_221,e_1,e_4) ),
inference(resolution,[status(thm)],[c_6557,c_62]) ).
tff(c_6800,plain,
product(e_4,e_3,e_2),
inference(resolution,[status(thm)],[c_4257,c_6791]) ).
tff(c_6855,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product(e_4,W_11,e_2) ),
inference(resolution,[status(thm)],[c_6800,c_58]) ).
tff(c_9543,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_9534,c_6855]) ).
tff(c_9581,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_38,c_9543]) ).
tff(c_9582,plain,
product(e_4,e_2,e_3),
inference(splitRight,[status(thm)],[c_9308]) ).
tff(c_10076,plain,
! [Y_261] :
( product(e_2,Y_261,e_3)
| ~ product(Y_261,e_4,e_2) ),
inference(resolution,[status(thm)],[c_9582,c_62]) ).
tff(c_10089,plain,
product(e_2,e_1,e_3),
inference(resolution,[status(thm)],[c_6557,c_10076]) ).
tff(c_3612,plain,
! [Y_18] :
( product(e_3,Y_18,e_3)
| ~ product(Y_18,e_1,e_3) ),
inference(resolution,[status(thm)],[c_3538,c_62]) ).
tff(c_10163,plain,
product(e_3,e_2,e_3),
inference(resolution,[status(thm)],[c_10089,c_3612]) ).
tff(c_9876,plain,
! [W_14] :
( equalish(W_14,e_4)
| ~ product(W_14,e_2,e_3) ),
inference(resolution,[status(thm)],[c_9582,c_60]) ).
tff(c_10224,plain,
equalish(e_3,e_4),
inference(resolution,[status(thm)],[c_10163,c_9876]) ).
tff(c_10262,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_10224]) ).
tff(c_10263,plain,
product(e_1,e_4,e_3),
inference(splitRight,[status(thm)],[c_6497]) ).
tff(c_3613,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product(e_1,W_11,e_3) ),
inference(resolution,[status(thm)],[c_3538,c_58]) ).
tff(c_10271,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_10263,c_3613]) ).
tff(c_10312,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_10271]) ).
tff(c_10313,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(splitRight,[status(thm)],[c_4255]) ).
tff(c_10321,plain,
product(e_3,e_3,e_2),
inference(splitLeft,[status(thm)],[c_10313]) ).
tff(c_10458,plain,
! [Y_268] :
( product(e_3,Y_268,e_2)
| ~ product(Y_268,e_3,e_3) ),
inference(resolution,[status(thm)],[c_10321,c_62]) ).
tff(c_10482,plain,
product(e_3,e_1,e_2),
inference(resolution,[status(thm)],[c_3538,c_10458]) ).
tff(c_10370,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product(e_3,W_11,e_2) ),
inference(resolution,[status(thm)],[c_10321,c_58]) ).
tff(c_10506,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_10482,c_10370]) ).
tff(c_10545,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_10506]) ).
tff(c_10546,plain,
product(e_3,e_3,e_3),
inference(splitRight,[status(thm)],[c_10313]) ).
tff(c_3614,plain,
! [W_14] :
( equalish(W_14,e_1)
| ~ product(W_14,e_3,e_3) ),
inference(resolution,[status(thm)],[c_3538,c_60]) ).
tff(c_10550,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_10546,c_3614]) ).
tff(c_10584,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_42,c_10550]) ).
tff(c_10585,plain,
! [X_47] :
( product(e_1,e_3,e_2)
| product(e_3,X_47,e_4)
| ~ next(X_47,e_3)
| product(X_47,e_1,e_2)
| product(X_47,e_1,e_1)
| ~ group_element(X_47) ),
inference(splitRight,[status(thm)],[c_3432]) ).
tff(c_10630,plain,
product(e_1,e_3,e_2),
inference(splitLeft,[status(thm)],[c_10585]) ).
tff(c_10642,plain,
( product(e_2,e_1,e_4)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_10630,c_113]) ).
tff(c_10675,plain,
( product(e_2,e_1,e_4)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_24,c_10642]) ).
tff(c_10874,plain,
product(e_3,e_2,e_1),
inference(splitLeft,[status(thm)],[c_10675]) ).
tff(c_11130,plain,
! [Y_276] :
( product(e_2,Y_276,e_1)
| ~ product(Y_276,e_3,e_2) ),
inference(resolution,[status(thm)],[c_10874,c_62]) ).
tff(c_11133,plain,
product(e_2,e_1,e_1),
inference(resolution,[status(thm)],[c_10630,c_11130]) ).
tff(c_11152,plain,
equalish(e_2,e_1),
inference(resolution,[status(thm)],[c_11133,c_1186]) ).
tff(c_11209,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_36,c_11152]) ).
tff(c_11210,plain,
( product(e_3,e_2,e_2)
| product(e_3,e_2,e_3)
| product(e_2,e_1,e_4) ),
inference(splitRight,[status(thm)],[c_10675]) ).
tff(c_11212,plain,
product(e_2,e_1,e_4),
inference(splitLeft,[status(thm)],[c_11210]) ).
tff(c_11248,plain,
~ next(e_2,e_3),
inference(resolution,[status(thm)],[c_11212,c_79]) ).
tff(c_11302,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_11248]) ).
tff(c_11303,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_2) ),
inference(splitRight,[status(thm)],[c_11210]) ).
tff(c_11312,plain,
product(e_3,e_2,e_2),
inference(splitLeft,[status(thm)],[c_11303]) ).
tff(c_11322,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_11312,c_113]) ).
tff(c_11351,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_11322]) ).
tff(c_14162,plain,
product(e_2,e_2,e_1),
inference(splitLeft,[status(thm)],[c_11351]) ).
tff(c_11448,plain,
! [Y_280] :
( product(e_2,Y_280,e_2)
| ~ product(Y_280,e_3,e_2) ),
inference(resolution,[status(thm)],[c_11312,c_62]) ).
tff(c_11451,plain,
product(e_2,e_1,e_2),
inference(resolution,[status(thm)],[c_10630,c_11448]) ).
tff(c_11526,plain,
! [Y_18] :
( product(e_1,Y_18,e_2)
| ~ product(Y_18,e_2,e_1) ),
inference(resolution,[status(thm)],[c_11451,c_62]) ).
tff(c_14225,plain,
product(e_1,e_2,e_2),
inference(resolution,[status(thm)],[c_14162,c_11526]) ).
tff(c_11362,plain,
! [W_14] :
( equalish(W_14,e_3)
| ~ product(W_14,e_2,e_2) ),
inference(resolution,[status(thm)],[c_11312,c_60]) ).
tff(c_14311,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_14225,c_11362]) ).
tff(c_14350,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_14311]) ).
tff(c_14351,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_3,e_4) ),
inference(splitRight,[status(thm)],[c_11351]) ).
tff(c_14353,plain,
product(e_2,e_3,e_4),
inference(splitLeft,[status(thm)],[c_14351]) ).
tff(c_50,plain,
~ equalish(e_4,e_2),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_14448,plain,
( product(e_4,e_2,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_14353,c_113]) ).
tff(c_14479,plain,
( product(e_4,e_2,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_28,c_14448]) ).
tff(c_14679,plain,
product(e_3,e_4,e_1),
inference(splitLeft,[status(thm)],[c_14479]) ).
tff(c_15008,plain,
! [Y_341] :
( product(e_4,Y_341,e_1)
| ~ product(Y_341,e_3,e_4) ),
inference(resolution,[status(thm)],[c_14679,c_62]) ).
tff(c_15017,plain,
product(e_4,e_2,e_1),
inference(resolution,[status(thm)],[c_14353,c_15008]) ).
tff(c_15097,plain,
product(e_1,e_4,e_2),
inference(resolution,[status(thm)],[c_15017,c_11526]) ).
tff(c_10685,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product(e_1,W_11,e_2) ),
inference(resolution,[status(thm)],[c_10630,c_58]) ).
tff(c_15154,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_15097,c_10685]) ).
tff(c_15194,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_15154]) ).
tff(c_15195,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_4,e_3)
| product(e_4,e_2,e_4) ),
inference(splitRight,[status(thm)],[c_14479]) ).
tff(c_15228,plain,
product(e_4,e_2,e_4),
inference(splitLeft,[status(thm)],[c_15195]) ).
tff(c_15240,plain,
( product(e_4,e_4,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_15228,c_113]) ).
tff(c_15274,plain,
( product(e_4,e_4,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_28,c_15240]) ).
tff(c_15396,plain,
product(e_2,e_4,e_1),
inference(splitLeft,[status(thm)],[c_15274]) ).
tff(c_15740,plain,
! [Y_355] :
( product(e_4,Y_355,e_1)
| ~ product(Y_355,e_2,e_4) ),
inference(resolution,[status(thm)],[c_15396,c_62]) ).
tff(c_15749,plain,
product(e_4,e_4,e_1),
inference(resolution,[status(thm)],[c_15228,c_15740]) ).
tff(c_15513,plain,
! [W_14] :
( equalish(W_14,e_2)
| ~ product(W_14,e_4,e_1) ),
inference(resolution,[status(thm)],[c_15396,c_60]) ).
tff(c_15851,plain,
equalish(e_4,e_2),
inference(resolution,[status(thm)],[c_15749,c_15513]) ).
tff(c_15909,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_50,c_15851]) ).
tff(c_15910,plain,
( product(e_2,e_4,e_2)
| product(e_2,e_4,e_3)
| product(e_4,e_4,e_4) ),
inference(splitRight,[status(thm)],[c_15274]) ).
tff(c_15912,plain,
product(e_4,e_4,e_4),
inference(splitLeft,[status(thm)],[c_15910]) ).
tff(c_15285,plain,
! [W_11] :
( equalish(W_11,e_2)
| ~ product(e_4,W_11,e_4) ),
inference(resolution,[status(thm)],[c_15228,c_58]) ).
tff(c_15915,plain,
equalish(e_4,e_2),
inference(resolution,[status(thm)],[c_15912,c_15285]) ).
tff(c_15947,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_50,c_15915]) ).
tff(c_15948,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_4,e_2) ),
inference(splitRight,[status(thm)],[c_15910]) ).
tff(c_15981,plain,
product(e_2,e_4,e_2),
inference(splitLeft,[status(thm)],[c_15948]) ).
tff(c_11527,plain,
! [W_11] :
( equalish(W_11,e_1)
| ~ product(e_2,W_11,e_2) ),
inference(resolution,[status(thm)],[c_11451,c_58]) ).
tff(c_15988,plain,
equalish(e_4,e_1),
inference(resolution,[status(thm)],[c_15981,c_11527]) ).
tff(c_16019,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_48,c_15988]) ).
tff(c_16020,plain,
product(e_2,e_4,e_3),
inference(splitRight,[status(thm)],[c_15948]) ).
tff(c_16388,plain,
! [Y_366] :
( product(e_4,Y_366,e_3)
| ~ product(Y_366,e_2,e_4) ),
inference(resolution,[status(thm)],[c_16020,c_62]) ).
tff(c_16397,plain,
product(e_4,e_4,e_3),
inference(resolution,[status(thm)],[c_15228,c_16388]) ).
tff(c_16196,plain,
! [W_14] :
( equalish(W_14,e_2)
| ~ product(W_14,e_4,e_3) ),
inference(resolution,[status(thm)],[c_16020,c_60]) ).
tff(c_16445,plain,
equalish(e_4,e_2),
inference(resolution,[status(thm)],[c_16397,c_16196]) ).
tff(c_16492,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_50,c_16445]) ).
tff(c_16493,plain,
( product(e_3,e_4,e_3)
| product(e_3,e_4,e_2) ),
inference(splitRight,[status(thm)],[c_15195]) ).
tff(c_16507,plain,
product(e_3,e_4,e_2),
inference(splitLeft,[status(thm)],[c_16493]) ).
tff(c_11361,plain,
! [W_11] :
( equalish(W_11,e_2)
| ~ product(e_3,W_11,e_2) ),
inference(resolution,[status(thm)],[c_11312,c_58]) ).
tff(c_16597,plain,
equalish(e_4,e_2),
inference(resolution,[status(thm)],[c_16507,c_11361]) ).
tff(c_16627,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_50,c_16597]) ).
tff(c_16628,plain,
product(e_3,e_4,e_3),
inference(splitRight,[status(thm)],[c_16493]) ).
tff(c_17098,plain,
! [Y_378] :
( product(e_4,Y_378,e_3)
| ~ product(Y_378,e_3,e_4) ),
inference(resolution,[status(thm)],[c_16628,c_62]) ).
tff(c_17107,plain,
product(e_4,e_2,e_3),
inference(resolution,[status(thm)],[c_14353,c_17098]) ).
tff(c_14489,plain,
! [Y_18] :
( product(e_3,Y_18,e_4)
| ~ product(Y_18,e_2,e_3) ),
inference(resolution,[status(thm)],[c_14353,c_62]) ).
tff(c_17161,plain,
product(e_3,e_4,e_4),
inference(resolution,[status(thm)],[c_17107,c_14489]) ).
tff(c_56,plain,
! [W_8,Z_9,X_6,Y_7] :
( equalish(W_8,Z_9)
| ~ product(X_6,Y_7,Z_9)
| ~ product(X_6,Y_7,W_8) ),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_16720,plain,
! [W_8] :
( equalish(W_8,e_3)
| ~ product(e_3,e_4,W_8) ),
inference(resolution,[status(thm)],[c_16628,c_56]) ).
tff(c_17281,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_17161,c_16720]) ).
tff(c_17313,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_17281]) ).
tff(c_17314,plain,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2) ),
inference(splitRight,[status(thm)],[c_14351]) ).
tff(c_17322,plain,
product(e_2,e_2,e_2),
inference(splitLeft,[status(thm)],[c_17314]) ).
tff(c_17325,plain,
equalish(e_2,e_1),
inference(resolution,[status(thm)],[c_17322,c_11527]) ).
tff(c_17354,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_36,c_17325]) ).
tff(c_17355,plain,
product(e_2,e_2,e_3),
inference(splitRight,[status(thm)],[c_17314]) ).
tff(c_17654,plain,
! [Y_386] :
( product(e_2,Y_386,e_3)
| ~ product(Y_386,e_2,e_2) ),
inference(resolution,[status(thm)],[c_17355,c_62]) ).
tff(c_17657,plain,
product(e_2,e_3,e_3),
inference(resolution,[status(thm)],[c_11312,c_17654]) ).
tff(c_17430,plain,
! [W_11] :
( equalish(W_11,e_2)
| ~ product(e_2,W_11,e_3) ),
inference(resolution,[status(thm)],[c_17355,c_58]) ).
tff(c_17660,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[c_17657,c_17430]) ).
tff(c_17698,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_44,c_17660]) ).
tff(c_17700,plain,
~ product(e_3,e_2,e_2),
inference(splitRight,[status(thm)],[c_11303]) ).
tff(c_17699,plain,
product(e_3,e_2,e_3),
inference(splitRight,[status(thm)],[c_11303]) ).
tff(c_17957,plain,
! [Y_390] :
( product(e_2,Y_390,e_3)
| ~ product(Y_390,e_3,e_2) ),
inference(resolution,[status(thm)],[c_17699,c_62]) ).
tff(c_17960,plain,
product(e_2,e_1,e_3),
inference(resolution,[status(thm)],[c_10630,c_17957]) ).
tff(c_10684,plain,
! [Y_18] :
( product(e_3,Y_18,e_2)
| ~ product(Y_18,e_1,e_3) ),
inference(resolution,[status(thm)],[c_10630,c_62]) ).
tff(c_17962,plain,
product(e_3,e_2,e_2),
inference(resolution,[status(thm)],[c_17960,c_10684]) ).
tff(c_18012,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_17700,c_17962]) ).
tff(c_18014,plain,
~ product(e_1,e_3,e_2),
inference(splitRight,[status(thm)],[c_10585]) ).
tff(c_54,plain,
! [X_4,Y_5] :
( product(X_4,Y_5,e_4)
| product(X_4,Y_5,e_3)
| product(X_4,Y_5,e_2)
| product(X_4,Y_5,e_1)
| ~ group_element(Y_5)
| ~ group_element(X_4) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_258,plain,
! [W_63,Y_64,X_65] :
( equalish(W_63,Y_64)
| ~ product(X_65,W_63,e_4)
| product(X_65,Y_64,e_3)
| product(X_65,Y_64,e_2)
| product(X_65,Y_64,e_1)
| ~ group_element(Y_64)
| ~ group_element(X_65) ),
inference(resolution,[status(thm)],[c_92,c_58]) ).
tff(c_261,plain,
! [Y_5,Y_64,X_4] :
( equalish(Y_5,Y_64)
| product(X_4,Y_64,e_3)
| product(X_4,Y_64,e_2)
| product(X_4,Y_64,e_1)
| ~ group_element(Y_64)
| product(X_4,Y_5,e_3)
| product(X_4,Y_5,e_2)
| product(X_4,Y_5,e_1)
| ~ group_element(Y_5)
| ~ group_element(X_4) ),
inference(resolution,[status(thm)],[c_54,c_258]) ).
tff(c_10586,plain,
~ product(e_1,e_3,e_3),
inference(splitRight,[status(thm)],[c_3432]) ).
tff(c_10601,plain,
! [Y_5] :
( equalish(Y_5,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| ~ group_element(e_3)
| product(e_1,Y_5,e_3)
| product(e_1,Y_5,e_2)
| product(e_1,Y_5,e_1)
| ~ group_element(Y_5)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_261,c_10586]) ).
tff(c_10624,plain,
! [Y_5] :
( equalish(Y_5,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_1,Y_5,e_3)
| product(e_1,Y_5,e_2)
| product(e_1,Y_5,e_1)
| ~ group_element(Y_5) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_26,c_10601]) ).
tff(c_10625,plain,
! [Y_5] :
( equalish(Y_5,e_3)
| product(e_1,e_3,e_2)
| product(e_1,Y_5,e_3)
| product(e_1,Y_5,e_2)
| product(e_1,Y_5,e_1)
| ~ group_element(Y_5) ),
inference(negUnitSimplification,[status(thm)],[c_3433,c_10624]) ).
tff(c_18842,plain,
! [Y_413] :
( equalish(Y_413,e_3)
| product(e_1,Y_413,e_3)
| product(e_1,Y_413,e_2)
| product(e_1,Y_413,e_1)
| ~ group_element(Y_413) ),
inference(negUnitSimplification,[status(thm)],[c_18014,c_10625]) ).
tff(c_20505,plain,
! [Y_446,Y_447] :
( product(Y_446,Y_447,e_3)
| ~ product(Y_447,e_1,Y_446)
| equalish(Y_446,e_3)
| product(e_1,Y_446,e_2)
| product(e_1,Y_446,e_1)
| ~ group_element(Y_446) ),
inference(resolution,[status(thm)],[c_18842,c_62]) ).
tff(c_20575,plain,
! [X_62] :
( product(e_2,X_62,e_3)
| equalish(e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| ~ group_element(e_2)
| ~ next(X_62,e_2)
| product(X_62,e_1,e_1)
| ~ group_element(X_62) ),
inference(resolution,[status(thm)],[c_255,c_20505]) ).
tff(c_20683,plain,
! [X_62] :
( product(e_2,X_62,e_3)
| equalish(e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| ~ next(X_62,e_2)
| product(X_62,e_1,e_1)
| ~ group_element(X_62) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_20575]) ).
tff(c_20684,plain,
! [X_62] :
( product(e_2,X_62,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| ~ next(X_62,e_2)
| product(X_62,e_1,e_1)
| ~ group_element(X_62) ),
inference(negUnitSimplification,[status(thm)],[c_38,c_20683]) ).
tff(c_20881,plain,
product(e_1,e_2,e_1),
inference(splitLeft,[status(thm)],[c_20684]) ).
tff(c_20906,plain,
equalish(e_2,e_1),
inference(resolution,[status(thm)],[c_20881,c_1185]) ).
tff(c_20966,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_36,c_20906]) ).
tff(c_20968,plain,
~ product(e_1,e_2,e_1),
inference(splitRight,[status(thm)],[c_20684]) ).
tff(c_30,plain,
~ equalish(e_1,e_2),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_10604,plain,
! [Y_64] :
( equalish(e_3,Y_64)
| product(e_1,Y_64,e_3)
| product(e_1,Y_64,e_2)
| product(e_1,Y_64,e_1)
| ~ group_element(Y_64)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_261,c_10586]) ).
tff(c_10628,plain,
! [Y_64] :
( equalish(e_3,Y_64)
| product(e_1,Y_64,e_3)
| product(e_1,Y_64,e_2)
| product(e_1,Y_64,e_1)
| ~ group_element(Y_64)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_26,c_10604]) ).
tff(c_10629,plain,
! [Y_64] :
( equalish(e_3,Y_64)
| product(e_1,Y_64,e_3)
| product(e_1,Y_64,e_2)
| product(e_1,Y_64,e_1)
| ~ group_element(Y_64)
| product(e_1,e_3,e_2) ),
inference(negUnitSimplification,[status(thm)],[c_3433,c_10628]) ).
tff(c_19500,plain,
! [Y_425] :
( equalish(e_3,Y_425)
| product(e_1,Y_425,e_3)
| product(e_1,Y_425,e_2)
| product(e_1,Y_425,e_1)
| ~ group_element(Y_425) ),
inference(negUnitSimplification,[status(thm)],[c_18014,c_10629]) ).
tff(c_20693,plain,
! [Y_448,Y_449] :
( product(Y_448,Y_449,e_3)
| ~ product(Y_449,e_1,Y_448)
| equalish(e_3,Y_448)
| product(e_1,Y_448,e_2)
| product(e_1,Y_448,e_1)
| ~ group_element(Y_448) ),
inference(resolution,[status(thm)],[c_19500,c_62]) ).
tff(c_20763,plain,
! [X_62] :
( product(e_2,X_62,e_3)
| equalish(e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| ~ group_element(e_2)
| ~ next(X_62,e_2)
| product(X_62,e_1,e_1)
| ~ group_element(X_62) ),
inference(resolution,[status(thm)],[c_255,c_20693]) ).
tff(c_20871,plain,
! [X_62] :
( product(e_2,X_62,e_3)
| equalish(e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| ~ next(X_62,e_2)
| product(X_62,e_1,e_1)
| ~ group_element(X_62) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_20763]) ).
tff(c_20872,plain,
! [X_62] :
( product(e_2,X_62,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| ~ next(X_62,e_2)
| product(X_62,e_1,e_1)
| ~ group_element(X_62) ),
inference(negUnitSimplification,[status(thm)],[c_44,c_20871]) ).
tff(c_21060,plain,
! [X_62] :
( product(e_2,X_62,e_3)
| product(e_1,e_2,e_2)
| ~ next(X_62,e_2)
| product(X_62,e_1,e_1)
| ~ group_element(X_62) ),
inference(negUnitSimplification,[status(thm)],[c_20968,c_20872]) ).
tff(c_21061,plain,
product(e_1,e_2,e_2),
inference(splitLeft,[status(thm)],[c_21060]) ).
tff(c_21079,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_21061,c_113]) ).
tff(c_21124,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_21079]) ).
tff(c_22244,plain,
product(e_2,e_2,e_1),
inference(splitLeft,[status(thm)],[c_21124]) ).
tff(c_22735,plain,
! [Y_475] :
( product(e_2,Y_475,e_1)
| ~ product(Y_475,e_2,e_2) ),
inference(resolution,[status(thm)],[c_22244,c_62]) ).
tff(c_22758,plain,
product(e_2,e_1,e_1),
inference(resolution,[status(thm)],[c_21061,c_22735]) ).
tff(c_22534,plain,
! [W_11] :
( equalish(W_11,e_2)
| ~ product(e_2,W_11,e_1) ),
inference(resolution,[status(thm)],[c_22244,c_58]) ).
tff(c_22761,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[c_22758,c_22534]) ).
tff(c_22825,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_30,c_22761]) ).
tff(c_22826,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_1,e_4) ),
inference(splitRight,[status(thm)],[c_21124]) ).
tff(c_22828,plain,
product(e_2,e_1,e_4),
inference(splitLeft,[status(thm)],[c_22826]) ).
tff(c_22875,plain,
~ next(e_2,e_3),
inference(resolution,[status(thm)],[c_22828,c_79]) ).
tff(c_22949,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_22875]) ).
tff(c_22950,plain,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2) ),
inference(splitRight,[status(thm)],[c_22826]) ).
tff(c_23153,plain,
product(e_2,e_2,e_2),
inference(splitLeft,[status(thm)],[c_22950]) ).
tff(c_21135,plain,
! [W_14] :
( equalish(W_14,e_1)
| ~ product(W_14,e_2,e_2) ),
inference(resolution,[status(thm)],[c_21061,c_60]) ).
tff(c_23166,plain,
equalish(e_2,e_1),
inference(resolution,[status(thm)],[c_23153,c_21135]) ).
tff(c_23207,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_36,c_23166]) ).
tff(c_23209,plain,
~ product(e_2,e_2,e_2),
inference(splitRight,[status(thm)],[c_22950]) ).
tff(c_23208,plain,
product(e_2,e_2,e_3),
inference(splitRight,[status(thm)],[c_22950]) ).
tff(c_199,plain,
! [X_60] :
( ~ next(X_60,e_3)
| product(X_60,e_1,e_3)
| product(X_60,e_1,e_2)
| product(X_60,e_1,e_1)
| ~ group_element(X_60) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_106]) ).
tff(c_215,plain,
! [W_11,X_60] :
( equalish(W_11,e_1)
| ~ product(X_60,W_11,e_3)
| ~ next(X_60,e_3)
| product(X_60,e_1,e_2)
| product(X_60,e_1,e_1)
| ~ group_element(X_60) ),
inference(resolution,[status(thm)],[c_199,c_58]) ).
tff(c_23435,plain,
( equalish(e_2,e_1)
| ~ next(e_2,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_23208,c_215]) ).
tff(c_23511,plain,
( equalish(e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_4,c_23435]) ).
tff(c_23512,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_36,c_23511]) ).
tff(c_23833,plain,
product(e_2,e_1,e_1),
inference(splitLeft,[status(thm)],[c_23512]) ).
tff(c_1184,plain,
! [Y_18] :
( product(e_1,Y_18,e_1)
| ~ product(Y_18,e_1,e_1) ),
inference(resolution,[status(thm)],[c_1124,c_62]) ).
tff(c_23864,plain,
product(e_1,e_2,e_1),
inference(resolution,[status(thm)],[c_23833,c_1184]) ).
tff(c_23951,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20968,c_23864]) ).
tff(c_23952,plain,
product(e_2,e_1,e_2),
inference(splitRight,[status(thm)],[c_23512]) ).
tff(c_21133,plain,
! [Y_18] :
( product(e_2,Y_18,e_2)
| ~ product(Y_18,e_1,e_2) ),
inference(resolution,[status(thm)],[c_21061,c_62]) ).
tff(c_24023,plain,
product(e_2,e_2,e_2),
inference(resolution,[status(thm)],[c_23952,c_21133]) ).
tff(c_24087,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_23209,c_24023]) ).
tff(c_24089,plain,
~ product(e_1,e_2,e_2),
inference(splitRight,[status(thm)],[c_21060]) ).
tff(c_19499,plain,
! [Y_64] :
( equalish(e_3,Y_64)
| product(e_1,Y_64,e_3)
| product(e_1,Y_64,e_2)
| product(e_1,Y_64,e_1)
| ~ group_element(Y_64) ),
inference(negUnitSimplification,[status(thm)],[c_18014,c_10629]) ).
tff(c_24090,plain,
! [X_488] :
( product(e_2,X_488,e_3)
| ~ next(X_488,e_2)
| product(X_488,e_1,e_1)
| ~ group_element(X_488) ),
inference(splitRight,[status(thm)],[c_21060]) ).
tff(c_195,plain,
! [W_57,X_58,Y_59] :
( equalish(W_57,X_58)
| ~ product(W_57,Y_59,e_4)
| product(X_58,Y_59,e_3)
| product(X_58,Y_59,e_2)
| product(X_58,Y_59,e_1)
| ~ group_element(Y_59)
| ~ group_element(X_58) ),
inference(resolution,[status(thm)],[c_92,c_60]) ).
tff(c_198,plain,
! [X_4,X_58,Y_5] :
( equalish(X_4,X_58)
| product(X_58,Y_5,e_3)
| product(X_58,Y_5,e_2)
| product(X_58,Y_5,e_1)
| ~ group_element(X_58)
| product(X_4,Y_5,e_3)
| product(X_4,Y_5,e_2)
| product(X_4,Y_5,e_1)
| ~ group_element(Y_5)
| ~ group_element(X_4) ),
inference(resolution,[status(thm)],[c_54,c_195]) ).
tff(c_10595,plain,
! [X_58] :
( equalish(e_1,X_58)
| product(X_58,e_3,e_3)
| product(X_58,e_3,e_2)
| product(X_58,e_3,e_1)
| ~ group_element(X_58)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_198,c_10586]) ).
tff(c_10616,plain,
! [X_58] :
( equalish(e_1,X_58)
| product(X_58,e_3,e_3)
| product(X_58,e_3,e_2)
| product(X_58,e_3,e_1)
| ~ group_element(X_58)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_26,c_10595]) ).
tff(c_10617,plain,
! [X_58] :
( equalish(e_1,X_58)
| product(X_58,e_3,e_3)
| product(X_58,e_3,e_2)
| product(X_58,e_3,e_1)
| ~ group_element(X_58)
| product(e_1,e_3,e_2) ),
inference(negUnitSimplification,[status(thm)],[c_3433,c_10616]) ).
tff(c_18502,plain,
! [X_404] :
( equalish(e_1,X_404)
| product(X_404,e_3,e_3)
| product(X_404,e_3,e_2)
| product(X_404,e_3,e_1)
| ~ group_element(X_404) ),
inference(negUnitSimplification,[status(thm)],[c_18014,c_10617]) ).
tff(c_18585,plain,
! [W_11,X_404] :
( equalish(W_11,e_3)
| ~ product(X_404,W_11,e_3)
| equalish(e_1,X_404)
| product(X_404,e_3,e_2)
| product(X_404,e_3,e_1)
| ~ group_element(X_404) ),
inference(resolution,[status(thm)],[c_18502,c_58]) ).
tff(c_24116,plain,
! [X_488] :
( equalish(X_488,e_3)
| equalish(e_1,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| ~ group_element(e_2)
| ~ next(X_488,e_2)
| product(X_488,e_1,e_1)
| ~ group_element(X_488) ),
inference(resolution,[status(thm)],[c_24090,c_18585]) ).
tff(c_24265,plain,
! [X_488] :
( equalish(X_488,e_3)
| equalish(e_1,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| ~ next(X_488,e_2)
| product(X_488,e_1,e_1)
| ~ group_element(X_488) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_24116]) ).
tff(c_24266,plain,
! [X_488] :
( equalish(X_488,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| ~ next(X_488,e_2)
| product(X_488,e_1,e_1)
| ~ group_element(X_488) ),
inference(negUnitSimplification,[status(thm)],[c_30,c_24265]) ).
tff(c_29252,plain,
product(e_2,e_3,e_1),
inference(splitLeft,[status(thm)],[c_24266]) ).
tff(c_29647,plain,
! [Y_581] :
( product(e_3,Y_581,e_1)
| ~ product(Y_581,e_2,e_3) ),
inference(resolution,[status(thm)],[c_29252,c_62]) ).
tff(c_29656,plain,
( product(e_3,e_1,e_1)
| equalish(e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_19499,c_29647]) ).
tff(c_29691,plain,
( product(e_3,e_1,e_1)
| equalish(e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_29656]) ).
tff(c_29692,plain,
product(e_3,e_1,e_1),
inference(negUnitSimplification,[status(thm)],[c_20968,c_24089,c_44,c_29691]) ).
tff(c_29755,plain,
product(e_1,e_3,e_1),
inference(resolution,[status(thm)],[c_29692,c_1184]) ).
tff(c_29856,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3433,c_29755]) ).
tff(c_29858,plain,
~ product(e_2,e_3,e_1),
inference(splitRight,[status(thm)],[c_24266]) ).
tff(c_25447,plain,
! [W_504,X_505] :
( equalish(W_504,X_505)
| ~ product(W_504,e_1,e_1)
| product(e_2,X_505,e_3)
| ~ next(X_505,e_2)
| ~ group_element(X_505) ),
inference(resolution,[status(thm)],[c_24090,c_60]) ).
tff(c_25511,plain,
! [X_506] :
( equalish(e_1,X_506)
| product(e_2,X_506,e_3)
| ~ next(X_506,e_2)
| ~ group_element(X_506) ),
inference(resolution,[status(thm)],[c_1124,c_25447]) ).
tff(c_25935,plain,
! [W_510,X_511] :
( equalish(W_510,X_511)
| ~ product(e_2,W_510,e_3)
| equalish(e_1,X_511)
| ~ next(X_511,e_2)
| ~ group_element(X_511) ),
inference(resolution,[status(thm)],[c_25511,c_58]) ).
tff(c_25974,plain,
! [X_511] :
( equalish(e_1,X_511)
| ~ next(X_511,e_2)
| ~ group_element(X_511)
| ~ next(e_2,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_121,c_25935]) ).
tff(c_26010,plain,
! [X_511] :
( equalish(e_1,X_511)
| ~ next(X_511,e_2)
| ~ group_element(X_511)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_4,c_25974]) ).
tff(c_26746,plain,
product(e_2,e_1,e_1),
inference(splitLeft,[status(thm)],[c_26010]) ).
tff(c_26786,plain,
product(e_1,e_2,e_1),
inference(resolution,[status(thm)],[c_26746,c_1184]) ).
tff(c_26885,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20968,c_26786]) ).
tff(c_26887,plain,
~ product(e_2,e_1,e_1),
inference(splitRight,[status(thm)],[c_26010]) ).
tff(c_26886,plain,
! [X_511] :
( product(e_2,e_1,e_2)
| equalish(e_1,X_511)
| ~ next(X_511,e_2)
| ~ group_element(X_511) ),
inference(splitRight,[status(thm)],[c_26010]) ).
tff(c_26983,plain,
product(e_2,e_1,e_2),
inference(splitLeft,[status(thm)],[c_26886]) ).
tff(c_19668,plain,
! [Y_425,Y_18] :
( product(Y_425,Y_18,e_3)
| ~ product(Y_18,e_1,Y_425)
| equalish(e_3,Y_425)
| product(e_1,Y_425,e_2)
| product(e_1,Y_425,e_1)
| ~ group_element(Y_425) ),
inference(resolution,[status(thm)],[c_19500,c_62]) ).
tff(c_26997,plain,
( product(e_2,e_2,e_3)
| equalish(e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_26983,c_19668]) ).
tff(c_27063,plain,
( product(e_2,e_2,e_3)
| equalish(e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_26997]) ).
tff(c_27064,plain,
product(e_2,e_2,e_3),
inference(negUnitSimplification,[status(thm)],[c_20968,c_24089,c_44,c_27063]) ).
tff(c_19670,plain,
! [W_14,Y_425] :
( equalish(W_14,e_1)
| ~ product(W_14,Y_425,e_3)
| equalish(e_3,Y_425)
| product(e_1,Y_425,e_2)
| product(e_1,Y_425,e_1)
| ~ group_element(Y_425) ),
inference(resolution,[status(thm)],[c_19500,c_60]) ).
tff(c_27164,plain,
( equalish(e_2,e_1)
| equalish(e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_27064,c_19670]) ).
tff(c_27253,plain,
( equalish(e_2,e_1)
| equalish(e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_27164]) ).
tff(c_27255,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20968,c_24089,c_44,c_36,c_27253]) ).
tff(c_27257,plain,
~ product(e_2,e_1,e_2),
inference(splitRight,[status(thm)],[c_26886]) ).
tff(c_18529,plain,
! [X_404] :
( equalish(e_3,e_1)
| ~ next(X_404,e_3)
| product(X_404,e_1,e_2)
| product(X_404,e_1,e_1)
| equalish(e_1,X_404)
| product(X_404,e_3,e_2)
| product(X_404,e_3,e_1)
| ~ group_element(X_404) ),
inference(resolution,[status(thm)],[c_18502,c_215]) ).
tff(c_37516,plain,
! [X_718] :
( ~ next(X_718,e_3)
| product(X_718,e_1,e_2)
| product(X_718,e_1,e_1)
| equalish(e_1,X_718)
| product(X_718,e_3,e_2)
| product(X_718,e_3,e_1)
| ~ group_element(X_718) ),
inference(negUnitSimplification,[status(thm)],[c_42,c_18529]) ).
tff(c_10592,plain,
! [X_4] :
( equalish(X_4,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| ~ group_element(e_1)
| product(X_4,e_3,e_3)
| product(X_4,e_3,e_2)
| product(X_4,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X_4) ),
inference(resolution,[status(thm)],[c_198,c_10586]) ).
tff(c_10612,plain,
! [X_4] :
( equalish(X_4,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(X_4,e_3,e_3)
| product(X_4,e_3,e_2)
| product(X_4,e_3,e_1)
| ~ group_element(X_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_22,c_10592]) ).
tff(c_10613,plain,
! [X_4] :
( equalish(X_4,e_1)
| product(e_1,e_3,e_2)
| product(X_4,e_3,e_3)
| product(X_4,e_3,e_2)
| product(X_4,e_3,e_1)
| ~ group_element(X_4) ),
inference(negUnitSimplification,[status(thm)],[c_3433,c_10612]) ).
tff(c_19942,plain,
! [X_432] :
( equalish(X_432,e_1)
| product(X_432,e_3,e_3)
| product(X_432,e_3,e_2)
| product(X_432,e_3,e_1)
| ~ group_element(X_432) ),
inference(negUnitSimplification,[status(thm)],[c_18014,c_10613]) ).
tff(c_20088,plain,
! [W_11,X_432] :
( equalish(W_11,e_3)
| ~ product(X_432,W_11,e_3)
| equalish(X_432,e_1)
| product(X_432,e_3,e_2)
| product(X_432,e_3,e_1)
| ~ group_element(X_432) ),
inference(resolution,[status(thm)],[c_19942,c_58]) ).
tff(c_24107,plain,
! [X_488] :
( equalish(X_488,e_3)
| equalish(e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| ~ group_element(e_2)
| ~ next(X_488,e_2)
| product(X_488,e_1,e_1)
| ~ group_element(X_488) ),
inference(resolution,[status(thm)],[c_24090,c_20088]) ).
tff(c_24255,plain,
! [X_488] :
( equalish(X_488,e_3)
| equalish(e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| ~ next(X_488,e_2)
| product(X_488,e_1,e_1)
| ~ group_element(X_488) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_24107]) ).
tff(c_24256,plain,
! [X_488] :
( equalish(X_488,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| ~ next(X_488,e_2)
| product(X_488,e_1,e_1)
| ~ group_element(X_488) ),
inference(negUnitSimplification,[status(thm)],[c_36,c_24255]) ).
tff(c_29859,plain,
! [X_488] :
( equalish(X_488,e_3)
| product(e_2,e_3,e_2)
| ~ next(X_488,e_2)
| product(X_488,e_1,e_1)
| ~ group_element(X_488) ),
inference(negUnitSimplification,[status(thm)],[c_29858,c_24256]) ).
tff(c_29860,plain,
product(e_2,e_3,e_2),
inference(splitLeft,[status(thm)],[c_29859]) ).
tff(c_18015,plain,
! [X_391] :
( product(e_3,X_391,e_4)
| ~ next(X_391,e_3)
| product(X_391,e_1,e_2)
| product(X_391,e_1,e_1)
| ~ group_element(X_391) ),
inference(splitRight,[status(thm)],[c_10585]) ).
tff(c_18141,plain,
! [X_391,Y_18] :
( product(X_391,Y_18,e_4)
| ~ product(Y_18,e_3,X_391)
| ~ next(X_391,e_3)
| product(X_391,e_1,e_2)
| product(X_391,e_1,e_1)
| ~ group_element(X_391) ),
inference(resolution,[status(thm)],[c_18015,c_62]) ).
tff(c_29877,plain,
( product(e_2,e_2,e_4)
| ~ next(e_2,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_29860,c_18141]) ).
tff(c_29934,plain,
( product(e_2,e_2,e_4)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_4,c_29877]) ).
tff(c_29935,plain,
product(e_2,e_2,e_4),
inference(negUnitSimplification,[status(thm)],[c_26887,c_27257,c_29934]) ).
tff(c_18143,plain,
! [W_14,X_391] :
( equalish(W_14,e_3)
| ~ product(W_14,X_391,e_4)
| ~ next(X_391,e_3)
| product(X_391,e_1,e_2)
| product(X_391,e_1,e_1)
| ~ group_element(X_391) ),
inference(resolution,[status(thm)],[c_18015,c_60]) ).
tff(c_29989,plain,
( equalish(e_2,e_3)
| ~ next(e_2,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_29935,c_18143]) ).
tff(c_30042,plain,
( equalish(e_2,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_4,c_29989]) ).
tff(c_30044,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_26887,c_27257,c_38,c_30042]) ).
tff(c_30046,plain,
~ product(e_2,e_3,e_2),
inference(splitRight,[status(thm)],[c_29859]) ).
tff(c_37535,plain,
( ~ next(e_2,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_2,e_3,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_37516,c_30046]) ).
tff(c_37617,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_2,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_4,c_37535]) ).
tff(c_37619,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_29858,c_30,c_26887,c_27257,c_37617]) ).
tff(c_37621,plain,
~ product(e_1,e_1,e_1),
inference(splitRight,[status(thm)],[c_856]) ).
tff(c_38628,plain,
product(e_1,e_3,e_1),
inference(splitLeft,[status(thm)],[c_350]) ).
tff(c_38638,plain,
( product(e_1,e_1,e_4)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_38628,c_113]) ).
tff(c_38668,plain,
( product(e_1,e_1,e_4)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_22,c_38638]) ).
tff(c_38837,plain,
product(e_3,e_1,e_1),
inference(splitLeft,[status(thm)],[c_38668]) ).
tff(c_38855,plain,
( product(e_1,e_3,e_2)
| ~ next(e_1,e_2)
| product(e_1,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_38837,c_274]) ).
tff(c_38895,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_2,c_38855]) ).
tff(c_38896,plain,
product(e_1,e_3,e_2),
inference(negUnitSimplification,[status(thm)],[c_37621,c_38895]) ).
tff(c_38679,plain,
! [W_8] :
( equalish(W_8,e_1)
| ~ product(e_1,e_3,W_8) ),
inference(resolution,[status(thm)],[c_38628,c_56]) ).
tff(c_38938,plain,
equalish(e_2,e_1),
inference(resolution,[status(thm)],[c_38896,c_38679]) ).
tff(c_38962,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_36,c_38938]) ).
tff(c_38964,plain,
~ product(e_3,e_1,e_1),
inference(splitRight,[status(thm)],[c_38668]) ).
tff(c_38963,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_1,e_1,e_4) ),
inference(splitRight,[status(thm)],[c_38668]) ).
tff(c_38983,plain,
product(e_1,e_1,e_4),
inference(splitLeft,[status(thm)],[c_38963]) ).
tff(c_277,plain,
! [W_8,X_66] :
( equalish(W_8,e_2)
| ~ product(X_66,e_1,W_8)
| ~ next(X_66,e_2)
| product(X_66,e_1,e_1)
| ~ group_element(X_66) ),
inference(resolution,[status(thm)],[c_262,c_56]) ).
tff(c_38997,plain,
( equalish(e_4,e_2)
| ~ next(e_1,e_2)
| product(e_1,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_38983,c_277]) ).
tff(c_39043,plain,
( equalish(e_4,e_2)
| product(e_1,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_2,c_38997]) ).
tff(c_39045,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_37621,c_50,c_39043]) ).
tff(c_39047,plain,
~ product(e_1,e_1,e_4),
inference(splitRight,[status(thm)],[c_38963]) ).
tff(c_39050,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_54,c_39047]) ).
tff(c_39053,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_39050]) ).
tff(c_39054,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_1,e_2) ),
inference(negUnitSimplification,[status(thm)],[c_37621,c_39053]) ).
tff(c_39265,plain,
product(e_1,e_1,e_2),
inference(splitLeft,[status(thm)],[c_39054]) ).
tff(c_39046,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2) ),
inference(splitRight,[status(thm)],[c_38963]) ).
tff(c_39063,plain,
product(e_3,e_1,e_2),
inference(splitLeft,[status(thm)],[c_39046]) ).
tff(c_39126,plain,
! [W_14] :
( equalish(W_14,e_3)
| ~ product(W_14,e_1,e_2) ),
inference(resolution,[status(thm)],[c_39063,c_60]) ).
tff(c_39268,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_39265,c_39126]) ).
tff(c_39305,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_39268]) ).
tff(c_39306,plain,
product(e_1,e_1,e_3),
inference(splitRight,[status(thm)],[c_39054]) ).
tff(c_38676,plain,
! [Y_18] :
( product(e_3,Y_18,e_1)
| ~ product(Y_18,e_1,e_3) ),
inference(resolution,[status(thm)],[c_38628,c_62]) ).
tff(c_39309,plain,
product(e_3,e_1,e_1),
inference(resolution,[status(thm)],[c_39306,c_38676]) ).
tff(c_39347,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_38964,c_39309]) ).
tff(c_39348,plain,
product(e_3,e_1,e_3),
inference(splitRight,[status(thm)],[c_39046]) ).
tff(c_39417,plain,
product(e_3,e_3,e_1),
inference(resolution,[status(thm)],[c_39348,c_38676]) ).
tff(c_38678,plain,
! [W_14] :
( equalish(W_14,e_1)
| ~ product(W_14,e_3,e_1) ),
inference(resolution,[status(thm)],[c_38628,c_60]) ).
tff(c_39528,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_39417,c_38678]) ).
tff(c_39552,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_42,c_39528]) ).
tff(c_39553,plain,
! [X_47] :
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_3,X_47,e_4)
| ~ next(X_47,e_3)
| product(X_47,e_1,e_2)
| product(X_47,e_1,e_1)
| ~ group_element(X_47) ),
inference(splitRight,[status(thm)],[c_350]) ).
tff(c_39555,plain,
product(e_1,e_3,e_3),
inference(splitLeft,[status(thm)],[c_39553]) ).
tff(c_39563,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_39555,c_113]) ).
tff(c_39587,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_39563]) ).
tff(c_39835,plain,
product(e_3,e_3,e_1),
inference(splitLeft,[status(thm)],[c_39587]) ).
tff(c_39982,plain,
! [Y_777] :
( product(e_3,Y_777,e_1)
| ~ product(Y_777,e_3,e_3) ),
inference(resolution,[status(thm)],[c_39835,c_62]) ).
tff(c_40006,plain,
product(e_3,e_1,e_1),
inference(resolution,[status(thm)],[c_39555,c_39982]) ).
tff(c_39878,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product(e_3,W_11,e_1) ),
inference(resolution,[status(thm)],[c_39835,c_58]) ).
tff(c_40030,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_40006,c_39878]) ).
tff(c_40064,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_40030]) ).
tff(c_40065,plain,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_3)
| product(e_3,e_1,e_4) ),
inference(splitRight,[status(thm)],[c_39587]) ).
tff(c_40067,plain,
product(e_3,e_1,e_4),
inference(splitLeft,[status(thm)],[c_40065]) ).
tff(c_40073,plain,
( product(e_4,e_3,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_40067,c_113]) ).
tff(c_40110,plain,
( product(e_4,e_3,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_28,c_40073]) ).
tff(c_40365,plain,
product(e_1,e_4,e_1),
inference(splitLeft,[status(thm)],[c_40110]) ).
tff(c_40533,plain,
! [Y_788] :
( product(e_4,Y_788,e_1)
| ~ product(Y_788,e_1,e_4) ),
inference(resolution,[status(thm)],[c_40365,c_62]) ).
tff(c_40542,plain,
product(e_4,e_3,e_1),
inference(resolution,[status(thm)],[c_40067,c_40533]) ).
tff(c_40128,plain,
! [Y_18] :
( product(e_1,Y_18,e_4)
| ~ product(Y_18,e_3,e_1) ),
inference(resolution,[status(thm)],[c_40067,c_62]) ).
tff(c_40577,plain,
product(e_1,e_4,e_4),
inference(resolution,[status(thm)],[c_40542,c_40128]) ).
tff(c_40422,plain,
! [W_8] :
( equalish(W_8,e_1)
| ~ product(e_1,e_4,W_8) ),
inference(resolution,[status(thm)],[c_40365,c_56]) ).
tff(c_40604,plain,
equalish(e_4,e_1),
inference(resolution,[status(thm)],[c_40577,c_40422]) ).
tff(c_40628,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_48,c_40604]) ).
tff(c_40629,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_4,e_3,e_4) ),
inference(splitRight,[status(thm)],[c_40110]) ).
tff(c_40699,plain,
product(e_4,e_3,e_4),
inference(splitLeft,[status(thm)],[c_40629]) ).
tff(c_40703,plain,
( product(e_4,e_4,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_40699,c_113]) ).
tff(c_40724,plain,
( product(e_4,e_4,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_28,c_40703]) ).
tff(c_41304,plain,
product(e_3,e_4,e_1),
inference(splitLeft,[status(thm)],[c_40724]) ).
tff(c_41494,plain,
! [Y_808] :
( product(e_4,Y_808,e_1)
| ~ product(Y_808,e_3,e_4) ),
inference(resolution,[status(thm)],[c_41304,c_62]) ).
tff(c_41503,plain,
product(e_4,e_4,e_1),
inference(resolution,[status(thm)],[c_40699,c_41494]) ).
tff(c_41382,plain,
! [W_14] :
( equalish(W_14,e_3)
| ~ product(W_14,e_4,e_1) ),
inference(resolution,[status(thm)],[c_41304,c_60]) ).
tff(c_41549,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_41503,c_41382]) ).
tff(c_41577,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_41549]) ).
tff(c_41578,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_4,e_3)
| product(e_4,e_4,e_4) ),
inference(splitRight,[status(thm)],[c_40724]) ).
tff(c_41580,plain,
product(e_4,e_4,e_4),
inference(splitLeft,[status(thm)],[c_41578]) ).
tff(c_40735,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product(e_4,W_11,e_4) ),
inference(resolution,[status(thm)],[c_40699,c_58]) ).
tff(c_41605,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_41580,c_40735]) ).
tff(c_41629,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_41605]) ).
tff(c_41630,plain,
( product(e_3,e_4,e_3)
| product(e_3,e_4,e_2) ),
inference(splitRight,[status(thm)],[c_41578]) ).
tff(c_41644,plain,
product(e_3,e_4,e_2),
inference(splitLeft,[status(thm)],[c_41630]) ).
tff(c_41843,plain,
! [Y_820] :
( product(e_4,Y_820,e_2)
| ~ product(Y_820,e_3,e_4) ),
inference(resolution,[status(thm)],[c_41644,c_62]) ).
tff(c_41852,plain,
product(e_4,e_4,e_2),
inference(resolution,[status(thm)],[c_40699,c_41843]) ).
tff(c_41690,plain,
! [W_14] :
( equalish(W_14,e_3)
| ~ product(W_14,e_4,e_2) ),
inference(resolution,[status(thm)],[c_41644,c_60]) ).
tff(c_41986,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_41852,c_41690]) ).
tff(c_42010,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_41986]) ).
tff(c_42011,plain,
product(e_3,e_4,e_3),
inference(splitRight,[status(thm)],[c_41630]) ).
tff(c_40734,plain,
! [Y_18] :
( product(e_3,Y_18,e_4)
| ~ product(Y_18,e_4,e_3) ),
inference(resolution,[status(thm)],[c_40699,c_62]) ).
tff(c_42040,plain,
product(e_3,e_3,e_4),
inference(resolution,[status(thm)],[c_42011,c_40734]) ).
tff(c_40736,plain,
! [W_14] :
( equalish(W_14,e_4)
| ~ product(W_14,e_3,e_4) ),
inference(resolution,[status(thm)],[c_40699,c_60]) ).
tff(c_42069,plain,
equalish(e_3,e_4),
inference(resolution,[status(thm)],[c_42040,c_40736]) ).
tff(c_42094,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_42069]) ).
tff(c_42095,plain,
( product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(splitRight,[status(thm)],[c_40629]) ).
tff(c_42146,plain,
product(e_1,e_4,e_2),
inference(splitLeft,[status(thm)],[c_42095]) ).
tff(c_275,plain,
! [W_11,X_66] :
( equalish(W_11,e_1)
| ~ product(X_66,W_11,e_2)
| ~ next(X_66,e_2)
| product(X_66,e_1,e_1)
| ~ group_element(X_66) ),
inference(resolution,[status(thm)],[c_262,c_58]) ).
tff(c_42162,plain,
( equalish(e_4,e_1)
| ~ next(e_1,e_2)
| product(e_1,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_42146,c_275]) ).
tff(c_42195,plain,
( equalish(e_4,e_1)
| product(e_1,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_2,c_42162]) ).
tff(c_42197,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_37621,c_48,c_42195]) ).
tff(c_42198,plain,
product(e_1,e_4,e_3),
inference(splitRight,[status(thm)],[c_42095]) ).
tff(c_39593,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product(e_1,W_11,e_3) ),
inference(resolution,[status(thm)],[c_39555,c_58]) ).
tff(c_42253,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_42198,c_39593]) ).
tff(c_42290,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_42253]) ).
tff(c_42291,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(splitRight,[status(thm)],[c_40065]) ).
tff(c_42299,plain,
product(e_3,e_3,e_2),
inference(splitLeft,[status(thm)],[c_42291]) ).
tff(c_42429,plain,
! [Y_832] :
( product(e_3,Y_832,e_2)
| ~ product(Y_832,e_3,e_3) ),
inference(resolution,[status(thm)],[c_42299,c_62]) ).
tff(c_42453,plain,
product(e_3,e_1,e_2),
inference(resolution,[status(thm)],[c_39555,c_42429]) ).
tff(c_42332,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product(e_3,W_11,e_2) ),
inference(resolution,[status(thm)],[c_42299,c_58]) ).
tff(c_42477,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_42453,c_42332]) ).
tff(c_42510,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_42477]) ).
tff(c_42511,plain,
product(e_3,e_3,e_3),
inference(splitRight,[status(thm)],[c_42291]) ).
tff(c_39594,plain,
! [W_14] :
( equalish(W_14,e_1)
| ~ product(W_14,e_3,e_3) ),
inference(resolution,[status(thm)],[c_39555,c_60]) ).
tff(c_42515,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_42511,c_39594]) ).
tff(c_42535,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_42,c_42515]) ).
tff(c_42536,plain,
! [X_47] :
( product(e_1,e_3,e_2)
| product(e_3,X_47,e_4)
| ~ next(X_47,e_3)
| product(X_47,e_1,e_2)
| product(X_47,e_1,e_1)
| ~ group_element(X_47) ),
inference(splitRight,[status(thm)],[c_39553]) ).
tff(c_42581,plain,
product(e_1,e_3,e_2),
inference(splitLeft,[status(thm)],[c_42536]) ).
tff(c_42593,plain,
( equalish(e_3,e_1)
| ~ next(e_1,e_2)
| product(e_1,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_42581,c_275]) ).
tff(c_42618,plain,
( equalish(e_3,e_1)
| product(e_1,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_2,c_42593]) ).
tff(c_42620,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_37621,c_42,c_42618]) ).
tff(c_42622,plain,
~ product(e_1,e_3,e_2),
inference(splitRight,[status(thm)],[c_42536]) ).
tff(c_39554,plain,
~ product(e_1,e_3,e_1),
inference(splitRight,[status(thm)],[c_350]) ).
tff(c_42537,plain,
~ product(e_1,e_3,e_3),
inference(splitRight,[status(thm)],[c_39553]) ).
tff(c_42552,plain,
! [Y_5] :
( equalish(Y_5,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| ~ group_element(e_3)
| product(e_1,Y_5,e_3)
| product(e_1,Y_5,e_2)
| product(e_1,Y_5,e_1)
| ~ group_element(Y_5)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_261,c_42537]) ).
tff(c_42575,plain,
! [Y_5] :
( equalish(Y_5,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_1,Y_5,e_3)
| product(e_1,Y_5,e_2)
| product(e_1,Y_5,e_1)
| ~ group_element(Y_5) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_26,c_42552]) ).
tff(c_42576,plain,
! [Y_5] :
( equalish(Y_5,e_3)
| product(e_1,e_3,e_2)
| product(e_1,Y_5,e_3)
| product(e_1,Y_5,e_2)
| product(e_1,Y_5,e_1)
| ~ group_element(Y_5) ),
inference(negUnitSimplification,[status(thm)],[c_39554,c_42575]) ).
tff(c_43283,plain,
! [Y_856] :
( equalish(Y_856,e_3)
| product(e_1,Y_856,e_3)
| product(e_1,Y_856,e_2)
| product(e_1,Y_856,e_1)
| ~ group_element(Y_856) ),
inference(negUnitSimplification,[status(thm)],[c_42622,c_42576]) ).
tff(c_43325,plain,
( equalish(e_3,e_2)
| ~ next(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_43283,c_277]) ).
tff(c_43398,plain,
( equalish(e_3,e_2)
| equalish(e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_2,c_43325]) ).
tff(c_43399,plain,
product(e_1,e_1,e_2),
inference(negUnitSimplification,[status(thm)],[c_37621,c_32,c_44,c_43398]) ).
tff(c_43429,plain,
( product(e_2,e_1,e_4)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_43399,c_113]) ).
tff(c_43476,plain,
( product(e_2,e_1,e_4)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_24,c_43429]) ).
tff(c_43894,plain,
product(e_1,e_2,e_1),
inference(splitLeft,[status(thm)],[c_43476]) ).
tff(c_44074,plain,
! [Y_871] :
( product(e_2,Y_871,e_1)
| ~ product(Y_871,e_1,e_2) ),
inference(resolution,[status(thm)],[c_43894,c_62]) ).
tff(c_44084,plain,
product(e_2,e_1,e_1),
inference(resolution,[status(thm)],[c_43399,c_44074]) ).
tff(c_43494,plain,
! [Y_18] :
( product(e_1,Y_18,e_2)
| ~ product(Y_18,e_1,e_1) ),
inference(resolution,[status(thm)],[c_43399,c_62]) ).
tff(c_44124,plain,
product(e_1,e_2,e_2),
inference(resolution,[status(thm)],[c_44084,c_43494]) ).
tff(c_43945,plain,
! [W_8] :
( equalish(W_8,e_1)
| ~ product(e_1,e_2,W_8) ),
inference(resolution,[status(thm)],[c_43894,c_56]) ).
tff(c_44172,plain,
equalish(e_2,e_1),
inference(resolution,[status(thm)],[c_44124,c_43945]) ).
tff(c_44201,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_36,c_44172]) ).
tff(c_44202,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_1,e_4) ),
inference(splitRight,[status(thm)],[c_43476]) ).
tff(c_44204,plain,
product(e_2,e_1,e_4),
inference(splitLeft,[status(thm)],[c_44202]) ).
tff(c_44236,plain,
~ next(e_2,e_3),
inference(resolution,[status(thm)],[c_44204,c_79]) ).
tff(c_44284,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_44236]) ).
tff(c_44285,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2) ),
inference(splitRight,[status(thm)],[c_44202]) ).
tff(c_44303,plain,
product(e_1,e_2,e_2),
inference(splitLeft,[status(thm)],[c_44285]) ).
tff(c_43495,plain,
! [W_11] :
( equalish(W_11,e_1)
| ~ product(e_1,W_11,e_2) ),
inference(resolution,[status(thm)],[c_43399,c_58]) ).
tff(c_44306,plain,
equalish(e_2,e_1),
inference(resolution,[status(thm)],[c_44303,c_43495]) ).
tff(c_44332,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_36,c_44306]) ).
tff(c_44333,plain,
product(e_1,e_2,e_3),
inference(splitRight,[status(thm)],[c_44285]) ).
tff(c_44750,plain,
! [Y_883] :
( product(e_2,Y_883,e_3)
| ~ product(Y_883,e_1,e_2) ),
inference(resolution,[status(thm)],[c_44333,c_62]) ).
tff(c_44760,plain,
product(e_2,e_1,e_3),
inference(resolution,[status(thm)],[c_43399,c_44750]) ).
tff(c_42546,plain,
! [X_58] :
( equalish(e_1,X_58)
| product(X_58,e_3,e_3)
| product(X_58,e_3,e_2)
| product(X_58,e_3,e_1)
| ~ group_element(X_58)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_198,c_42537]) ).
tff(c_42567,plain,
! [X_58] :
( equalish(e_1,X_58)
| product(X_58,e_3,e_3)
| product(X_58,e_3,e_2)
| product(X_58,e_3,e_1)
| ~ group_element(X_58)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_26,c_42546]) ).
tff(c_42568,plain,
! [X_58] :
( equalish(e_1,X_58)
| product(X_58,e_3,e_3)
| product(X_58,e_3,e_2)
| product(X_58,e_3,e_1)
| ~ group_element(X_58)
| product(e_1,e_3,e_2) ),
inference(negUnitSimplification,[status(thm)],[c_39554,c_42567]) ).
tff(c_43069,plain,
! [X_849] :
( equalish(e_1,X_849)
| product(X_849,e_3,e_3)
| product(X_849,e_3,e_2)
| product(X_849,e_3,e_1)
| ~ group_element(X_849) ),
inference(negUnitSimplification,[status(thm)],[c_42622,c_42568]) ).
tff(c_43121,plain,
! [W_11,X_849] :
( equalish(W_11,e_3)
| ~ product(X_849,W_11,e_3)
| equalish(e_1,X_849)
| product(X_849,e_3,e_2)
| product(X_849,e_3,e_1)
| ~ group_element(X_849) ),
inference(resolution,[status(thm)],[c_43069,c_58]) ).
tff(c_44771,plain,
( equalish(e_1,e_3)
| equalish(e_1,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_44760,c_43121]) ).
tff(c_44814,plain,
( equalish(e_1,e_3)
| equalish(e_1,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_44771]) ).
tff(c_44815,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_30,c_32,c_44814]) ).
tff(c_45307,plain,
product(e_2,e_3,e_1),
inference(splitLeft,[status(thm)],[c_44815]) ).
tff(c_45563,plain,
! [Y_901] :
( product(e_3,Y_901,e_1)
| ~ product(Y_901,e_2,e_3) ),
inference(resolution,[status(thm)],[c_45307,c_62]) ).
tff(c_45590,plain,
product(e_3,e_1,e_1),
inference(resolution,[status(thm)],[c_44333,c_45563]) ).
tff(c_45621,plain,
product(e_1,e_3,e_2),
inference(resolution,[status(thm)],[c_45590,c_43494]) ).
tff(c_45664,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_42622,c_45621]) ).
tff(c_45665,plain,
product(e_2,e_3,e_2),
inference(splitRight,[status(thm)],[c_44815]) ).
tff(c_45899,plain,
! [Y_908] :
( product(e_3,Y_908,e_2)
| ~ product(Y_908,e_2,e_3) ),
inference(resolution,[status(thm)],[c_45665,c_62]) ).
tff(c_45926,plain,
product(e_3,e_1,e_2),
inference(resolution,[status(thm)],[c_44333,c_45899]) ).
tff(c_43496,plain,
! [W_14] :
( equalish(W_14,e_1)
| ~ product(W_14,e_1,e_2) ),
inference(resolution,[status(thm)],[c_43399,c_60]) ).
tff(c_45958,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_45926,c_43496]) ).
tff(c_46004,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_42,c_45958]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP129-2.004 : 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
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 3 22:16:23 EDT 2023
% 0.14/0.34 % CPUTime :
% 14.63/6.32 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.84/6.38
% 14.84/6.38 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.30/6.46
% 15.30/6.46 Inference rules
% 15.30/6.46 ----------------------
% 15.30/6.46 #Ref : 0
% 15.30/6.46 #Sup : 8555
% 15.30/6.46 #Fact : 20
% 15.30/6.46 #Define : 0
% 15.30/6.46 #Split : 92
% 15.30/6.46 #Chain : 0
% 15.30/6.46 #Close : 0
% 15.30/6.46
% 15.30/6.46 Ordering : KBO
% 15.30/6.46
% 15.30/6.46 Simplification rules
% 15.30/6.46 ----------------------
% 15.30/6.46 #Subsume : 2658
% 15.30/6.46 #Demod : 11941
% 15.30/6.46 #Tautology : 2816
% 15.30/6.46 #SimpNegUnit : 3482
% 15.30/6.46 #BackRed : 0
% 15.30/6.46
% 15.30/6.46 #Partial instantiations: 0
% 15.30/6.46 #Strategies tried : 1
% 15.30/6.46
% 15.30/6.46 Timing (in seconds)
% 15.30/6.46 ----------------------
% 15.30/6.46 Preprocessing : 0.48
% 15.30/6.46 Parsing : 0.27
% 15.30/6.47 CNF conversion : 0.02
% 15.30/6.47 Main loop : 4.81
% 15.30/6.47 Inferencing : 1.06
% 15.30/6.47 Reduction : 1.54
% 15.30/6.47 Demodulation : 0.99
% 15.30/6.47 BG Simplification : 0.07
% 15.30/6.47 Subsumption : 1.90
% 15.30/6.47 Abstraction : 0.12
% 15.30/6.47 MUC search : 0.00
% 15.30/6.47 Cooper : 0.00
% 15.30/6.47 Total : 5.44
% 15.30/6.47 Index Insertion : 0.00
% 15.30/6.47 Index Deletion : 0.00
% 15.30/6.47 Index Matching : 0.00
% 15.30/6.47 BG Taut test : 0.00
%------------------------------------------------------------------------------