TSTP Solution File: GRP130-3.003 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP130-3.003 : 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 : n001.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 10:40:13 EDT 2023
% Result : Unsatisfiable 11.02s 3.51s
% Output : CNFRefutation 11.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 38
% Syntax : Number of formulae : 302 ( 125 unt; 10 typ; 0 def)
% Number of atoms : 796 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 848 ( 344 ~; 504 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 6 >; 6 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 191 (; 191 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > next > greater > equalish > cycle > group_element > #nlpp > e_3 > e_2 > e_1 > e_0
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(group_element,type,
group_element: $i > $o ).
tff(greater,type,
greater: ( $i * $i ) > $o ).
tff(cycle,type,
cycle: ( $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_0,type,
e_0: $i ).
tff(e_3,type,
e_3: $i ).
tff(equalish,type,
equalish: ( $i * $i ) > $o ).
tff(e_1,type,
e_1: $i ).
tff(f_123,axiom,
~ equalish(e_2,e_1),
file(unknown,unknown) ).
tff(f_129,axiom,
~ equalish(e_3,e_2),
file(unknown,unknown) ).
tff(f_119,axiom,
~ equalish(e_1,e_2),
file(unknown,unknown) ).
tff(f_115,axiom,
group_element(e_1),
file(unknown,unknown) ).
tff(f_116,axiom,
group_element(e_2),
file(unknown,unknown) ).
tff(f_141,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(X,Y,e_1)
| product(X,Y,e_2)
| product(X,Y,e_3) ),
file(unknown,unknown) ).
tff(f_125,axiom,
~ equalish(e_2,e_3),
file(unknown,unknown) ).
tff(f_121,axiom,
~ equalish(e_1,e_3),
file(unknown,unknown) ).
tff(f_56,axiom,
cycle(e_3,e_0),
file(unknown,unknown) ).
tff(f_32,axiom,
next(e_2,e_3),
file(unknown,unknown) ).
tff(f_36,axiom,
greater(e_2,e_1),
file(unknown,unknown) ).
tff(f_33,axiom,
greater(e_1,e_0),
file(unknown,unknown) ).
tff(f_31,axiom,
next(e_1,e_2),
file(unknown,unknown) ).
tff(f_114,axiom,
! [X,Y,Z,X1] :
( ~ cycle(X,Y)
| ~ product(X,e_1,Z)
| ~ greater(Y,e_0)
| ~ next(X,X1)
| equalish(Z,X1) ),
file(unknown,unknown) ).
tff(f_55,axiom,
! [X] :
( ~ group_element(X)
| cycle(X,e_0)
| cycle(X,e_1)
| cycle(X,e_2) ),
file(unknown,unknown) ).
tff(f_34,axiom,
greater(e_2,e_0),
file(unknown,unknown) ).
tff(f_37,axiom,
greater(e_3,e_1),
file(unknown,unknown) ).
tff(f_38,axiom,
greater(e_3,e_2),
file(unknown,unknown) ).
tff(f_117,axiom,
group_element(e_3),
file(unknown,unknown) ).
tff(f_100,axiom,
! [X,Y] :
( ~ cycle(X,e_0)
| ~ product(X,e_1,Y)
| ~ greater(Y,X) ),
file(unknown,unknown) ).
tff(f_173,axiom,
! [X,Y,Z1,Z2] :
( ~ product(X,Y,Z1)
| ~ product(X,Z1,Z2)
| product(Z2,Y,X) ),
file(unknown,unknown) ).
tff(f_157,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_165,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_127,axiom,
~ equalish(e_3,e_1),
file(unknown,unknown) ).
tff(f_149,axiom,
! [X,Y,W,Z] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_30,axiom,
next(e_0,e_1),
file(unknown,unknown) ).
tff(f_73,axiom,
! [W,Z,X,Y,Z1] :
( ~ cycle(X,Y)
| ~ cycle(W,Z)
| ~ next(X,W)
| ~ greater(Y,e_0)
| ~ next(Z,Z1)
| equalish(Y,Z1) ),
file(unknown,unknown) ).
tff(f_91,axiom,
! [W,Z2,X,Y,Z1] :
( ~ cycle(X,Z1)
| ~ cycle(Y,e_0)
| ~ cycle(W,Z2)
| ~ next(Y,W)
| ~ greater(Y,X)
| ~ greater(Z1,Z2) ),
file(unknown,unknown) ).
tff(c_44,plain,
~ equalish(e_2,e_1),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_50,plain,
~ equalish(e_3,e_2),
inference(cnfTransformation,[status(thm)],[f_129]) ).
tff(c_40,plain,
~ equalish(e_1,e_2),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_34,plain,
group_element(e_1),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_36,plain,
group_element(e_2),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_52,plain,
! [X_21,Y_22] :
( product(X_21,Y_22,e_3)
| product(X_21,Y_22,e_2)
| product(X_21,Y_22,e_1)
| ~ group_element(Y_22)
| ~ group_element(X_21) ),
inference(cnfTransformation,[status(thm)],[f_141]) ).
tff(c_46,plain,
~ equalish(e_2,e_3),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_42,plain,
~ equalish(e_1,e_3),
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_24,plain,
cycle(e_3,e_0),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_6,plain,
next(e_2,e_3),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_14,plain,
greater(e_2,e_1),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_8,plain,
greater(e_1,e_0),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_4,plain,
next(e_1,e_2),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_105,plain,
! [Z_66,X1_67,X_68,Y_69] :
( equalish(Z_66,X1_67)
| ~ next(X_68,X1_67)
| ~ greater(Y_69,e_0)
| ~ product(X_68,e_1,Z_66)
| ~ cycle(X_68,Y_69) ),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_114,plain,
! [Z_66,Y_69] :
( equalish(Z_66,e_2)
| ~ greater(Y_69,e_0)
| ~ product(e_1,e_1,Z_66)
| ~ cycle(e_1,Y_69) ),
inference(resolution,[status(thm)],[c_4,c_105]) ).
tff(c_194,plain,
! [Y_83] :
( ~ greater(Y_83,e_0)
| ~ cycle(e_1,Y_83) ),
inference(splitLeft,[status(thm)],[c_114]) ).
tff(c_206,plain,
~ cycle(e_1,e_1),
inference(resolution,[status(thm)],[c_8,c_194]) ).
tff(c_22,plain,
! [X_4] :
( cycle(X_4,e_2)
| cycle(X_4,e_1)
| cycle(X_4,e_0)
| ~ group_element(X_4) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_10,plain,
greater(e_2,e_0),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_205,plain,
~ cycle(e_1,e_2),
inference(resolution,[status(thm)],[c_10,c_194]) ).
tff(c_209,plain,
( cycle(e_1,e_1)
| cycle(e_1,e_0)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_22,c_205]) ).
tff(c_212,plain,
( cycle(e_1,e_1)
| cycle(e_1,e_0) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_209]) ).
tff(c_213,plain,
cycle(e_1,e_0),
inference(negUnitSimplification,[status(thm)],[c_206,c_212]) ).
tff(c_16,plain,
greater(e_3,e_1),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_112,plain,
! [Z_66,Y_69] :
( equalish(Z_66,e_3)
| ~ greater(Y_69,e_0)
| ~ product(e_2,e_1,Z_66)
| ~ cycle(e_2,Y_69) ),
inference(resolution,[status(thm)],[c_6,c_105]) ).
tff(c_116,plain,
! [Y_70] :
( ~ greater(Y_70,e_0)
| ~ cycle(e_2,Y_70) ),
inference(splitLeft,[status(thm)],[c_112]) ).
tff(c_128,plain,
~ cycle(e_2,e_1),
inference(resolution,[status(thm)],[c_8,c_116]) ).
tff(c_127,plain,
~ cycle(e_2,e_2),
inference(resolution,[status(thm)],[c_10,c_116]) ).
tff(c_150,plain,
( cycle(e_2,e_1)
| cycle(e_2,e_0)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_22,c_127]) ).
tff(c_153,plain,
( cycle(e_2,e_1)
| cycle(e_2,e_0) ),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_150]) ).
tff(c_154,plain,
cycle(e_2,e_0),
inference(negUnitSimplification,[status(thm)],[c_128,c_153]) ).
tff(c_18,plain,
greater(e_3,e_2),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_38,plain,
group_element(e_3),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_85,plain,
! [X_64,Y_65] :
( product(X_64,Y_65,e_3)
| product(X_64,Y_65,e_2)
| product(X_64,Y_65,e_1)
| ~ group_element(Y_65)
| ~ group_element(X_64) ),
inference(cnfTransformation,[status(thm)],[f_141]) ).
tff(c_30,plain,
! [Y_16,X_15] :
( ~ greater(Y_16,X_15)
| ~ product(X_15,e_1,Y_16)
| ~ cycle(X_15,e_0) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_97,plain,
! [X_64] :
( ~ greater(e_3,X_64)
| ~ cycle(X_64,e_0)
| product(X_64,e_1,e_2)
| product(X_64,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X_64) ),
inference(resolution,[status(thm)],[c_85,c_30]) ).
tff(c_104,plain,
! [X_64] :
( ~ greater(e_3,X_64)
| ~ cycle(X_64,e_0)
| product(X_64,e_1,e_2)
| product(X_64,e_1,e_1)
| ~ group_element(X_64) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_97]) ).
tff(c_60,plain,
! [Z2_38,Y_36,X_35,Z1_37] :
( product(Z2_38,Y_36,X_35)
| ~ product(X_35,Z1_37,Z2_38)
| ~ product(X_35,Y_36,Z1_37) ),
inference(cnfTransformation,[status(thm)],[f_173]) ).
tff(c_734,plain,
! [Y_156,X_157,Y_158] :
( product(e_3,Y_156,X_157)
| ~ product(X_157,Y_156,Y_158)
| product(X_157,Y_158,e_2)
| product(X_157,Y_158,e_1)
| ~ group_element(Y_158)
| ~ group_element(X_157) ),
inference(resolution,[status(thm)],[c_85,c_60]) ).
tff(c_738,plain,
! [X_64] :
( product(e_3,e_1,X_64)
| product(X_64,e_2,e_2)
| product(X_64,e_2,e_1)
| ~ group_element(e_2)
| ~ greater(e_3,X_64)
| ~ cycle(X_64,e_0)
| product(X_64,e_1,e_1)
| ~ group_element(X_64) ),
inference(resolution,[status(thm)],[c_104,c_734]) ).
tff(c_1119,plain,
! [X_176] :
( product(e_3,e_1,X_176)
| product(X_176,e_2,e_2)
| product(X_176,e_2,e_1)
| ~ greater(e_3,X_176)
| ~ cycle(X_176,e_0)
| product(X_176,e_1,e_1)
| ~ group_element(X_176) ),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_738]) ).
tff(c_579,plain,
! [X_128] :
( ~ greater(e_3,X_128)
| ~ cycle(X_128,e_0)
| product(X_128,e_1,e_2)
| product(X_128,e_1,e_1)
| ~ group_element(X_128) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_97]) ).
tff(c_56,plain,
! [W_28,Z_30,X_27,Y_29] :
( equalish(W_28,Z_30)
| ~ product(X_27,Z_30,Y_29)
| ~ product(X_27,W_28,Y_29) ),
inference(cnfTransformation,[status(thm)],[f_157]) ).
tff(c_593,plain,
! [W_28,X_128] :
( equalish(W_28,e_1)
| ~ product(X_128,W_28,e_2)
| ~ greater(e_3,X_128)
| ~ cycle(X_128,e_0)
| product(X_128,e_1,e_1)
| ~ group_element(X_128) ),
inference(resolution,[status(thm)],[c_579,c_56]) ).
tff(c_1173,plain,
! [X_176] :
( equalish(e_2,e_1)
| product(e_3,e_1,X_176)
| product(X_176,e_2,e_1)
| ~ greater(e_3,X_176)
| ~ cycle(X_176,e_0)
| product(X_176,e_1,e_1)
| ~ group_element(X_176) ),
inference(resolution,[status(thm)],[c_1119,c_593]) ).
tff(c_1232,plain,
! [X_176] :
( product(e_3,e_1,X_176)
| product(X_176,e_2,e_1)
| ~ greater(e_3,X_176)
| ~ cycle(X_176,e_0)
| product(X_176,e_1,e_1)
| ~ group_element(X_176) ),
inference(negUnitSimplification,[status(thm)],[c_44,c_1173]) ).
tff(c_740,plain,
! [Y_22,X_21] :
( product(e_3,Y_22,X_21)
| product(X_21,e_3,e_2)
| product(X_21,e_3,e_1)
| ~ group_element(e_3)
| product(X_21,Y_22,e_2)
| product(X_21,Y_22,e_1)
| ~ group_element(Y_22)
| ~ group_element(X_21) ),
inference(resolution,[status(thm)],[c_52,c_734]) ).
tff(c_749,plain,
! [Y_22,X_21] :
( product(e_3,Y_22,X_21)
| product(X_21,e_3,e_2)
| product(X_21,e_3,e_1)
| product(X_21,Y_22,e_2)
| product(X_21,Y_22,e_1)
| ~ group_element(Y_22)
| ~ group_element(X_21) ),
inference(demodulation,[status(thm),theory(equality)],[c_38,c_740]) ).
tff(c_1639,plain,
! [X_21] :
( product(e_3,e_3,X_21)
| product(X_21,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X_21)
| product(X_21,e_3,e_2) ),
inference(factorization,[status(thm),theory(equality)],[c_749]) ).
tff(c_1821,plain,
! [X_185] :
( product(e_3,e_3,X_185)
| product(X_185,e_3,e_1)
| ~ group_element(X_185)
| product(X_185,e_3,e_2) ),
inference(demodulation,[status(thm),theory(equality)],[c_38,c_1639]) ).
tff(c_2019,plain,
! [W_192,X_193] :
( equalish(W_192,e_3)
| ~ product(X_193,W_192,e_2)
| product(e_3,e_3,X_193)
| product(X_193,e_3,e_1)
| ~ group_element(X_193) ),
inference(resolution,[status(thm)],[c_1821,c_56]) ).
tff(c_2040,plain,
( equalish(e_1,e_3)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_1)
| ~ group_element(e_3)
| product(e_2,e_2,e_1)
| ~ greater(e_3,e_2)
| ~ cycle(e_2,e_0)
| product(e_2,e_1,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_1232,c_2019]) ).
tff(c_2067,plain,
( equalish(e_1,e_3)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_1)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_154,c_18,c_38,c_2040]) ).
tff(c_2068,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_1)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_42,c_2067]) ).
tff(c_2076,plain,
product(e_2,e_1,e_1),
inference(splitLeft,[status(thm)],[c_2068]) ).
tff(c_595,plain,
! [X_128] :
( ~ greater(e_2,X_128)
| ~ greater(e_3,X_128)
| ~ cycle(X_128,e_0)
| product(X_128,e_1,e_1)
| ~ group_element(X_128) ),
inference(resolution,[status(thm)],[c_579,c_30]) ).
tff(c_606,plain,
! [X_132] :
( ~ greater(e_2,X_132)
| ~ greater(e_3,X_132)
| ~ cycle(X_132,e_0)
| product(X_132,e_1,e_1)
| ~ group_element(X_132) ),
inference(resolution,[status(thm)],[c_579,c_30]) ).
tff(c_750,plain,
! [Y_159,X_160] :
( product(e_1,Y_159,X_160)
| ~ product(X_160,Y_159,e_1)
| ~ greater(e_2,X_160)
| ~ greater(e_3,X_160)
| ~ cycle(X_160,e_0)
| ~ group_element(X_160) ),
inference(resolution,[status(thm)],[c_606,c_60]) ).
tff(c_754,plain,
! [X_161] :
( product(e_1,e_1,X_161)
| ~ greater(e_2,X_161)
| ~ greater(e_3,X_161)
| ~ cycle(X_161,e_0)
| ~ group_element(X_161) ),
inference(resolution,[status(thm)],[c_595,c_750]) ).
tff(c_58,plain,
! [W_31,Z_34,Y_32,X_33] :
( equalish(W_31,Z_34)
| ~ product(Z_34,Y_32,X_33)
| ~ product(W_31,Y_32,X_33) ),
inference(cnfTransformation,[status(thm)],[f_165]) ).
tff(c_833,plain,
! [W_31,X_161] :
( equalish(W_31,e_1)
| ~ product(W_31,e_1,X_161)
| ~ greater(e_2,X_161)
| ~ greater(e_3,X_161)
| ~ cycle(X_161,e_0)
| ~ group_element(X_161) ),
inference(resolution,[status(thm)],[c_754,c_58]) ).
tff(c_2079,plain,
( equalish(e_2,e_1)
| ~ greater(e_2,e_1)
| ~ greater(e_3,e_1)
| ~ cycle(e_1,e_0)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_2076,c_833]) ).
tff(c_2114,plain,
equalish(e_2,e_1),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_213,c_16,c_14,c_2079]) ).
tff(c_2116,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_44,c_2114]) ).
tff(c_2118,plain,
~ product(e_2,e_1,e_1),
inference(splitRight,[status(thm)],[c_2068]) ).
tff(c_48,plain,
~ equalish(e_3,e_1),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_2117,plain,
( product(e_2,e_2,e_1)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_3) ),
inference(splitRight,[status(thm)],[c_2068]) ).
tff(c_2347,plain,
product(e_3,e_3,e_3),
inference(splitLeft,[status(thm)],[c_2117]) ).
tff(c_2440,plain,
! [W_198] :
( equalish(W_198,e_3)
| ~ product(e_3,W_198,e_3) ),
inference(resolution,[status(thm)],[c_2347,c_56]) ).
tff(c_2457,plain,
! [Y_22] :
( equalish(Y_22,e_3)
| product(e_3,Y_22,e_2)
| product(e_3,Y_22,e_1)
| ~ group_element(Y_22)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_52,c_2440]) ).
tff(c_2468,plain,
! [Y_22] :
( equalish(Y_22,e_3)
| product(e_3,Y_22,e_2)
| product(e_3,Y_22,e_1)
| ~ group_element(Y_22) ),
inference(demodulation,[status(thm),theory(equality)],[c_38,c_2457]) ).
tff(c_100,plain,
! [W_28,Y_65,X_64] :
( equalish(W_28,Y_65)
| ~ product(X_64,W_28,e_3)
| product(X_64,Y_65,e_2)
| product(X_64,Y_65,e_1)
| ~ group_element(Y_65)
| ~ group_element(X_64) ),
inference(resolution,[status(thm)],[c_85,c_56]) ).
tff(c_2355,plain,
! [Y_65] :
( equalish(e_3,Y_65)
| product(e_3,Y_65,e_2)
| product(e_3,Y_65,e_1)
| ~ group_element(Y_65)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_2347,c_100]) ).
tff(c_2560,plain,
! [Y_201] :
( equalish(e_3,Y_201)
| product(e_3,Y_201,e_2)
| product(e_3,Y_201,e_1)
| ~ group_element(Y_201) ),
inference(demodulation,[status(thm),theory(equality)],[c_38,c_2355]) ).
tff(c_3972,plain,
! [W_225,Y_226] :
( equalish(W_225,Y_226)
| ~ product(e_3,W_225,e_2)
| equalish(e_3,Y_226)
| product(e_3,Y_226,e_1)
| ~ group_element(Y_226) ),
inference(resolution,[status(thm)],[c_2560,c_56]) ).
tff(c_4017,plain,
! [Y_226] :
( equalish(e_1,Y_226)
| equalish(e_3,Y_226)
| product(e_3,Y_226,e_1)
| ~ group_element(Y_226)
| product(e_2,e_2,e_1)
| ~ greater(e_3,e_2)
| ~ cycle(e_2,e_0)
| product(e_2,e_1,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_1232,c_3972]) ).
tff(c_4061,plain,
! [Y_226] :
( equalish(e_1,Y_226)
| equalish(e_3,Y_226)
| product(e_3,Y_226,e_1)
| ~ group_element(Y_226)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_154,c_18,c_4017]) ).
tff(c_4062,plain,
! [Y_226] :
( equalish(e_1,Y_226)
| equalish(e_3,Y_226)
| product(e_3,Y_226,e_1)
| ~ group_element(Y_226)
| product(e_2,e_2,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_2118,c_4061]) ).
tff(c_4669,plain,
product(e_2,e_2,e_1),
inference(splitLeft,[status(thm)],[c_4062]) ).
tff(c_591,plain,
! [Y_36,X_128] :
( product(e_2,Y_36,X_128)
| ~ product(X_128,Y_36,e_1)
| ~ greater(e_3,X_128)
| ~ cycle(X_128,e_0)
| product(X_128,e_1,e_1)
| ~ group_element(X_128) ),
inference(resolution,[status(thm)],[c_579,c_60]) ).
tff(c_4671,plain,
( product(e_2,e_2,e_2)
| ~ greater(e_3,e_2)
| ~ cycle(e_2,e_0)
| product(e_2,e_1,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_4669,c_591]) ).
tff(c_4691,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_154,c_18,c_4671]) ).
tff(c_4692,plain,
product(e_2,e_2,e_2),
inference(negUnitSimplification,[status(thm)],[c_2118,c_4691]) ).
tff(c_4725,plain,
( equalish(e_2,e_1)
| ~ greater(e_3,e_2)
| ~ cycle(e_2,e_0)
| product(e_2,e_1,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_4692,c_593]) ).
tff(c_4761,plain,
( equalish(e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_154,c_18,c_4725]) ).
tff(c_4763,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2118,c_44,c_4761]) ).
tff(c_5082,plain,
! [Y_241] :
( equalish(e_1,Y_241)
| equalish(e_3,Y_241)
| product(e_3,Y_241,e_1)
| ~ group_element(Y_241) ),
inference(splitRight,[status(thm)],[c_4062]) ).
tff(c_5567,plain,
! [Y_248,Y_249] :
( product(e_1,Y_248,e_3)
| ~ product(e_3,Y_248,Y_249)
| equalish(e_1,Y_249)
| equalish(e_3,Y_249)
| ~ group_element(Y_249) ),
inference(resolution,[status(thm)],[c_5082,c_60]) ).
tff(c_5597,plain,
! [Y_22] :
( product(e_1,Y_22,e_3)
| equalish(e_1,e_2)
| equalish(e_3,e_2)
| ~ group_element(e_2)
| equalish(Y_22,e_3)
| product(e_3,Y_22,e_1)
| ~ group_element(Y_22) ),
inference(resolution,[status(thm)],[c_2468,c_5567]) ).
tff(c_5699,plain,
! [Y_22] :
( product(e_1,Y_22,e_3)
| equalish(e_1,e_2)
| equalish(e_3,e_2)
| equalish(Y_22,e_3)
| product(e_3,Y_22,e_1)
| ~ group_element(Y_22) ),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_5597]) ).
tff(c_5908,plain,
! [Y_251] :
( product(e_1,Y_251,e_3)
| equalish(Y_251,e_3)
| product(e_3,Y_251,e_1)
| ~ group_element(Y_251) ),
inference(negUnitSimplification,[status(thm)],[c_50,c_40,c_5699]) ).
tff(c_5942,plain,
( equalish(e_3,e_1)
| ~ greater(e_2,e_1)
| ~ greater(e_3,e_1)
| ~ cycle(e_1,e_0)
| product(e_1,e_1,e_3)
| equalish(e_1,e_3)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_5908,c_833]) ).
tff(c_6013,plain,
( equalish(e_3,e_1)
| product(e_1,e_1,e_3)
| equalish(e_1,e_3) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_213,c_16,c_14,c_5942]) ).
tff(c_6014,plain,
product(e_1,e_1,e_3),
inference(negUnitSimplification,[status(thm)],[c_42,c_48,c_6013]) ).
tff(c_624,plain,
! [Y_36,X_132] :
( product(e_1,Y_36,X_132)
| ~ product(X_132,Y_36,e_1)
| ~ greater(e_2,X_132)
| ~ greater(e_3,X_132)
| ~ cycle(X_132,e_0)
| ~ group_element(X_132) ),
inference(resolution,[status(thm)],[c_606,c_60]) ).
tff(c_757,plain,
( product(e_1,e_1,e_1)
| ~ greater(e_2,e_1)
| ~ greater(e_3,e_1)
| ~ cycle(e_1,e_0)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_754,c_624]) ).
tff(c_799,plain,
product(e_1,e_1,e_1),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_213,c_16,c_14,c_757]) ).
tff(c_54,plain,
! [W_25,Z_26,X_23,Y_24] :
( equalish(W_25,Z_26)
| ~ product(X_23,Y_24,Z_26)
| ~ product(X_23,Y_24,W_25) ),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_886,plain,
! [W_25] :
( equalish(W_25,e_1)
| ~ product(e_1,e_1,W_25) ),
inference(resolution,[status(thm)],[c_799,c_54]) ).
tff(c_6065,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_6014,c_886]) ).
tff(c_6100,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_48,c_6065]) ).
tff(c_6102,plain,
~ product(e_3,e_3,e_3),
inference(splitRight,[status(thm)],[c_2117]) ).
tff(c_6101,plain,
( product(e_3,e_3,e_1)
| product(e_2,e_2,e_1) ),
inference(splitRight,[status(thm)],[c_2117]) ).
tff(c_6342,plain,
product(e_2,e_2,e_1),
inference(splitLeft,[status(thm)],[c_6101]) ).
tff(c_6344,plain,
( product(e_2,e_2,e_2)
| ~ greater(e_3,e_2)
| ~ cycle(e_2,e_0)
| product(e_2,e_1,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_6342,c_591]) ).
tff(c_6364,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_154,c_18,c_6344]) ).
tff(c_6365,plain,
product(e_2,e_2,e_2),
inference(negUnitSimplification,[status(thm)],[c_2118,c_6364]) ).
tff(c_6390,plain,
( equalish(e_2,e_1)
| ~ greater(e_3,e_2)
| ~ cycle(e_2,e_0)
| product(e_2,e_1,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_6365,c_593]) ).
tff(c_6410,plain,
( equalish(e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_154,c_18,c_6390]) ).
tff(c_6412,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2118,c_44,c_6410]) ).
tff(c_6413,plain,
product(e_3,e_3,e_1),
inference(splitRight,[status(thm)],[c_6101]) ).
tff(c_98,plain,
! [Y_36,X_64,Y_65] :
( product(e_3,Y_36,X_64)
| ~ product(X_64,Y_36,Y_65)
| product(X_64,Y_65,e_2)
| product(X_64,Y_65,e_1)
| ~ group_element(Y_65)
| ~ group_element(X_64) ),
inference(resolution,[status(thm)],[c_85,c_60]) ).
tff(c_6480,plain,
( product(e_3,e_3,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_6413,c_98]) ).
tff(c_6510,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_38,c_34,c_6480]) ).
tff(c_6511,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_6102,c_6510]) ).
tff(c_6833,plain,
product(e_3,e_1,e_1),
inference(splitLeft,[status(thm)],[c_6511]) ).
tff(c_6522,plain,
! [W_28] :
( equalish(W_28,e_3)
| ~ product(e_3,W_28,e_1) ),
inference(resolution,[status(thm)],[c_6413,c_56]) ).
tff(c_6899,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_6833,c_6522]) ).
tff(c_6940,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_42,c_6899]) ).
tff(c_6941,plain,
product(e_3,e_1,e_2),
inference(splitRight,[status(thm)],[c_6511]) ).
tff(c_1897,plain,
! [W_28,X_185] :
( equalish(W_28,e_3)
| ~ product(e_3,W_28,X_185)
| product(X_185,e_3,e_1)
| ~ group_element(X_185)
| product(X_185,e_3,e_2) ),
inference(resolution,[status(thm)],[c_1821,c_56]) ).
tff(c_6946,plain,
( equalish(e_1,e_3)
| product(e_2,e_3,e_1)
| ~ group_element(e_2)
| product(e_2,e_3,e_2) ),
inference(resolution,[status(thm)],[c_6941,c_1897]) ).
tff(c_6980,plain,
( equalish(e_1,e_3)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2) ),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_6946]) ).
tff(c_6981,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2) ),
inference(negUnitSimplification,[status(thm)],[c_42,c_6980]) ).
tff(c_7420,plain,
product(e_2,e_3,e_2),
inference(splitLeft,[status(thm)],[c_6981]) ).
tff(c_7430,plain,
( equalish(e_3,e_1)
| ~ greater(e_3,e_2)
| ~ cycle(e_2,e_0)
| product(e_2,e_1,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_7420,c_593]) ).
tff(c_7454,plain,
( equalish(e_3,e_1)
| product(e_2,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_154,c_18,c_7430]) ).
tff(c_7456,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2118,c_48,c_7454]) ).
tff(c_7457,plain,
product(e_2,e_3,e_1),
inference(splitRight,[status(thm)],[c_6981]) ).
tff(c_6523,plain,
! [W_31] :
( equalish(W_31,e_3)
| ~ product(W_31,e_3,e_1) ),
inference(resolution,[status(thm)],[c_6413,c_58]) ).
tff(c_7461,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_7457,c_6523]) ).
tff(c_7486,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_7461]) ).
tff(c_7488,plain,
! [Z_270] :
( equalish(Z_270,e_2)
| ~ product(e_1,e_1,Z_270) ),
inference(splitRight,[status(thm)],[c_114]) ).
tff(c_7492,plain,
( equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_52,c_7488]) ).
tff(c_7495,plain,
( equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_7492]) ).
tff(c_7496,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_50,c_7495]) ).
tff(c_7497,plain,
product(e_1,e_1,e_1),
inference(splitLeft,[status(thm)],[c_7496]) ).
tff(c_7487,plain,
! [Z_66] :
( equalish(Z_66,e_2)
| ~ product(e_1,e_1,Z_66) ),
inference(splitRight,[status(thm)],[c_114]) ).
tff(c_7529,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[c_7497,c_7487]) ).
tff(c_7544,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_40,c_7529]) ).
tff(c_7545,plain,
product(e_1,e_1,e_2),
inference(splitRight,[status(thm)],[c_7496]) ).
tff(c_7560,plain,
( ~ greater(e_2,e_1)
| ~ cycle(e_1,e_0) ),
inference(resolution,[status(thm)],[c_7545,c_30]) ).
tff(c_7569,plain,
~ cycle(e_1,e_0),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_7560]) ).
tff(c_2,plain,
next(e_0,e_1),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_164,plain,
! [Y_76,Z1_79,W_80,Z_77,X_78] :
( equalish(Y_76,Z1_79)
| ~ next(Z_77,Z1_79)
| ~ greater(Y_76,e_0)
| ~ next(X_78,W_80)
| ~ cycle(W_80,Z_77)
| ~ cycle(X_78,Y_76) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_7697,plain,
! [Y_291,X_292,W_293] :
( equalish(Y_291,e_1)
| ~ greater(Y_291,e_0)
| ~ next(X_292,W_293)
| ~ cycle(W_293,e_0)
| ~ cycle(X_292,Y_291) ),
inference(resolution,[status(thm)],[c_2,c_164]) ).
tff(c_7701,plain,
! [X_292,W_293] :
( equalish(e_2,e_1)
| ~ next(X_292,W_293)
| ~ cycle(W_293,e_0)
| ~ cycle(X_292,e_2) ),
inference(resolution,[status(thm)],[c_10,c_7697]) ).
tff(c_7729,plain,
! [X_296,W_297] :
( ~ next(X_296,W_297)
| ~ cycle(W_297,e_0)
| ~ cycle(X_296,e_2) ),
inference(negUnitSimplification,[status(thm)],[c_44,c_7701]) ).
tff(c_7738,plain,
( ~ cycle(e_2,e_0)
| ~ cycle(e_1,e_2) ),
inference(resolution,[status(thm)],[c_4,c_7729]) ).
tff(c_7745,plain,
~ cycle(e_1,e_2),
inference(demodulation,[status(thm),theory(equality)],[c_154,c_7738]) ).
tff(c_7748,plain,
( cycle(e_1,e_1)
| cycle(e_1,e_0)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_22,c_7745]) ).
tff(c_7751,plain,
( cycle(e_1,e_1)
| cycle(e_1,e_0) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_7748]) ).
tff(c_7752,plain,
cycle(e_1,e_1),
inference(negUnitSimplification,[status(thm)],[c_7569,c_7751]) ).
tff(c_129,plain,
! [Z1_71,W_75,Z2_72,X_73,Y_74] :
( ~ greater(Z1_71,Z2_72)
| ~ greater(Y_74,X_73)
| ~ next(Y_74,W_75)
| ~ cycle(W_75,Z2_72)
| ~ cycle(Y_74,e_0)
| ~ cycle(X_73,Z1_71) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_7932,plain,
! [Y_321,X_322,W_323] :
( ~ greater(Y_321,X_322)
| ~ next(Y_321,W_323)
| ~ cycle(W_323,e_0)
| ~ cycle(Y_321,e_0)
| ~ cycle(X_322,e_1) ),
inference(resolution,[status(thm)],[c_8,c_129]) ).
tff(c_7938,plain,
! [W_323] :
( ~ next(e_2,W_323)
| ~ cycle(W_323,e_0)
| ~ cycle(e_2,e_0)
| ~ cycle(e_1,e_1) ),
inference(resolution,[status(thm)],[c_14,c_7932]) ).
tff(c_7962,plain,
! [W_325] :
( ~ next(e_2,W_325)
| ~ cycle(W_325,e_0) ),
inference(demodulation,[status(thm),theory(equality)],[c_7752,c_154,c_7938]) ).
tff(c_7965,plain,
~ cycle(e_3,e_0),
inference(resolution,[status(thm)],[c_6,c_7962]) ).
tff(c_7969,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_24,c_7965]) ).
tff(c_7971,plain,
! [Z_326] :
( equalish(Z_326,e_3)
| ~ product(e_2,e_1,Z_326) ),
inference(splitRight,[status(thm)],[c_112]) ).
tff(c_7975,plain,
( equalish(e_3,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_52,c_7971]) ).
tff(c_7978,plain,
( equalish(e_3,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_34,c_7975]) ).
tff(c_7998,plain,
product(e_2,e_1,e_1),
inference(splitLeft,[status(thm)],[c_7978]) ).
tff(c_7970,plain,
! [Z_66] :
( equalish(Z_66,e_3)
| ~ product(e_2,e_1,Z_66) ),
inference(splitRight,[status(thm)],[c_112]) ).
tff(c_8001,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_7998,c_7970]) ).
tff(c_8016,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_42,c_8001]) ).
tff(c_8018,plain,
~ product(e_2,e_1,e_1),
inference(splitRight,[status(thm)],[c_7978]) ).
tff(c_8031,plain,
! [Y_337] :
( ~ greater(Y_337,e_0)
| ~ cycle(e_1,Y_337) ),
inference(splitLeft,[status(thm)],[c_114]) ).
tff(c_8043,plain,
~ cycle(e_1,e_1),
inference(resolution,[status(thm)],[c_8,c_8031]) ).
tff(c_8042,plain,
~ cycle(e_1,e_2),
inference(resolution,[status(thm)],[c_10,c_8031]) ).
tff(c_8047,plain,
( cycle(e_1,e_1)
| cycle(e_1,e_0)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_22,c_8042]) ).
tff(c_8050,plain,
( cycle(e_1,e_1)
| cycle(e_1,e_0) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_8047]) ).
tff(c_8051,plain,
cycle(e_1,e_0),
inference(negUnitSimplification,[status(thm)],[c_8043,c_8050]) ).
tff(c_9235,plain,
! [Y_469,X_470,Y_471] :
( product(e_3,Y_469,X_470)
| ~ product(X_470,Y_469,Y_471)
| product(X_470,Y_471,e_2)
| product(X_470,Y_471,e_1)
| ~ group_element(Y_471)
| ~ group_element(X_470) ),
inference(resolution,[status(thm)],[c_85,c_60]) ).
tff(c_9245,plain,
! [Y_22,X_21] :
( product(e_3,Y_22,X_21)
| product(X_21,e_3,e_2)
| product(X_21,e_3,e_1)
| ~ group_element(e_3)
| product(X_21,Y_22,e_2)
| product(X_21,Y_22,e_1)
| ~ group_element(Y_22)
| ~ group_element(X_21) ),
inference(resolution,[status(thm)],[c_52,c_9235]) ).
tff(c_9260,plain,
! [Y_22,X_21] :
( product(e_3,Y_22,X_21)
| product(X_21,e_3,e_2)
| product(X_21,e_3,e_1)
| product(X_21,Y_22,e_2)
| product(X_21,Y_22,e_1)
| ~ group_element(Y_22)
| ~ group_element(X_21) ),
inference(demodulation,[status(thm),theory(equality)],[c_38,c_9245]) ).
tff(c_9501,plain,
! [X_21] :
( product(e_3,e_3,X_21)
| product(X_21,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X_21)
| product(X_21,e_3,e_2) ),
inference(factorization,[status(thm),theory(equality)],[c_9260]) ).
tff(c_9504,plain,
! [X_21] :
( product(e_3,e_3,X_21)
| product(X_21,e_3,e_1)
| ~ group_element(X_21)
| product(X_21,e_3,e_2) ),
inference(demodulation,[status(thm),theory(equality)],[c_38,c_9501]) ).
tff(c_9686,plain,
! [X_488] :
( product(e_3,e_3,X_488)
| product(X_488,e_3,e_1)
| ~ group_element(X_488)
| product(X_488,e_3,e_2) ),
inference(demodulation,[status(thm),theory(equality)],[c_38,c_9501]) ).
tff(c_9950,plain,
! [Y_501,X_502] :
( product(e_2,Y_501,X_502)
| ~ product(X_502,Y_501,e_3)
| product(e_3,e_3,X_502)
| product(X_502,e_3,e_1)
| ~ group_element(X_502) ),
inference(resolution,[status(thm)],[c_9686,c_60]) ).
tff(c_9953,plain,
( product(e_2,e_3,e_3)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_1)
| ~ group_element(e_3)
| product(e_3,e_3,e_2) ),
inference(resolution,[status(thm)],[c_9504,c_9950]) ).
tff(c_9964,plain,
( product(e_2,e_3,e_3)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2) ),
inference(demodulation,[status(thm),theory(equality)],[c_38,c_9953]) ).
tff(c_10122,plain,
product(e_3,e_3,e_2),
inference(splitLeft,[status(thm)],[c_9964]) ).
tff(c_10136,plain,
( product(e_3,e_3,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_10122,c_98]) ).
tff(c_10165,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_38,c_36,c_10136]) ).
tff(c_10323,plain,
product(e_3,e_2,e_1),
inference(splitLeft,[status(thm)],[c_10165]) ).
tff(c_9762,plain,
! [W_28,X_488] :
( equalish(W_28,e_3)
| ~ product(e_3,W_28,X_488)
| product(X_488,e_3,e_1)
| ~ group_element(X_488)
| product(X_488,e_3,e_2) ),
inference(resolution,[status(thm)],[c_9686,c_56]) ).
tff(c_10325,plain,
( equalish(e_2,e_3)
| product(e_1,e_3,e_1)
| ~ group_element(e_1)
| product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[c_10323,c_9762]) ).
tff(c_10347,plain,
( equalish(e_2,e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_10325]) ).
tff(c_10348,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(negUnitSimplification,[status(thm)],[c_46,c_10347]) ).
tff(c_10836,plain,
product(e_1,e_3,e_2),
inference(splitLeft,[status(thm)],[c_10348]) ).
tff(c_10177,plain,
! [W_31] :
( equalish(W_31,e_3)
| ~ product(W_31,e_3,e_2) ),
inference(resolution,[status(thm)],[c_10122,c_58]) ).
tff(c_10839,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_10836,c_10177]) ).
tff(c_10868,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_42,c_10839]) ).
tff(c_10869,plain,
product(e_1,e_3,e_1),
inference(splitRight,[status(thm)],[c_10348]) ).
tff(c_8933,plain,
! [X_440] :
( ~ greater(e_3,X_440)
| ~ cycle(X_440,e_0)
| product(X_440,e_1,e_2)
| product(X_440,e_1,e_1)
| ~ group_element(X_440) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_97]) ).
tff(c_8957,plain,
! [X_440] :
( ~ greater(e_2,X_440)
| ~ greater(e_3,X_440)
| ~ cycle(X_440,e_0)
| product(X_440,e_1,e_1)
| ~ group_element(X_440) ),
inference(resolution,[status(thm)],[c_8933,c_30]) ).
tff(c_8974,plain,
! [X_443] :
( ~ greater(e_2,X_443)
| ~ greater(e_3,X_443)
| ~ cycle(X_443,e_0)
| product(X_443,e_1,e_1)
| ~ group_element(X_443) ),
inference(resolution,[status(thm)],[c_8933,c_30]) ).
tff(c_9103,plain,
! [Y_466,X_467] :
( product(e_1,Y_466,X_467)
| ~ product(X_467,Y_466,e_1)
| ~ greater(e_2,X_467)
| ~ greater(e_3,X_467)
| ~ cycle(X_467,e_0)
| ~ group_element(X_467) ),
inference(resolution,[status(thm)],[c_8974,c_60]) ).
tff(c_9107,plain,
! [X_468] :
( product(e_1,e_1,X_468)
| ~ greater(e_2,X_468)
| ~ greater(e_3,X_468)
| ~ cycle(X_468,e_0)
| ~ group_element(X_468) ),
inference(resolution,[status(thm)],[c_8957,c_9103]) ).
tff(c_9180,plain,
! [W_28,X_468] :
( equalish(W_28,e_1)
| ~ product(e_1,W_28,X_468)
| ~ greater(e_2,X_468)
| ~ greater(e_3,X_468)
| ~ cycle(X_468,e_0)
| ~ group_element(X_468) ),
inference(resolution,[status(thm)],[c_9107,c_56]) ).
tff(c_10892,plain,
( equalish(e_3,e_1)
| ~ greater(e_2,e_1)
| ~ greater(e_3,e_1)
| ~ cycle(e_1,e_0)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_10869,c_9180]) ).
tff(c_10925,plain,
equalish(e_3,e_1),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_8051,c_16,c_14,c_10892]) ).
tff(c_10927,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_48,c_10925]) ).
tff(c_10928,plain,
( product(e_3,e_2,e_2)
| product(e_3,e_3,e_3) ),
inference(splitRight,[status(thm)],[c_10165]) ).
tff(c_10936,plain,
product(e_3,e_3,e_3),
inference(splitLeft,[status(thm)],[c_10928]) ).
tff(c_10175,plain,
! [W_25] :
( equalish(W_25,e_2)
| ~ product(e_3,e_3,W_25) ),
inference(resolution,[status(thm)],[c_10122,c_54]) ).
tff(c_11245,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[c_10936,c_10175]) ).
tff(c_11276,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_50,c_11245]) ).
tff(c_11277,plain,
product(e_3,e_2,e_2),
inference(splitRight,[status(thm)],[c_10928]) ).
tff(c_10176,plain,
! [W_28] :
( equalish(W_28,e_3)
| ~ product(e_3,W_28,e_2) ),
inference(resolution,[status(thm)],[c_10122,c_56]) ).
tff(c_11299,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_11277,c_10176]) ).
tff(c_11321,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_11299]) ).
tff(c_11323,plain,
~ product(e_3,e_3,e_2),
inference(splitRight,[status(thm)],[c_9964]) ).
tff(c_11346,plain,
( product(e_2,e_3,e_1)
| ~ group_element(e_2)
| product(e_2,e_3,e_2) ),
inference(resolution,[status(thm)],[c_9504,c_11323]) ).
tff(c_11357,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2) ),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_11346]) ).
tff(c_11364,plain,
product(e_2,e_3,e_2),
inference(splitLeft,[status(thm)],[c_11357]) ).
tff(c_11374,plain,
( product(e_3,e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_11364,c_98]) ).
tff(c_11402,plain,
( product(e_3,e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_11374]) ).
tff(c_11403,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_11323,c_11402]) ).
tff(c_11937,plain,
product(e_2,e_2,e_1),
inference(splitLeft,[status(thm)],[c_11403]) ).
tff(c_12466,plain,
! [Y_534] :
( product(e_1,Y_534,e_2)
| ~ product(e_2,Y_534,e_2) ),
inference(resolution,[status(thm)],[c_11937,c_60]) ).
tff(c_12514,plain,
product(e_1,e_3,e_2),
inference(resolution,[status(thm)],[c_11364,c_12466]) ).
tff(c_11415,plain,
! [W_31] :
( equalish(W_31,e_2)
| ~ product(W_31,e_3,e_2) ),
inference(resolution,[status(thm)],[c_11364,c_58]) ).
tff(c_12562,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[c_12514,c_11415]) ).
tff(c_12591,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_40,c_12562]) ).
tff(c_12592,plain,
product(e_2,e_2,e_2),
inference(splitRight,[status(thm)],[c_11403]) ).
tff(c_11414,plain,
! [W_28] :
( equalish(W_28,e_3)
| ~ product(e_2,W_28,e_2) ),
inference(resolution,[status(thm)],[c_11364,c_56]) ).
tff(c_12596,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_12592,c_11414]) ).
tff(c_12616,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_12596]) ).
tff(c_12617,plain,
product(e_2,e_3,e_1),
inference(splitRight,[status(thm)],[c_11357]) ).
tff(c_12626,plain,
( product(e_3,e_3,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_12617,c_98]) ).
tff(c_12656,plain,
( product(e_3,e_3,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_34,c_12626]) ).
tff(c_12657,plain,
product(e_2,e_1,e_2),
inference(negUnitSimplification,[status(thm)],[c_8018,c_11323,c_12656]) ).
tff(c_12981,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_12657,c_7970]) ).
tff(c_13024,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_12981]) ).
tff(c_13026,plain,
! [Z_538] :
( equalish(Z_538,e_2)
| ~ product(e_1,e_1,Z_538) ),
inference(splitRight,[status(thm)],[c_114]) ).
tff(c_13030,plain,
( equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_52,c_13026]) ).
tff(c_13033,plain,
( equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_13030]) ).
tff(c_13034,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_50,c_13033]) ).
tff(c_13035,plain,
product(e_1,e_1,e_1),
inference(splitLeft,[status(thm)],[c_13034]) ).
tff(c_13025,plain,
! [Z_66] :
( equalish(Z_66,e_2)
| ~ product(e_1,e_1,Z_66) ),
inference(splitRight,[status(thm)],[c_114]) ).
tff(c_13038,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[c_13035,c_13025]) ).
tff(c_13053,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_40,c_13038]) ).
tff(c_13054,plain,
product(e_1,e_1,e_2),
inference(splitRight,[status(thm)],[c_13034]) ).
tff(c_15159,plain,
! [Y_757,X_758,Y_759] :
( product(e_3,Y_757,X_758)
| ~ product(X_758,Y_757,Y_759)
| product(X_758,Y_759,e_2)
| product(X_758,Y_759,e_1)
| ~ group_element(Y_759)
| ~ group_element(X_758) ),
inference(resolution,[status(thm)],[c_85,c_60]) ).
tff(c_15171,plain,
( product(e_3,e_1,e_1)
| 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_13054,c_15159]) ).
tff(c_15192,plain,
( product(e_3,e_1,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_36,c_15171]) ).
tff(c_15196,plain,
product(e_1,e_2,e_1),
inference(splitLeft,[status(thm)],[c_15192]) ).
tff(c_13108,plain,
! [Y_542] :
( product(e_2,Y_542,e_1)
| ~ product(e_1,Y_542,e_1) ),
inference(resolution,[status(thm)],[c_13054,c_60]) ).
tff(c_13134,plain,
! [W_31,Y_542] :
( equalish(W_31,e_2)
| ~ product(W_31,Y_542,e_1)
| ~ product(e_1,Y_542,e_1) ),
inference(resolution,[status(thm)],[c_13108,c_58]) ).
tff(c_15213,plain,
( equalish(e_1,e_2)
| ~ product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[c_15196,c_13134]) ).
tff(c_15247,plain,
equalish(e_1,e_2),
inference(demodulation,[status(thm),theory(equality)],[c_15196,c_15213]) ).
tff(c_15249,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_40,c_15247]) ).
tff(c_15250,plain,
( product(e_1,e_2,e_2)
| product(e_3,e_1,e_1) ),
inference(splitRight,[status(thm)],[c_15192]) ).
tff(c_15268,plain,
product(e_3,e_1,e_1),
inference(splitLeft,[status(thm)],[c_15250]) ).
tff(c_15488,plain,
! [Y_767] :
( product(e_1,Y_767,e_3)
| ~ product(e_3,Y_767,e_1) ),
inference(resolution,[status(thm)],[c_15268,c_60]) ).
tff(c_15504,plain,
product(e_1,e_1,e_3),
inference(resolution,[status(thm)],[c_15268,c_15488]) ).
tff(c_15537,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[c_15504,c_13025]) ).
tff(c_15582,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_50,c_15537]) ).
tff(c_15583,plain,
product(e_1,e_2,e_2),
inference(splitRight,[status(thm)],[c_15250]) ).
tff(c_13074,plain,
! [W_28] :
( equalish(W_28,e_1)
| ~ product(e_1,W_28,e_2) ),
inference(resolution,[status(thm)],[c_13054,c_56]) ).
tff(c_15593,plain,
equalish(e_2,e_1),
inference(resolution,[status(thm)],[c_15583,c_13074]) ).
tff(c_15617,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_44,c_15593]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP130-3.003 : 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
% 0.15/0.34 % Computer : n001.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Thu Aug 3 22:39:11 EDT 2023
% 0.15/0.34 % CPUTime :
% 11.02/3.51 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.02/3.55
% 11.02/3.55 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.02/3.62
% 11.02/3.62 Inference rules
% 11.02/3.62 ----------------------
% 11.02/3.62 #Ref : 0
% 11.02/3.62 #Sup : 2917
% 11.02/3.62 #Fact : 20
% 11.02/3.62 #Define : 0
% 11.02/3.62 #Split : 59
% 11.02/3.62 #Chain : 0
% 11.02/3.62 #Close : 0
% 11.02/3.62
% 11.02/3.62 Ordering : KBO
% 11.02/3.62
% 11.02/3.62 Simplification rules
% 11.02/3.62 ----------------------
% 11.02/3.62 #Subsume : 995
% 11.02/3.62 #Demod : 3527
% 11.02/3.62 #Tautology : 637
% 11.02/3.62 #SimpNegUnit : 671
% 11.02/3.62 #BackRed : 0
% 11.02/3.62
% 11.02/3.62 #Partial instantiations: 0
% 11.02/3.62 #Strategies tried : 1
% 11.02/3.62
% 11.02/3.62 Timing (in seconds)
% 11.02/3.62 ----------------------
% 11.02/3.62 Preprocessing : 0.47
% 11.02/3.62 Parsing : 0.26
% 11.02/3.62 CNF conversion : 0.03
% 11.02/3.62 Main loop : 2.08
% 11.02/3.62 Inferencing : 0.67
% 11.02/3.62 Reduction : 0.64
% 11.02/3.62 Demodulation : 0.42
% 11.02/3.62 BG Simplification : 0.05
% 11.02/3.62 Subsumption : 0.61
% 11.02/3.62 Abstraction : 0.06
% 11.02/3.62 MUC search : 0.00
% 11.02/3.62 Cooper : 0.00
% 11.02/3.62 Total : 2.67
% 11.02/3.62 Index Insertion : 0.00
% 11.02/3.62 Index Deletion : 0.00
% 11.02/3.62 Index Matching : 0.00
% 11.02/3.62 BG Taut test : 0.00
%------------------------------------------------------------------------------