TSTP Solution File: GRP039-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP039-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:39:42 EDT 2023
% Result : Unsatisfiable 13.62s 4.70s
% Output : CNFRefutation 13.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 26
% Syntax : Number of formulae : 103 ( 50 unt; 10 typ; 0 def)
% Number of atoms : 168 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 150 ( 75 ~; 75 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 5 >; 4 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 121 (; 121 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > subgroup_member > multiply > element_in_O2 > #nlpp > inverse > identity > d > c > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(product,type,
product: ( $i * $i * $i ) > $o ).
tff(inverse,type,
inverse: $i > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(b,type,
b: $i ).
tff(element_in_O2,type,
element_in_O2: ( $i * $i ) > $i ).
tff(d,type,
d: $i ).
tff(identity,type,
identity: $i ).
tff(subgroup_member,type,
subgroup_member: $i > $o ).
tff(c,type,
c: $i ).
tff(f_174,axiom,
~ subgroup_member(d),
file(unknown,unknown) ).
tff(f_172,axiom,
product(a,c,d),
file(unknown,unknown) ).
tff(f_153,axiom,
! [A,B,C] :
( ~ subgroup_member(A)
| ~ subgroup_member(B)
| ~ product(A,B,C)
| subgroup_member(C) ),
file(unknown,unknown) ).
tff(f_162,axiom,
! [A,B] :
( subgroup_member(element_in_O2(A,B))
| subgroup_member(B)
| subgroup_member(A) ),
file(unknown,unknown) ).
tff(f_170,axiom,
subgroup_member(b),
file(unknown,unknown) ).
tff(f_171,axiom,
product(b,inverse(a),c),
file(unknown,unknown) ).
tff(f_79,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file(unknown,unknown) ).
tff(f_70,axiom,
! [X] : product(identity,X,X),
file(unknown,unknown) ).
tff(f_88,axiom,
! [X,Y,Z,W] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ),
file(unknown,unknown) ).
tff(f_74,axiom,
! [X] : product(inverse(X),X,identity),
file(unknown,unknown) ).
tff(f_72,axiom,
! [X] : product(X,identity,X),
file(unknown,unknown) ).
tff(f_110,axiom,
! [W,U,Z,X,Y,V] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) ),
file(unknown,unknown) ).
tff(f_99,axiom,
! [W,U,Z,X,Y,V] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W)
| product(X,V,W) ),
file(unknown,unknown) ).
tff(f_168,axiom,
! [A,B] :
( product(A,element_in_O2(A,B),B)
| subgroup_member(B)
| subgroup_member(A) ),
file(unknown,unknown) ).
tff(f_76,axiom,
! [X] : product(X,inverse(X),identity),
file(unknown,unknown) ).
tff(f_142,axiom,
! [X] :
( ~ subgroup_member(X)
| subgroup_member(inverse(X)) ),
file(unknown,unknown) ).
tff(c_32,plain,
~ subgroup_member(d),
inference(cnfTransformation,[status(thm)],[f_174]) ).
tff(c_30,plain,
product(a,c,d),
inference(cnfTransformation,[status(thm)],[f_172]) ).
tff(c_178,plain,
! [C_53,A_54,B_55] :
( subgroup_member(C_53)
| ~ product(A_54,B_55,C_53)
| ~ subgroup_member(B_55)
| ~ subgroup_member(A_54) ),
inference(cnfTransformation,[status(thm)],[f_153]) ).
tff(c_202,plain,
( subgroup_member(d)
| ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(resolution,[status(thm)],[c_30,c_178]) ).
tff(c_214,plain,
( ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(negUnitSimplification,[status(thm)],[c_32,c_202]) ).
tff(c_215,plain,
~ subgroup_member(a),
inference(splitLeft,[status(thm)],[c_214]) ).
tff(c_22,plain,
! [A_27,B_28] :
( subgroup_member(A_27)
| subgroup_member(B_28)
| subgroup_member(element_in_O2(A_27,B_28)) ),
inference(cnfTransformation,[status(thm)],[f_162]) ).
tff(c_26,plain,
subgroup_member(b),
inference(cnfTransformation,[status(thm)],[f_170]) ).
tff(c_28,plain,
product(b,inverse(a),c),
inference(cnfTransformation,[status(thm)],[f_171]) ).
tff(c_190,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a))
| ~ subgroup_member(b) ),
inference(resolution,[status(thm)],[c_28,c_178]) ).
tff(c_208,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_190]) ).
tff(c_224,plain,
~ subgroup_member(inverse(a)),
inference(splitLeft,[status(thm)],[c_208]) ).
tff(c_10,plain,
! [X_5,Y_6] : product(X_5,Y_6,multiply(X_5,Y_6)),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_2,plain,
! [X_1] : product(identity,X_1,X_1),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_40,plain,
! [Z_40,W_41,X_42,Y_43] :
( ( Z_40 = W_41 )
| ~ product(X_42,Y_43,W_41)
| ~ product(X_42,Y_43,Z_40) ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_116,plain,
! [Z_49,X_50] :
( ( Z_49 = X_50 )
| ~ product(identity,X_50,Z_49) ),
inference(resolution,[status(thm)],[c_2,c_40]) ).
tff(c_137,plain,
! [Y_6] : ( multiply(identity,Y_6) = Y_6 ),
inference(resolution,[status(thm)],[c_10,c_116]) ).
tff(c_6,plain,
! [X_3] : product(inverse(X_3),X_3,identity),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_4,plain,
! [X_2] : product(X_2,identity,X_2),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_229,plain,
! [X_57,Z_61,U_58,W_60,Y_56,V_59] :
( product(U_58,Z_61,W_60)
| ~ product(X_57,V_59,W_60)
| ~ product(Y_56,Z_61,V_59)
| ~ product(X_57,Y_56,U_58) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_755,plain,
! [U_105,Z_106,X_107,Y_108] :
( product(U_105,Z_106,X_107)
| ~ product(Y_108,Z_106,identity)
| ~ product(X_107,Y_108,U_105) ),
inference(resolution,[status(thm)],[c_4,c_229]) ).
tff(c_802,plain,
! [U_112,X_113,X_114] :
( product(U_112,X_113,X_114)
| ~ product(X_114,inverse(X_113),U_112) ),
inference(resolution,[status(thm)],[c_6,c_755]) ).
tff(c_828,plain,
! [X_5,X_113] : product(multiply(X_5,inverse(X_113)),X_113,X_5),
inference(resolution,[status(thm)],[c_10,c_802]) ).
tff(c_310,plain,
! [Z_70,U_68,V_71,W_66,Y_67,X_69] :
( product(X_69,V_71,W_66)
| ~ product(U_68,Z_70,W_66)
| ~ product(Y_67,Z_70,V_71)
| ~ product(X_69,Y_67,U_68) ),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_1274,plain,
! [X_129,V_130,X_131,Y_132] :
( product(X_129,V_130,X_131)
| ~ product(Y_132,X_131,V_130)
| ~ product(X_129,Y_132,identity) ),
inference(resolution,[status(thm)],[c_2,c_310]) ).
tff(c_1463,plain,
! [X_136] :
( product(X_136,d,c)
| ~ product(X_136,a,identity) ),
inference(resolution,[status(thm)],[c_30,c_1274]) ).
tff(c_55,plain,
! [X_5,Y_6,Z_40] :
( ( multiply(X_5,Y_6) = Z_40 )
| ~ product(X_5,Y_6,Z_40) ),
inference(resolution,[status(thm)],[c_10,c_40]) ).
tff(c_1582,plain,
! [X_143] :
( ( multiply(X_143,d) = c )
| ~ product(X_143,a,identity) ),
inference(resolution,[status(thm)],[c_1463,c_55]) ).
tff(c_1590,plain,
multiply(multiply(identity,inverse(a)),d) = c,
inference(resolution,[status(thm)],[c_828,c_1582]) ).
tff(c_1597,plain,
multiply(inverse(a),d) = c,
inference(demodulation,[status(thm),theory(equality)],[c_137,c_1590]) ).
tff(c_868,plain,
! [X_115] : product(identity,X_115,inverse(inverse(X_115))),
inference(resolution,[status(thm)],[c_6,c_802]) ).
tff(c_891,plain,
! [X_115] : ( inverse(inverse(X_115)) = multiply(identity,X_115) ),
inference(resolution,[status(thm)],[c_868,c_55]) ).
tff(c_925,plain,
! [X_115] : ( inverse(inverse(X_115)) = X_115 ),
inference(demodulation,[status(thm),theory(equality)],[c_137,c_891]) ).
tff(c_1035,plain,
! [X_123,X_124] : product(multiply(X_123,inverse(X_124)),X_124,X_123),
inference(resolution,[status(thm)],[c_10,c_802]) ).
tff(c_1131,plain,
! [X_125,X_126] : ( multiply(multiply(X_125,inverse(X_126)),X_126) = X_125 ),
inference(resolution,[status(thm)],[c_1035,c_55]) ).
tff(c_1162,plain,
! [X_125,X_115] : ( multiply(multiply(X_125,X_115),inverse(X_115)) = X_125 ),
inference(superposition,[status(thm),theory(equality)],[c_925,c_1131]) ).
tff(c_1602,plain,
multiply(c,inverse(d)) = inverse(a),
inference(superposition,[status(thm),theory(equality)],[c_1597,c_1162]) ).
tff(c_204,plain,
! [X_5,Y_6] :
( subgroup_member(multiply(X_5,Y_6))
| ~ subgroup_member(Y_6)
| ~ subgroup_member(X_5) ),
inference(resolution,[status(thm)],[c_10,c_178]) ).
tff(c_1658,plain,
( subgroup_member(inverse(a))
| ~ subgroup_member(inverse(d))
| ~ subgroup_member(c) ),
inference(superposition,[status(thm),theory(equality)],[c_1602,c_204]) ).
tff(c_1668,plain,
( ~ subgroup_member(inverse(d))
| ~ subgroup_member(c) ),
inference(negUnitSimplification,[status(thm)],[c_224,c_1658]) ).
tff(c_1699,plain,
~ subgroup_member(c),
inference(splitLeft,[status(thm)],[c_1668]) ).
tff(c_1611,plain,
product(inverse(a),d,c),
inference(superposition,[status(thm),theory(equality)],[c_1597,c_10]) ).
tff(c_24,plain,
! [A_29,B_30] :
( subgroup_member(A_29)
| subgroup_member(B_30)
| product(A_29,element_in_O2(A_29,B_30),B_30) ),
inference(cnfTransformation,[status(thm)],[f_168]) ).
tff(c_1940,plain,
! [U_155,Z_156,Y_157,X_158] :
( product(U_155,Z_156,identity)
| ~ product(Y_157,Z_156,X_158)
| ~ product(inverse(X_158),Y_157,U_155) ),
inference(resolution,[status(thm)],[c_6,c_229]) ).
tff(c_18741,plain,
! [U_492,A_493,B_494] :
( product(U_492,element_in_O2(A_493,B_494),identity)
| ~ product(inverse(B_494),A_493,U_492)
| subgroup_member(A_493)
| subgroup_member(B_494) ),
inference(resolution,[status(thm)],[c_24,c_1940]) ).
tff(c_18874,plain,
( product(c,element_in_O2(d,a),identity)
| subgroup_member(d)
| subgroup_member(a) ),
inference(resolution,[status(thm)],[c_1611,c_18741]) ).
tff(c_18991,plain,
product(c,element_in_O2(d,a),identity),
inference(negUnitSimplification,[status(thm)],[c_215,c_32,c_18874]) ).
tff(c_62,plain,
! [Z_44,X_45] :
( ( Z_44 = X_45 )
| ~ product(X_45,identity,Z_44) ),
inference(resolution,[status(thm)],[c_4,c_40]) ).
tff(c_78,plain,
! [X_5] : ( multiply(X_5,identity) = X_5 ),
inference(resolution,[status(thm)],[c_10,c_62]) ).
tff(c_8,plain,
! [X_4] : product(X_4,inverse(X_4),identity),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_2932,plain,
! [Y_199,Z_196,X_198,Y_195,U_197] :
( product(U_197,Z_196,multiply(X_198,Y_195))
| ~ product(Y_199,Z_196,Y_195)
| ~ product(X_198,Y_199,U_197) ),
inference(resolution,[status(thm)],[c_10,c_229]) ).
tff(c_2974,plain,
! [U_197,X_4,X_198] :
( product(U_197,inverse(X_4),multiply(X_198,identity))
| ~ product(X_198,X_4,U_197) ),
inference(resolution,[status(thm)],[c_8,c_2932]) ).
tff(c_3262,plain,
! [U_210,X_211,X_212] :
( product(U_210,inverse(X_211),X_212)
| ~ product(X_212,X_211,U_210) ),
inference(demodulation,[status(thm),theory(equality)],[c_78,c_2974]) ).
tff(c_60,plain,
! [Z_40,X_1] :
( ( Z_40 = X_1 )
| ~ product(identity,X_1,Z_40) ),
inference(resolution,[status(thm)],[c_2,c_40]) ).
tff(c_3380,plain,
! [X_211,X_212] :
( ( inverse(X_211) = X_212 )
| ~ product(X_212,X_211,identity) ),
inference(resolution,[status(thm)],[c_3262,c_60]) ).
tff(c_19040,plain,
inverse(element_in_O2(d,a)) = c,
inference(resolution,[status(thm)],[c_18991,c_3380]) ).
tff(c_18,plain,
! [X_23] :
( subgroup_member(inverse(X_23))
| ~ subgroup_member(X_23) ),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_19232,plain,
( subgroup_member(c)
| ~ subgroup_member(element_in_O2(d,a)) ),
inference(superposition,[status(thm),theory(equality)],[c_19040,c_18]) ).
tff(c_19247,plain,
~ subgroup_member(element_in_O2(d,a)),
inference(negUnitSimplification,[status(thm)],[c_1699,c_19232]) ).
tff(c_19252,plain,
( subgroup_member(d)
| subgroup_member(a) ),
inference(resolution,[status(thm)],[c_22,c_19247]) ).
tff(c_19256,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_215,c_32,c_19252]) ).
tff(c_19258,plain,
subgroup_member(c),
inference(splitRight,[status(thm)],[c_1668]) ).
tff(c_831,plain,
product(c,a,b),
inference(resolution,[status(thm)],[c_28,c_802]) ).
tff(c_19703,plain,
! [X_511] :
( product(X_511,b,a)
| ~ product(X_511,c,identity) ),
inference(resolution,[status(thm)],[c_831,c_1274]) ).
tff(c_19710,plain,
product(multiply(identity,inverse(c)),b,a),
inference(resolution,[status(thm)],[c_828,c_19703]) ).
tff(c_19717,plain,
product(inverse(c),b,a),
inference(demodulation,[status(thm),theory(equality)],[c_137,c_19710]) ).
tff(c_20,plain,
! [C_26,A_24,B_25] :
( subgroup_member(C_26)
| ~ product(A_24,B_25,C_26)
| ~ subgroup_member(B_25)
| ~ subgroup_member(A_24) ),
inference(cnfTransformation,[status(thm)],[f_153]) ).
tff(c_19736,plain,
( subgroup_member(a)
| ~ subgroup_member(b)
| ~ subgroup_member(inverse(c)) ),
inference(resolution,[status(thm)],[c_19717,c_20]) ).
tff(c_19748,plain,
( subgroup_member(a)
| ~ subgroup_member(inverse(c)) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_19736]) ).
tff(c_19749,plain,
~ subgroup_member(inverse(c)),
inference(negUnitSimplification,[status(thm)],[c_215,c_19748]) ).
tff(c_19789,plain,
~ subgroup_member(c),
inference(resolution,[status(thm)],[c_18,c_19749]) ).
tff(c_19793,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_19258,c_19789]) ).
tff(c_19795,plain,
subgroup_member(a),
inference(splitRight,[status(thm)],[c_214]) ).
tff(c_19794,plain,
~ subgroup_member(c),
inference(splitRight,[status(thm)],[c_214]) ).
tff(c_19829,plain,
~ subgroup_member(inverse(a)),
inference(negUnitSimplification,[status(thm)],[c_19794,c_208]) ).
tff(c_19832,plain,
~ subgroup_member(a),
inference(resolution,[status(thm)],[c_18,c_19829]) ).
tff(c_19836,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_19795,c_19832]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : GRP039-1 : TPTP v8.1.2. Released v1.0.0.
% 0.09/0.15 % 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
% 0.15/0.37 % Computer : n024.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu Aug 3 22:01:00 EDT 2023
% 0.15/0.37 % CPUTime :
% 13.62/4.70 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.62/4.72
% 13.62/4.72 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.91/4.76
% 13.91/4.76 Inference rules
% 13.91/4.76 ----------------------
% 13.91/4.76 #Ref : 0
% 13.91/4.76 #Sup : 4690
% 13.91/4.76 #Fact : 0
% 13.91/4.76 #Define : 0
% 13.91/4.76 #Split : 48
% 13.91/4.76 #Chain : 0
% 13.91/4.76 #Close : 0
% 13.91/4.76
% 13.91/4.76 Ordering : KBO
% 13.91/4.76
% 13.91/4.76 Simplification rules
% 13.91/4.76 ----------------------
% 13.91/4.76 #Subsume : 1005
% 13.91/4.76 #Demod : 2120
% 13.91/4.76 #Tautology : 1170
% 13.91/4.76 #SimpNegUnit : 221
% 13.91/4.76 #BackRed : 9
% 13.91/4.76
% 13.91/4.76 #Partial instantiations: 0
% 13.91/4.76 #Strategies tried : 1
% 13.91/4.76
% 13.91/4.76 Timing (in seconds)
% 13.91/4.76 ----------------------
% 13.91/4.76 Preprocessing : 0.44
% 13.91/4.76 Parsing : 0.24
% 13.91/4.76 CNF conversion : 0.02
% 13.91/4.76 Main loop : 3.18
% 13.91/4.76 Inferencing : 0.85
% 13.91/4.76 Reduction : 1.02
% 13.91/4.76 Demodulation : 0.69
% 13.91/4.76 BG Simplification : 0.06
% 13.91/4.76 Subsumption : 0.98
% 13.91/4.76 Abstraction : 0.06
% 13.91/4.76 MUC search : 0.00
% 13.91/4.76 Cooper : 0.00
% 13.91/4.76 Total : 3.68
% 13.91/4.76 Index Insertion : 0.00
% 13.91/4.76 Index Deletion : 0.00
% 13.91/4.76 Index Matching : 0.00
% 13.91/4.76 BG Taut test : 0.00
%------------------------------------------------------------------------------