TSTP Solution File: GRP039-4 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP039-4 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n032.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 12.14s 4.28s
% Output : CNFRefutation 12.45s
% 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_179,axiom,
~ subgroup_member(d),
file(unknown,unknown) ).
tff(f_177,axiom,
product(a,c,d),
file(unknown,unknown) ).
tff(f_156,axiom,
! [A,B,C] :
( ~ subgroup_member(A)
| ~ subgroup_member(B)
| ~ product(A,B,C)
| subgroup_member(C) ),
file(unknown,unknown) ).
tff(f_167,axiom,
! [A,B] :
( subgroup_member(element_in_O2(A,B))
| subgroup_member(B)
| subgroup_member(A) ),
file(unknown,unknown) ).
tff(f_175,axiom,
subgroup_member(b),
file(unknown,unknown) ).
tff(f_176,axiom,
product(b,inverse(a),c),
file(unknown,unknown) ).
tff(f_82,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file(unknown,unknown) ).
tff(f_73,axiom,
! [X] : product(identity,X,X),
file(unknown,unknown) ).
tff(f_91,axiom,
! [X,Y,Z,W] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ),
file(unknown,unknown) ).
tff(f_77,axiom,
! [X] : product(inverse(X),X,identity),
file(unknown,unknown) ).
tff(f_75,axiom,
! [X] : product(X,identity,X),
file(unknown,unknown) ).
tff(f_113,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_102,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_173,axiom,
! [A,B] :
( product(A,element_in_O2(A,B),B)
| subgroup_member(B)
| subgroup_member(A) ),
file(unknown,unknown) ).
tff(f_79,axiom,
! [X] : product(X,inverse(X),identity),
file(unknown,unknown) ).
tff(f_145,axiom,
! [X] :
( ~ subgroup_member(X)
| subgroup_member(inverse(X)) ),
file(unknown,unknown) ).
tff(c_34,plain,
~ subgroup_member(d),
inference(cnfTransformation,[status(thm)],[f_179]) ).
tff(c_32,plain,
product(a,c,d),
inference(cnfTransformation,[status(thm)],[f_177]) ).
tff(c_42,plain,
! [C_40,A_41,B_42] :
( subgroup_member(C_40)
| ~ product(A_41,B_42,C_40)
| ~ subgroup_member(B_42)
| ~ subgroup_member(A_41) ),
inference(cnfTransformation,[status(thm)],[f_156]) ).
tff(c_60,plain,
( subgroup_member(d)
| ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(resolution,[status(thm)],[c_32,c_42]) ).
tff(c_77,plain,
( ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(negUnitSimplification,[status(thm)],[c_34,c_60]) ).
tff(c_81,plain,
~ subgroup_member(a),
inference(splitLeft,[status(thm)],[c_77]) ).
tff(c_24,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_167]) ).
tff(c_28,plain,
subgroup_member(b),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_30,plain,
product(b,inverse(a),c),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_48,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a))
| ~ subgroup_member(b) ),
inference(resolution,[status(thm)],[c_30,c_42]) ).
tff(c_67,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_48]) ).
tff(c_87,plain,
~ subgroup_member(inverse(a)),
inference(splitLeft,[status(thm)],[c_67]) ).
tff(c_10,plain,
! [X_5,Y_6] : product(X_5,Y_6,multiply(X_5,Y_6)),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_2,plain,
! [X_1] : product(identity,X_1,X_1),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_93,plain,
! [Z_47,W_48,X_49,Y_50] :
( ( Z_47 = W_48 )
| ~ product(X_49,Y_50,W_48)
| ~ product(X_49,Y_50,Z_47) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_175,plain,
! [Z_54,X_55] :
( ( Z_54 = X_55 )
| ~ product(identity,X_55,Z_54) ),
inference(resolution,[status(thm)],[c_2,c_93]) ).
tff(c_197,plain,
! [Y_6] : ( multiply(identity,Y_6) = Y_6 ),
inference(resolution,[status(thm)],[c_10,c_175]) ).
tff(c_6,plain,
! [X_3] : product(inverse(X_3),X_3,identity),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_4,plain,
! [X_2] : product(X_2,identity,X_2),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_291,plain,
! [U_67,V_68,Z_70,W_69,Y_65,X_66] :
( product(U_67,Z_70,W_69)
| ~ product(X_66,V_68,W_69)
| ~ product(Y_65,Z_70,V_68)
| ~ product(X_66,Y_65,U_67) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_492,plain,
! [U_82,Z_83,X_84,Y_85] :
( product(U_82,Z_83,X_84)
| ~ product(Y_85,Z_83,identity)
| ~ product(X_84,Y_85,U_82) ),
inference(resolution,[status(thm)],[c_4,c_291]) ).
tff(c_532,plain,
! [U_88,X_89,X_90] :
( product(U_88,X_89,X_90)
| ~ product(X_90,inverse(X_89),U_88) ),
inference(resolution,[status(thm)],[c_6,c_492]) ).
tff(c_554,plain,
! [X_5,X_89] : product(multiply(X_5,inverse(X_89)),X_89,X_5),
inference(resolution,[status(thm)],[c_10,c_532]) ).
tff(c_232,plain,
! [X_60,Y_58,W_57,Z_61,V_62,U_59] :
( product(X_60,V_62,W_57)
| ~ product(U_59,Z_61,W_57)
| ~ product(Y_58,Z_61,V_62)
| ~ product(X_60,Y_58,U_59) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_1332,plain,
! [X_124,V_125,X_126,Y_127] :
( product(X_124,V_125,X_126)
| ~ product(Y_127,X_126,V_125)
| ~ product(X_124,Y_127,identity) ),
inference(resolution,[status(thm)],[c_2,c_232]) ).
tff(c_1407,plain,
! [X_129] :
( product(X_129,d,c)
| ~ product(X_129,a,identity) ),
inference(resolution,[status(thm)],[c_32,c_1332]) ).
tff(c_111,plain,
! [X_5,Y_6,Z_47] :
( ( multiply(X_5,Y_6) = Z_47 )
| ~ product(X_5,Y_6,Z_47) ),
inference(resolution,[status(thm)],[c_10,c_93]) ).
tff(c_1546,plain,
! [X_137] :
( ( multiply(X_137,d) = c )
| ~ product(X_137,a,identity) ),
inference(resolution,[status(thm)],[c_1407,c_111]) ).
tff(c_1550,plain,
multiply(multiply(identity,inverse(a)),d) = c,
inference(resolution,[status(thm)],[c_554,c_1546]) ).
tff(c_1556,plain,
multiply(inverse(a),d) = c,
inference(demodulation,[status(thm),theory(equality)],[c_197,c_1550]) ).
tff(c_591,plain,
! [X_91] : product(identity,X_91,inverse(inverse(X_91))),
inference(resolution,[status(thm)],[c_6,c_532]) ).
tff(c_601,plain,
! [X_91] : ( inverse(inverse(X_91)) = multiply(identity,X_91) ),
inference(resolution,[status(thm)],[c_591,c_111]) ).
tff(c_629,plain,
! [X_91] : ( inverse(inverse(X_91)) = X_91 ),
inference(demodulation,[status(thm),theory(equality)],[c_197,c_601]) ).
tff(c_738,plain,
! [X_99,X_100] : product(multiply(X_99,inverse(X_100)),X_100,X_99),
inference(resolution,[status(thm)],[c_10,c_532]) ).
tff(c_809,plain,
! [X_101,X_102] : ( multiply(multiply(X_101,inverse(X_102)),X_102) = X_101 ),
inference(resolution,[status(thm)],[c_738,c_111]) ).
tff(c_840,plain,
! [X_101,X_91] : ( multiply(multiply(X_101,X_91),inverse(X_91)) = X_101 ),
inference(superposition,[status(thm),theory(equality)],[c_629,c_809]) ).
tff(c_1561,plain,
multiply(c,inverse(d)) = inverse(a),
inference(superposition,[status(thm),theory(equality)],[c_1556,c_840]) ).
tff(c_64,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_42]) ).
tff(c_1614,plain,
( subgroup_member(inverse(a))
| ~ subgroup_member(inverse(d))
| ~ subgroup_member(c) ),
inference(superposition,[status(thm),theory(equality)],[c_1561,c_64]) ).
tff(c_1624,plain,
( ~ subgroup_member(inverse(d))
| ~ subgroup_member(c) ),
inference(negUnitSimplification,[status(thm)],[c_87,c_1614]) ).
tff(c_1659,plain,
~ subgroup_member(c),
inference(splitLeft,[status(thm)],[c_1624]) ).
tff(c_1570,plain,
product(inverse(a),d,c),
inference(superposition,[status(thm),theory(equality)],[c_1556,c_10]) ).
tff(c_26,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_173]) ).
tff(c_2092,plain,
! [U_159,Z_160,Y_161,X_162] :
( product(U_159,Z_160,identity)
| ~ product(Y_161,Z_160,X_162)
| ~ product(inverse(X_162),Y_161,U_159) ),
inference(resolution,[status(thm)],[c_6,c_291]) ).
tff(c_18304,plain,
! [U_489,A_490,B_491] :
( product(U_489,element_in_O2(A_490,B_491),identity)
| ~ product(inverse(B_491),A_490,U_489)
| subgroup_member(A_490)
| subgroup_member(B_491) ),
inference(resolution,[status(thm)],[c_26,c_2092]) ).
tff(c_18434,plain,
( product(c,element_in_O2(d,a),identity)
| subgroup_member(d)
| subgroup_member(a) ),
inference(resolution,[status(thm)],[c_1570,c_18304]) ).
tff(c_18549,plain,
product(c,element_in_O2(d,a),identity),
inference(negUnitSimplification,[status(thm)],[c_81,c_34,c_18434]) ).
tff(c_118,plain,
! [Z_51,X_52] :
( ( Z_51 = X_52 )
| ~ product(X_52,identity,Z_51) ),
inference(resolution,[status(thm)],[c_4,c_93]) ).
tff(c_134,plain,
! [X_5] : ( multiply(X_5,identity) = X_5 ),
inference(resolution,[status(thm)],[c_10,c_118]) ).
tff(c_8,plain,
! [X_4] : product(X_4,inverse(X_4),identity),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_3011,plain,
! [Y_205,U_208,Y_204,Z_206,X_207] :
( product(U_208,Z_206,multiply(X_207,Y_204))
| ~ product(Y_205,Z_206,Y_204)
| ~ product(X_207,Y_205,U_208) ),
inference(resolution,[status(thm)],[c_10,c_291]) ).
tff(c_3055,plain,
! [U_208,X_4,X_207] :
( product(U_208,inverse(X_4),multiply(X_207,identity))
| ~ product(X_207,X_4,U_208) ),
inference(resolution,[status(thm)],[c_8,c_3011]) ).
tff(c_3340,plain,
! [U_215,X_216,X_217] :
( product(U_215,inverse(X_216),X_217)
| ~ product(X_217,X_216,U_215) ),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_3055]) ).
tff(c_117,plain,
! [Z_47,X_1] :
( ( Z_47 = X_1 )
| ~ product(identity,X_1,Z_47) ),
inference(resolution,[status(thm)],[c_2,c_93]) ).
tff(c_3476,plain,
! [X_216,X_217] :
( ( inverse(X_216) = X_217 )
| ~ product(X_217,X_216,identity) ),
inference(resolution,[status(thm)],[c_3340,c_117]) ).
tff(c_18601,plain,
inverse(element_in_O2(d,a)) = c,
inference(resolution,[status(thm)],[c_18549,c_3476]) ).
tff(c_18,plain,
! [X_23] :
( subgroup_member(inverse(X_23))
| ~ subgroup_member(X_23) ),
inference(cnfTransformation,[status(thm)],[f_145]) ).
tff(c_18818,plain,
( subgroup_member(c)
| ~ subgroup_member(element_in_O2(d,a)) ),
inference(superposition,[status(thm),theory(equality)],[c_18601,c_18]) ).
tff(c_18840,plain,
~ subgroup_member(element_in_O2(d,a)),
inference(negUnitSimplification,[status(thm)],[c_1659,c_18818]) ).
tff(c_18845,plain,
( subgroup_member(d)
| subgroup_member(a) ),
inference(resolution,[status(thm)],[c_24,c_18840]) ).
tff(c_18849,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_81,c_34,c_18845]) ).
tff(c_18851,plain,
subgroup_member(c),
inference(splitRight,[status(thm)],[c_1624]) ).
tff(c_555,plain,
product(c,a,b),
inference(resolution,[status(thm)],[c_30,c_532]) ).
tff(c_18989,plain,
! [X_500] :
( product(X_500,b,a)
| ~ product(X_500,c,identity) ),
inference(resolution,[status(thm)],[c_555,c_1332]) ).
tff(c_18993,plain,
product(multiply(identity,inverse(c)),b,a),
inference(resolution,[status(thm)],[c_554,c_18989]) ).
tff(c_18999,plain,
product(inverse(c),b,a),
inference(demodulation,[status(thm),theory(equality)],[c_197,c_18993]) ).
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_156]) ).
tff(c_19016,plain,
( subgroup_member(a)
| ~ subgroup_member(b)
| ~ subgroup_member(inverse(c)) ),
inference(resolution,[status(thm)],[c_18999,c_20]) ).
tff(c_19025,plain,
( subgroup_member(a)
| ~ subgroup_member(inverse(c)) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_19016]) ).
tff(c_19026,plain,
~ subgroup_member(inverse(c)),
inference(negUnitSimplification,[status(thm)],[c_81,c_19025]) ).
tff(c_19091,plain,
~ subgroup_member(c),
inference(resolution,[status(thm)],[c_18,c_19026]) ).
tff(c_19095,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_18851,c_19091]) ).
tff(c_19097,plain,
subgroup_member(a),
inference(splitRight,[status(thm)],[c_77]) ).
tff(c_19096,plain,
~ subgroup_member(c),
inference(splitRight,[status(thm)],[c_77]) ).
tff(c_19103,plain,
~ subgroup_member(inverse(a)),
inference(negUnitSimplification,[status(thm)],[c_19096,c_67]) ).
tff(c_19106,plain,
~ subgroup_member(a),
inference(resolution,[status(thm)],[c_18,c_19103]) ).
tff(c_19110,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_19097,c_19106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP039-4 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.11 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Thu Aug 3 22:11:06 EDT 2023
% 0.11/0.31 % CPUTime :
% 12.14/4.28 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.14/4.29
% 12.14/4.29 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.45/4.33
% 12.45/4.33 Inference rules
% 12.45/4.33 ----------------------
% 12.45/4.33 #Ref : 0
% 12.45/4.33 #Sup : 4503
% 12.45/4.33 #Fact : 0
% 12.45/4.33 #Define : 0
% 12.45/4.33 #Split : 43
% 12.45/4.33 #Chain : 0
% 12.45/4.33 #Close : 0
% 12.45/4.33
% 12.45/4.33 Ordering : KBO
% 12.45/4.33
% 12.45/4.33 Simplification rules
% 12.45/4.33 ----------------------
% 12.45/4.33 #Subsume : 1020
% 12.45/4.33 #Demod : 2033
% 12.45/4.33 #Tautology : 1104
% 12.45/4.33 #SimpNegUnit : 223
% 12.45/4.33 #BackRed : 6
% 12.45/4.33
% 12.45/4.33 #Partial instantiations: 0
% 12.45/4.33 #Strategies tried : 1
% 12.45/4.33
% 12.45/4.33 Timing (in seconds)
% 12.45/4.33 ----------------------
% 12.45/4.33 Preprocessing : 0.45
% 12.45/4.33 Parsing : 0.24
% 12.45/4.33 CNF conversion : 0.02
% 12.45/4.33 Main loop : 2.88
% 12.45/4.33 Inferencing : 0.79
% 12.45/4.33 Reduction : 0.94
% 12.45/4.33 Demodulation : 0.62
% 12.45/4.33 BG Simplification : 0.07
% 12.45/4.33 Subsumption : 0.84
% 12.45/4.33 Abstraction : 0.05
% 12.45/4.33 MUC search : 0.00
% 12.45/4.33 Cooper : 0.00
% 12.45/4.33 Total : 3.39
% 12.45/4.33 Index Insertion : 0.00
% 12.45/4.33 Index Deletion : 0.00
% 12.45/4.33 Index Matching : 0.00
% 12.45/4.33 BG Taut test : 0.00
%------------------------------------------------------------------------------