TSTP Solution File: GRP040-4 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP040-4 : 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 : n006.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 10:39:43 EDT 2023
% Result : Unsatisfiable 6.54s 2.63s
% Output : CNFRefutation 6.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 29
% Syntax : Number of formulae : 76 ( 33 unt; 10 typ; 0 def)
% Number of atoms : 130 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 120 ( 56 ~; 64 |; 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 : 108 (; 108 !; 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_168,axiom,
subgroup_member(b),
file(unknown,unknown) ).
tff(f_136,axiom,
! [A] :
( ~ subgroup_member(A)
| subgroup_member(inverse(A)) ),
file(unknown,unknown) ).
tff(f_167,axiom,
~ subgroup_member(a),
file(unknown,unknown) ).
tff(f_170,axiom,
~ subgroup_member(d),
file(unknown,unknown) ).
tff(f_60,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file(unknown,unknown) ).
tff(f_55,axiom,
! [X] : product(inverse(X),X,identity),
file(unknown,unknown) ).
tff(f_53,axiom,
! [X] : product(X,identity,X),
file(unknown,unknown) ).
tff(f_91,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_172,axiom,
product(a,c,d),
file(unknown,unknown) ).
tff(f_152,axiom,
! [A,B,C,D] :
( ~ product(A,B,C)
| ~ product(D,B,C)
| ( D = A ) ),
file(unknown,unknown) ).
tff(f_165,axiom,
! [A,B] :
( product(A,element_in_O2(A,B),B)
| subgroup_member(B)
| subgroup_member(A) ),
file(unknown,unknown) ).
tff(f_144,axiom,
! [A,B,C,D] :
( ~ product(A,B,C)
| ~ product(A,D,C)
| ( D = B ) ),
file(unknown,unknown) ).
tff(f_159,axiom,
! [A,B] :
( subgroup_member(element_in_O2(A,B))
| subgroup_member(B)
| subgroup_member(A) ),
file(unknown,unknown) ).
tff(f_171,axiom,
product(b,inverse(a),c),
file(unknown,unknown) ).
tff(f_57,axiom,
! [X] : product(X,inverse(X),identity),
file(unknown,unknown) ).
tff(f_80,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_174,axiom,
! [A] : ( inverse(inverse(A)) = A ),
file(unknown,unknown) ).
tff(f_69,axiom,
! [X,Y,Z,W] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ),
file(unknown,unknown) ).
tff(f_127,axiom,
! [A,B,C] :
( ~ subgroup_member(A)
| ~ subgroup_member(B)
| ~ product(A,inverse(B),C)
| subgroup_member(C) ),
file(unknown,unknown) ).
tff(c_34,plain,
subgroup_member(b),
inference(cnfTransformation,[status(thm)],[f_168]) ).
tff(c_22,plain,
! [A_26] :
( subgroup_member(inverse(A_26))
| ~ subgroup_member(A_26) ),
inference(cnfTransformation,[status(thm)],[f_136]) ).
tff(c_32,plain,
~ subgroup_member(a),
inference(cnfTransformation,[status(thm)],[f_167]) ).
tff(c_36,plain,
~ subgroup_member(d),
inference(cnfTransformation,[status(thm)],[f_170]) ).
tff(c_10,plain,
! [X_5,Y_6] : product(X_5,Y_6,multiply(X_5,Y_6)),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_6,plain,
! [X_3] : product(inverse(X_3),X_3,identity),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_4,plain,
! [X_2] : product(X_2,identity,X_2),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_494,plain,
! [V_89,X_87,U_88,W_90,Z_91,Y_86] :
( product(U_88,Z_91,W_90)
| ~ product(X_87,V_89,W_90)
| ~ product(Y_86,Z_91,V_89)
| ~ product(X_87,Y_86,U_88) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_1878,plain,
! [U_171,Z_172,X_173,Y_174] :
( product(U_171,Z_172,X_173)
| ~ product(Y_174,Z_172,identity)
| ~ product(X_173,Y_174,U_171) ),
inference(resolution,[status(thm)],[c_4,c_494]) ).
tff(c_2088,plain,
! [U_180,X_181,X_182] :
( product(U_180,X_181,X_182)
| ~ product(X_182,inverse(X_181),U_180) ),
inference(resolution,[status(thm)],[c_6,c_1878]) ).
tff(c_2231,plain,
! [X_189,X_190] : product(multiply(X_189,inverse(X_190)),X_190,X_189),
inference(resolution,[status(thm)],[c_10,c_2088]) ).
tff(c_40,plain,
product(a,c,d),
inference(cnfTransformation,[status(thm)],[f_172]) ).
tff(c_86,plain,
! [D_51,A_52,B_53,C_54] :
( ( D_51 = A_52 )
| ~ product(D_51,B_53,C_54)
| ~ product(A_52,B_53,C_54) ),
inference(cnfTransformation,[status(thm)],[f_152]) ).
tff(c_106,plain,
! [A_52] :
( ( a = A_52 )
| ~ product(A_52,c,d) ),
inference(resolution,[status(thm)],[c_40,c_86]) ).
tff(c_2377,plain,
multiply(d,inverse(c)) = a,
inference(resolution,[status(thm)],[c_2231,c_106]) ).
tff(c_2407,plain,
product(d,inverse(c),a),
inference(superposition,[status(thm),theory(equality)],[c_2377,c_10]) ).
tff(c_30,plain,
! [A_37,B_38] :
( subgroup_member(A_37)
| subgroup_member(B_38)
| product(A_37,element_in_O2(A_37,B_38),B_38) ),
inference(cnfTransformation,[status(thm)],[f_165]) ).
tff(c_244,plain,
! [D_67,B_68,A_69,C_70] :
( ( D_67 = B_68 )
| ~ product(A_69,D_67,C_70)
| ~ product(A_69,B_68,C_70) ),
inference(cnfTransformation,[status(thm)],[f_144]) ).
tff(c_261,plain,
! [A_37,B_38,B_68] :
( ( element_in_O2(A_37,B_38) = B_68 )
| ~ product(A_37,B_68,B_38)
| subgroup_member(A_37)
| subgroup_member(B_38) ),
inference(resolution,[status(thm)],[c_30,c_244]) ).
tff(c_2428,plain,
( ( element_in_O2(d,a) = inverse(c) )
| subgroup_member(d)
| subgroup_member(a) ),
inference(resolution,[status(thm)],[c_2407,c_261]) ).
tff(c_2452,plain,
element_in_O2(d,a) = inverse(c),
inference(negUnitSimplification,[status(thm)],[c_32,c_36,c_2428]) ).
tff(c_28,plain,
! [A_35,B_36] :
( subgroup_member(A_35)
| subgroup_member(B_36)
| subgroup_member(element_in_O2(A_35,B_36)) ),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_2483,plain,
( subgroup_member(d)
| subgroup_member(a)
| subgroup_member(inverse(c)) ),
inference(superposition,[status(thm),theory(equality)],[c_2452,c_28]) ).
tff(c_2492,plain,
subgroup_member(inverse(c)),
inference(negUnitSimplification,[status(thm)],[c_32,c_36,c_2483]) ).
tff(c_2121,plain,
! [X_5,X_181] : product(multiply(X_5,inverse(X_181)),X_181,X_5),
inference(resolution,[status(thm)],[c_10,c_2088]) ).
tff(c_38,plain,
product(b,inverse(a),c),
inference(cnfTransformation,[status(thm)],[f_171]) ).
tff(c_8,plain,
! [X_4] : product(X_4,inverse(X_4),identity),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_607,plain,
! [Z_101,Y_98,X_100,W_97,U_99,V_102] :
( product(X_100,V_102,W_97)
| ~ product(U_99,Z_101,W_97)
| ~ product(Y_98,Z_101,V_102)
| ~ product(X_100,Y_98,U_99) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_3613,plain,
! [X_227,V_228,Y_229,X_230] :
( product(X_227,V_228,identity)
| ~ product(Y_229,inverse(X_230),V_228)
| ~ product(X_227,Y_229,X_230) ),
inference(resolution,[status(thm)],[c_8,c_607]) ).
tff(c_3865,plain,
! [X_238] :
( product(X_238,c,identity)
| ~ product(X_238,b,a) ),
inference(resolution,[status(thm)],[c_38,c_3613]) ).
tff(c_263,plain,
! [X_4,B_68] :
( ( inverse(X_4) = B_68 )
| ~ product(X_4,B_68,identity) ),
inference(resolution,[status(thm)],[c_8,c_244]) ).
tff(c_3972,plain,
! [X_239] :
( ( inverse(X_239) = c )
| ~ product(X_239,b,a) ),
inference(resolution,[status(thm)],[c_3865,c_263]) ).
tff(c_3977,plain,
inverse(multiply(a,inverse(b))) = c,
inference(resolution,[status(thm)],[c_2121,c_3972]) ).
tff(c_42,plain,
! [A_39] : ( inverse(inverse(A_39)) = A_39 ),
inference(cnfTransformation,[status(thm)],[f_174]) ).
tff(c_4132,plain,
multiply(a,inverse(b)) = inverse(c),
inference(superposition,[status(thm),theory(equality)],[c_3977,c_42]) ).
tff(c_318,plain,
! [Z_74,W_75,X_76,Y_77] :
( ( Z_74 = W_75 )
| ~ product(X_76,Y_77,W_75)
| ~ product(X_76,Y_77,Z_74) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_336,plain,
! [X_5,Y_6,Z_74] :
( ( multiply(X_5,Y_6) = Z_74 )
| ~ product(X_5,Y_6,Z_74) ),
inference(resolution,[status(thm)],[c_10,c_318]) ).
tff(c_2359,plain,
! [X_189,X_190] : ( multiply(multiply(X_189,inverse(X_190)),X_190) = X_189 ),
inference(resolution,[status(thm)],[c_2231,c_336]) ).
tff(c_4155,plain,
multiply(inverse(c),b) = a,
inference(superposition,[status(thm),theory(equality)],[c_4132,c_2359]) ).
tff(c_414,plain,
! [C_82,A_83,B_84] :
( subgroup_member(C_82)
| ~ product(A_83,inverse(B_84),C_82)
| ~ subgroup_member(B_84)
| ~ subgroup_member(A_83) ),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_884,plain,
! [X_122,B_123] :
( subgroup_member(multiply(X_122,inverse(B_123)))
| ~ subgroup_member(B_123)
| ~ subgroup_member(X_122) ),
inference(resolution,[status(thm)],[c_10,c_414]) ).
tff(c_904,plain,
! [X_122,A_39] :
( subgroup_member(multiply(X_122,A_39))
| ~ subgroup_member(inverse(A_39))
| ~ subgroup_member(X_122) ),
inference(superposition,[status(thm),theory(equality)],[c_42,c_884]) ).
tff(c_4262,plain,
( subgroup_member(a)
| ~ subgroup_member(inverse(b))
| ~ subgroup_member(inverse(c)) ),
inference(superposition,[status(thm),theory(equality)],[c_4155,c_904]) ).
tff(c_4277,plain,
( subgroup_member(a)
| ~ subgroup_member(inverse(b)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2492,c_4262]) ).
tff(c_4278,plain,
~ subgroup_member(inverse(b)),
inference(negUnitSimplification,[status(thm)],[c_32,c_4277]) ).
tff(c_4286,plain,
~ subgroup_member(b),
inference(resolution,[status(thm)],[c_22,c_4278]) ).
tff(c_4291,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_34,c_4286]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP040-4 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 22:07:44 EDT 2023
% 0.13/0.35 % CPUTime :
% 6.54/2.63 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.54/2.64
% 6.54/2.64 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.54/2.67
% 6.54/2.67 Inference rules
% 6.54/2.67 ----------------------
% 6.54/2.67 #Ref : 0
% 6.54/2.67 #Sup : 997
% 6.54/2.67 #Fact : 0
% 6.54/2.67 #Define : 0
% 6.54/2.67 #Split : 15
% 6.54/2.67 #Chain : 0
% 6.54/2.67 #Close : 0
% 6.54/2.67
% 6.54/2.67 Ordering : KBO
% 6.54/2.67
% 6.54/2.67 Simplification rules
% 6.54/2.67 ----------------------
% 6.54/2.67 #Subsume : 193
% 6.54/2.67 #Demod : 498
% 6.54/2.67 #Tautology : 379
% 6.54/2.67 #SimpNegUnit : 39
% 6.54/2.67 #BackRed : 2
% 6.54/2.67
% 6.54/2.67 #Partial instantiations: 0
% 6.54/2.68 #Strategies tried : 1
% 6.54/2.68
% 6.54/2.68 Timing (in seconds)
% 6.54/2.68 ----------------------
% 6.54/2.68 Preprocessing : 0.51
% 6.54/2.68 Parsing : 0.26
% 6.54/2.68 CNF conversion : 0.03
% 6.54/2.68 Main loop : 1.06
% 6.54/2.68 Inferencing : 0.40
% 6.54/2.68 Reduction : 0.31
% 6.54/2.68 Demodulation : 0.21
% 6.54/2.68 BG Simplification : 0.03
% 6.54/2.68 Subsumption : 0.25
% 6.54/2.68 Abstraction : 0.04
% 6.54/2.68 MUC search : 0.00
% 6.54/2.68 Cooper : 0.00
% 6.54/2.68 Total : 1.63
% 6.54/2.68 Index Insertion : 0.00
% 6.54/2.68 Index Deletion : 0.00
% 6.54/2.68 Index Matching : 0.00
% 6.54/2.68 BG Taut test : 0.00
%------------------------------------------------------------------------------