TSTP Solution File: GRP039-3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP039-3 : 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 : n007.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 6.79s 2.59s
% Output : CNFRefutation 6.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 29
% Syntax : Number of formulae : 87 ( 36 unt; 10 typ; 0 def)
% Number of atoms : 154 ( 21 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 146 ( 69 ~; 77 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 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 : 106 (; 106 !; 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_186,axiom,
subgroup_member(b),
file(unknown,unknown) ).
tff(f_171,axiom,
! [A] :
( ~ subgroup_member(A)
| subgroup_member(inverse(A)) ),
file(unknown,unknown) ).
tff(f_190,axiom,
~ subgroup_member(d),
file(unknown,unknown) ).
tff(f_184,axiom,
! [A,B] :
( product(A,element_in_O2(A,B),B)
| subgroup_member(B)
| subgroup_member(A) ),
file(unknown,unknown) ).
tff(f_188,axiom,
product(a,c,d),
file(unknown,unknown) ).
tff(f_155,axiom,
! [A,B,C,D] :
( ~ product(A,B,C)
| ~ product(A,D,C)
| ( D = B ) ),
file(unknown,unknown) ).
tff(f_187,axiom,
product(b,inverse(a),c),
file(unknown,unknown) ).
tff(f_144,axiom,
! [A,B,C] :
( ~ subgroup_member(A)
| ~ subgroup_member(B)
| ~ product(A,inverse(B),C)
| subgroup_member(C) ),
file(unknown,unknown) ).
tff(f_77,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file(unknown,unknown) ).
tff(f_86,axiom,
! [X,Y,Z,W] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ),
file(unknown,unknown) ).
tff(f_165,axiom,
! [A] : ( inverse(inverse(A)) = A ),
file(unknown,unknown) ).
tff(f_74,axiom,
! [X] : product(X,inverse(X),identity),
file(unknown,unknown) ).
tff(f_70,axiom,
! [X] : product(X,identity,X),
file(unknown,unknown) ).
tff(f_108,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_178,axiom,
! [A,B] :
( subgroup_member(element_in_O2(A,B))
| subgroup_member(B)
| subgroup_member(A) ),
file(unknown,unknown) ).
tff(f_72,axiom,
! [X] : product(inverse(X),X,identity),
file(unknown,unknown) ).
tff(f_163,axiom,
! [A,B,C,D] :
( ~ product(A,B,C)
| ~ product(D,B,C)
| ( D = A ) ),
file(unknown,unknown) ).
tff(f_68,axiom,
! [X] : product(identity,X,X),
file(unknown,unknown) ).
tff(f_97,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(c_34,plain,
subgroup_member(b),
inference(cnfTransformation,[status(thm)],[f_186]) ).
tff(c_28,plain,
! [A_35] :
( subgroup_member(inverse(A_35))
| ~ subgroup_member(A_35) ),
inference(cnfTransformation,[status(thm)],[f_171]) ).
tff(c_40,plain,
~ subgroup_member(d),
inference(cnfTransformation,[status(thm)],[f_190]) ).
tff(c_32,plain,
! [A_38,B_39] :
( subgroup_member(A_38)
| subgroup_member(B_39)
| product(A_38,element_in_O2(A_38,B_39),B_39) ),
inference(cnfTransformation,[status(thm)],[f_184]) ).
tff(c_38,plain,
product(a,c,d),
inference(cnfTransformation,[status(thm)],[f_188]) ).
tff(c_310,plain,
! [D_72,B_73,A_74,C_75] :
( ( D_72 = B_73 )
| ~ product(A_74,D_72,C_75)
| ~ product(A_74,B_73,C_75) ),
inference(cnfTransformation,[status(thm)],[f_155]) ).
tff(c_335,plain,
! [B_76] :
( ( c = B_76 )
| ~ product(a,B_76,d) ),
inference(resolution,[status(thm)],[c_38,c_310]) ).
tff(c_339,plain,
( ( element_in_O2(a,d) = c )
| subgroup_member(a)
| subgroup_member(d) ),
inference(resolution,[status(thm)],[c_32,c_335]) ).
tff(c_345,plain,
( ( element_in_O2(a,d) = c )
| subgroup_member(a) ),
inference(negUnitSimplification,[status(thm)],[c_40,c_339]) ).
tff(c_371,plain,
subgroup_member(a),
inference(splitLeft,[status(thm)],[c_345]) ).
tff(c_36,plain,
product(b,inverse(a),c),
inference(cnfTransformation,[status(thm)],[f_187]) ).
tff(c_394,plain,
! [C_80,A_81,B_82] :
( subgroup_member(C_80)
| ~ product(A_81,inverse(B_82),C_80)
| ~ subgroup_member(B_82)
| ~ subgroup_member(A_81) ),
inference(cnfTransformation,[status(thm)],[f_144]) ).
tff(c_411,plain,
( subgroup_member(c)
| ~ subgroup_member(a)
| ~ subgroup_member(b) ),
inference(resolution,[status(thm)],[c_36,c_394]) ).
tff(c_428,plain,
subgroup_member(c),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_371,c_411]) ).
tff(c_10,plain,
! [X_5,Y_6] : product(X_5,Y_6,multiply(X_5,Y_6)),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_84,plain,
! [Z_51,W_52,X_53,Y_54] :
( ( Z_51 = W_52 )
| ~ product(X_53,Y_54,W_52)
| ~ product(X_53,Y_54,Z_51) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_177,plain,
! [Z_60] :
( ( d = Z_60 )
| ~ product(a,c,Z_60) ),
inference(resolution,[status(thm)],[c_38,c_84]) ).
tff(c_185,plain,
multiply(a,c) = d,
inference(resolution,[status(thm)],[c_10,c_177]) ).
tff(c_24,plain,
! [A_34] : ( inverse(inverse(A_34)) = A_34 ),
inference(cnfTransformation,[status(thm)],[f_165]) ).
tff(c_825,plain,
! [X_120,B_121] :
( subgroup_member(multiply(X_120,inverse(B_121)))
| ~ subgroup_member(B_121)
| ~ subgroup_member(X_120) ),
inference(resolution,[status(thm)],[c_10,c_394]) ).
tff(c_879,plain,
! [X_124,A_125] :
( subgroup_member(multiply(X_124,A_125))
| ~ subgroup_member(inverse(A_125))
| ~ subgroup_member(X_124) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_825]) ).
tff(c_894,plain,
( subgroup_member(d)
| ~ subgroup_member(inverse(c))
| ~ subgroup_member(a) ),
inference(superposition,[status(thm),theory(equality)],[c_185,c_879]) ).
tff(c_905,plain,
( subgroup_member(d)
| ~ subgroup_member(inverse(c)) ),
inference(demodulation,[status(thm),theory(equality)],[c_371,c_894]) ).
tff(c_906,plain,
~ subgroup_member(inverse(c)),
inference(negUnitSimplification,[status(thm)],[c_40,c_905]) ).
tff(c_912,plain,
~ subgroup_member(c),
inference(resolution,[status(thm)],[c_28,c_906]) ).
tff(c_916,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_428,c_912]) ).
tff(c_918,plain,
~ subgroup_member(a),
inference(splitRight,[status(thm)],[c_345]) ).
tff(c_8,plain,
! [X_4] : product(X_4,inverse(X_4),identity),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_4,plain,
! [X_2] : product(X_2,identity,X_2),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_1082,plain,
! [V_141,X_139,U_140,Y_138,Z_143,W_142] :
( product(U_140,Z_143,W_142)
| ~ product(X_139,V_141,W_142)
| ~ product(Y_138,Z_143,V_141)
| ~ product(X_139,Y_138,U_140) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_1621,plain,
! [U_185,Z_186,X_187,Y_188] :
( product(U_185,Z_186,X_187)
| ~ product(Y_188,Z_186,identity)
| ~ product(X_187,Y_188,U_185) ),
inference(resolution,[status(thm)],[c_4,c_1082]) ).
tff(c_1661,plain,
! [U_191,X_192,X_193] :
( product(U_191,inverse(X_192),X_193)
| ~ product(X_193,X_192,U_191) ),
inference(resolution,[status(thm)],[c_8,c_1621]) ).
tff(c_333,plain,
! [B_73] :
( ( c = B_73 )
| ~ product(a,B_73,d) ),
inference(resolution,[status(thm)],[c_38,c_310]) ).
tff(c_1884,plain,
! [X_201] :
( ( inverse(X_201) = c )
| ~ product(d,X_201,a) ),
inference(resolution,[status(thm)],[c_1661,c_333]) ).
tff(c_1892,plain,
( ( inverse(element_in_O2(d,a)) = c )
| subgroup_member(d)
| subgroup_member(a) ),
inference(resolution,[status(thm)],[c_32,c_1884]) ).
tff(c_1897,plain,
inverse(element_in_O2(d,a)) = c,
inference(negUnitSimplification,[status(thm)],[c_918,c_40,c_1892]) ).
tff(c_1967,plain,
element_in_O2(d,a) = inverse(c),
inference(superposition,[status(thm),theory(equality)],[c_1897,c_24]) ).
tff(c_30,plain,
! [A_36,B_37] :
( subgroup_member(A_36)
| subgroup_member(B_37)
| subgroup_member(element_in_O2(A_36,B_37)) ),
inference(cnfTransformation,[status(thm)],[f_178]) ).
tff(c_1992,plain,
( subgroup_member(d)
| subgroup_member(a)
| subgroup_member(inverse(c)) ),
inference(superposition,[status(thm),theory(equality)],[c_1967,c_30]) ).
tff(c_1999,plain,
subgroup_member(inverse(c)),
inference(negUnitSimplification,[status(thm)],[c_918,c_40,c_1992]) ).
tff(c_6,plain,
! [X_3] : product(inverse(X_3),X_3,identity),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_253,plain,
! [D_65,A_66,B_67,C_68] :
( ( D_65 = A_66 )
| ~ product(D_65,B_67,C_68)
| ~ product(A_66,B_67,C_68) ),
inference(cnfTransformation,[status(thm)],[f_163]) ).
tff(c_274,plain,
! [A_66] :
( ( b = A_66 )
| ~ product(A_66,inverse(a),c) ),
inference(resolution,[status(thm)],[c_36,c_253]) ).
tff(c_1804,plain,
! [U_198] :
( ( b = U_198 )
| ~ product(c,a,U_198) ),
inference(resolution,[status(thm)],[c_1661,c_274]) ).
tff(c_1809,plain,
multiply(c,a) = b,
inference(resolution,[status(thm)],[c_10,c_1804]) ).
tff(c_1822,plain,
product(c,a,b),
inference(superposition,[status(thm),theory(equality)],[c_1809,c_10]) ).
tff(c_2,plain,
! [X_1] : product(identity,X_1,X_1),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_996,plain,
! [Z_134,Y_131,X_133,V_135,U_132,W_130] :
( product(X_133,V_135,W_130)
| ~ product(U_132,Z_134,W_130)
| ~ product(Y_131,Z_134,V_135)
| ~ product(X_133,Y_131,U_132) ),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_2509,plain,
! [X_231,V_232,X_233,Y_234] :
( product(X_231,V_232,X_233)
| ~ product(Y_234,X_233,V_232)
| ~ product(X_231,Y_234,identity) ),
inference(resolution,[status(thm)],[c_2,c_996]) ).
tff(c_4657,plain,
! [X_323] :
( product(X_323,b,a)
| ~ product(X_323,c,identity) ),
inference(resolution,[status(thm)],[c_1822,c_2509]) ).
tff(c_4666,plain,
product(inverse(c),b,a),
inference(resolution,[status(thm)],[c_6,c_4657]) ).
tff(c_919,plain,
! [C_126,A_127,B_128] :
( subgroup_member(C_126)
| ~ product(A_127,inverse(B_128),C_126)
| ~ subgroup_member(B_128)
| ~ subgroup_member(A_127) ),
inference(cnfTransformation,[status(thm)],[f_144]) ).
tff(c_943,plain,
! [C_126,A_127,A_34] :
( subgroup_member(C_126)
| ~ product(A_127,A_34,C_126)
| ~ subgroup_member(inverse(A_34))
| ~ subgroup_member(A_127) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_919]) ).
tff(c_4695,plain,
( subgroup_member(a)
| ~ subgroup_member(inverse(b))
| ~ subgroup_member(inverse(c)) ),
inference(resolution,[status(thm)],[c_4666,c_943]) ).
tff(c_4728,plain,
( subgroup_member(a)
| ~ subgroup_member(inverse(b)) ),
inference(demodulation,[status(thm),theory(equality)],[c_1999,c_4695]) ).
tff(c_4729,plain,
~ subgroup_member(inverse(b)),
inference(negUnitSimplification,[status(thm)],[c_918,c_4728]) ).
tff(c_4739,plain,
~ subgroup_member(b),
inference(resolution,[status(thm)],[c_28,c_4729]) ).
tff(c_4743,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_34,c_4739]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP039-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % 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
% 0.15/0.35 % Computer : n007.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 3 21:55:54 EDT 2023
% 0.15/0.35 % CPUTime :
% 6.79/2.59 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.79/2.61
% 6.79/2.61 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.93/2.65
% 6.93/2.65 Inference rules
% 6.93/2.65 ----------------------
% 6.93/2.65 #Ref : 0
% 6.93/2.65 #Sup : 1097
% 6.93/2.65 #Fact : 0
% 6.93/2.65 #Define : 0
% 6.93/2.65 #Split : 21
% 6.93/2.65 #Chain : 0
% 6.93/2.65 #Close : 0
% 6.93/2.65
% 6.93/2.65 Ordering : KBO
% 6.93/2.65
% 6.93/2.65 Simplification rules
% 6.93/2.65 ----------------------
% 6.93/2.65 #Subsume : 222
% 6.93/2.65 #Demod : 457
% 6.93/2.65 #Tautology : 391
% 6.93/2.65 #SimpNegUnit : 60
% 6.93/2.65 #BackRed : 2
% 6.93/2.65
% 6.93/2.65 #Partial instantiations: 0
% 6.93/2.65 #Strategies tried : 1
% 6.93/2.65
% 6.93/2.65 Timing (in seconds)
% 6.93/2.65 ----------------------
% 6.93/2.65 Preprocessing : 0.50
% 6.93/2.65 Parsing : 0.27
% 6.93/2.65 CNF conversion : 0.03
% 6.93/2.65 Main loop : 1.07
% 6.93/2.65 Inferencing : 0.39
% 6.93/2.65 Reduction : 0.30
% 6.93/2.65 Demodulation : 0.21
% 6.93/2.65 BG Simplification : 0.03
% 6.93/2.65 Subsumption : 0.26
% 6.93/2.65 Abstraction : 0.04
% 6.93/2.65 MUC search : 0.00
% 6.93/2.65 Cooper : 0.00
% 6.93/2.65 Total : 1.63
% 6.93/2.65 Index Insertion : 0.00
% 6.93/2.65 Index Deletion : 0.00
% 6.93/2.65 Index Matching : 0.00
% 6.93/2.65 BG Taut test : 0.00
%------------------------------------------------------------------------------