TSTP Solution File: GRP025-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP025-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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 : n023.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 10:39:39 EDT 2023
% Result : Unsatisfiable 5.01s 2.22s
% Output : CNFRefutation 5.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 32
% Syntax : Number of formulae : 136 ( 95 unt; 15 typ; 0 def)
% Number of atoms : 160 ( 77 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 81 ( 42 ~; 39 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 6 >; 7 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-3 aty)
% Number of variables : 76 (; 76 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > group_member > multiply > inverse > #nlpp > identity_for > an_isomorphism > g2 > g1 > d3 > d2 > d1 > d > c > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(group_member,type,
group_member: ( $i * $i ) > $o ).
tff(product,type,
product: ( $i * $i * $i * $i ) > $o ).
tff(g2,type,
g2: $i ).
tff(an_isomorphism,type,
an_isomorphism: $i > $i ).
tff(g1,type,
g1: $i ).
tff(b,type,
b: $i ).
tff(d2,type,
d2: $i ).
tff(d1,type,
d1: $i ).
tff(identity_for,type,
identity_for: $i > $i ).
tff(inverse,type,
inverse: ( $i * $i ) > $i ).
tff(d,type,
d: $i ).
tff(multiply,type,
multiply: ( $i * $i * $i ) > $i ).
tff(d3,type,
d3: $i ).
tff(c,type,
c: $i ).
tff(f_56,axiom,
! [Xg] : group_member(identity_for(Xg),Xg),
file(unknown,unknown) ).
tff(f_138,axiom,
! [X] :
( ~ group_member(X,g2)
| ( X = c )
| ( X = d ) ),
file(unknown,unknown) ).
tff(f_58,axiom,
! [Xg,X] : product(Xg,identity_for(Xg),X,X),
file(unknown,unknown) ).
tff(f_149,axiom,
an_isomorphism(b) = d,
file(unknown,unknown) ).
tff(f_148,axiom,
an_isomorphism(a) = c,
file(unknown,unknown) ).
tff(f_153,axiom,
group_member(d3,g1),
file(unknown,unknown) ).
tff(f_131,axiom,
! [X] :
( ~ group_member(X,g1)
| ( X = a )
| ( X = b ) ),
file(unknown,unknown) ).
tff(f_152,axiom,
group_member(d2,g1),
file(unknown,unknown) ).
tff(f_151,axiom,
group_member(d1,g1),
file(unknown,unknown) ).
tff(f_156,axiom,
~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
file(unknown,unknown) ).
tff(f_60,axiom,
! [Xg,X] : product(Xg,X,identity_for(Xg),X),
file(unknown,unknown) ).
tff(f_154,axiom,
product(g1,d1,d2,d3),
file(unknown,unknown) ).
tff(f_95,axiom,
! [Xg,W,Z,X,Y] :
( ~ product(Xg,X,Y,Z)
| ~ product(Xg,X,Y,W)
| ( W = Z ) ),
file(unknown,unknown) ).
tff(f_140,axiom,
product(g1,a,b,b),
file(unknown,unknown) ).
tff(f_142,axiom,
product(g1,b,b,a),
file(unknown,unknown) ).
tff(f_146,axiom,
product(g2,d,d,c),
file(unknown,unknown) ).
tff(f_145,axiom,
product(g2,d,c,d),
file(unknown,unknown) ).
tff(c_2,plain,
! [Xg_1] : group_member(identity_for(Xg_1),Xg_1),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_76,plain,
! [X_44] :
( ( d = X_44 )
| ( c = X_44 )
| ~ group_member(X_44,g2) ),
inference(cnfTransformation,[status(thm)],[f_138]) ).
tff(c_87,plain,
( ( identity_for(g2) = d )
| ( identity_for(g2) = c ) ),
inference(resolution,[status(thm)],[c_2,c_76]) ).
tff(c_92,plain,
identity_for(g2) = c,
inference(splitLeft,[status(thm)],[c_87]) ).
tff(c_4,plain,
! [Xg_2,X_3] : product(Xg_2,identity_for(Xg_2),X_3,X_3),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_96,plain,
! [X_3] : product(g2,c,X_3,X_3),
inference(superposition,[status(thm),theory(equality)],[c_92,c_4]) ).
tff(c_54,plain,
an_isomorphism(b) = d,
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_52,plain,
an_isomorphism(a) = c,
inference(cnfTransformation,[status(thm)],[f_148]) ).
tff(c_60,plain,
group_member(d3,g1),
inference(cnfTransformation,[status(thm)],[f_153]) ).
tff(c_110,plain,
! [X_46] :
( ( b = X_46 )
| ( a = X_46 )
| ~ group_member(X_46,g1) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_137,plain,
( ( d3 = b )
| ( d3 = a ) ),
inference(resolution,[status(thm)],[c_60,c_110]) ).
tff(c_157,plain,
d3 = a,
inference(splitLeft,[status(thm)],[c_137]) ).
tff(c_58,plain,
group_member(d2,g1),
inference(cnfTransformation,[status(thm)],[f_152]) ).
tff(c_136,plain,
( ( d2 = b )
| ( d2 = a ) ),
inference(resolution,[status(thm)],[c_58,c_110]) ).
tff(c_146,plain,
d2 = a,
inference(splitLeft,[status(thm)],[c_136]) ).
tff(c_56,plain,
group_member(d1,g1),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_135,plain,
( ( d1 = b )
| ( d1 = a ) ),
inference(resolution,[status(thm)],[c_56,c_110]) ).
tff(c_138,plain,
d1 = a,
inference(splitLeft,[status(thm)],[c_135]) ).
tff(c_64,plain,
~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
inference(cnfTransformation,[status(thm)],[f_156]) ).
tff(c_168,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_96,c_52,c_157,c_52,c_146,c_52,c_138,c_64]) ).
tff(c_169,plain,
d3 = b,
inference(splitRight,[status(thm)],[c_137]) ).
tff(c_170,plain,
d3 != a,
inference(splitRight,[status(thm)],[c_137]) ).
tff(c_177,plain,
b != a,
inference(demodulation,[status(thm),theory(equality)],[c_169,c_170]) ).
tff(c_130,plain,
( ( identity_for(g1) = b )
| ( identity_for(g1) = a ) ),
inference(resolution,[status(thm)],[c_2,c_110]) ).
tff(c_182,plain,
identity_for(g1) = a,
inference(splitLeft,[status(thm)],[c_130]) ).
tff(c_6,plain,
! [Xg_4,X_5] : product(Xg_4,X_5,identity_for(Xg_4),X_5),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_192,plain,
! [X_5] : product(g1,X_5,a,X_5),
inference(superposition,[status(thm),theory(equality)],[c_182,c_6]) ).
tff(c_62,plain,
product(g1,d1,d2,d3),
inference(cnfTransformation,[status(thm)],[f_154]) ).
tff(c_139,plain,
product(g1,a,d2,d3),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_62]) ).
tff(c_178,plain,
product(g1,a,a,b),
inference(demodulation,[status(thm),theory(equality)],[c_169,c_146,c_139]) ).
tff(c_274,plain,
! [X_64,Y_66,W_62,Z_63,Xg_65] :
( ( Z_63 = W_62 )
| ~ product(Xg_65,X_64,Y_66,W_62)
| ~ product(Xg_65,X_64,Y_66,Z_63) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_379,plain,
! [Z_72] :
( ( b = Z_72 )
| ~ product(g1,a,a,Z_72) ),
inference(resolution,[status(thm)],[c_178,c_274]) ).
tff(c_383,plain,
b = a,
inference(resolution,[status(thm)],[c_192,c_379]) ).
tff(c_394,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_177,c_383]) ).
tff(c_395,plain,
identity_for(g1) = b,
inference(splitRight,[status(thm)],[c_130]) ).
tff(c_414,plain,
! [X_5] : product(g1,X_5,b,X_5),
inference(superposition,[status(thm),theory(equality)],[c_395,c_6]) ).
tff(c_38,plain,
product(g1,a,b,b),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_439,plain,
! [W_83,Z_84,Y_87,Xg_86,X_85] :
( ( Z_84 = W_83 )
| ~ product(Xg_86,X_85,Y_87,W_83)
| ~ product(Xg_86,X_85,Y_87,Z_84) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_494,plain,
! [Z_88] :
( ( b = Z_88 )
| ~ product(g1,a,b,Z_88) ),
inference(resolution,[status(thm)],[c_38,c_439]) ).
tff(c_498,plain,
b = a,
inference(resolution,[status(thm)],[c_414,c_494]) ).
tff(c_505,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_177,c_498]) ).
tff(c_506,plain,
d2 = b,
inference(splitRight,[status(thm)],[c_136]) ).
tff(c_507,plain,
d2 != a,
inference(splitRight,[status(thm)],[c_136]) ).
tff(c_514,plain,
b != a,
inference(demodulation,[status(thm),theory(equality)],[c_506,c_507]) ).
tff(c_529,plain,
identity_for(g1) = a,
inference(splitLeft,[status(thm)],[c_130]) ).
tff(c_537,plain,
! [X_3] : product(g1,a,X_3,X_3),
inference(superposition,[status(thm),theory(equality)],[c_529,c_4]) ).
tff(c_519,plain,
d3 = a,
inference(splitLeft,[status(thm)],[c_137]) ).
tff(c_526,plain,
product(g1,a,b,a),
inference(demodulation,[status(thm),theory(equality)],[c_519,c_506,c_139]) ).
tff(c_575,plain,
! [X_104,Xg_105,Y_106,Z_103,W_102] :
( ( Z_103 = W_102 )
| ~ product(Xg_105,X_104,Y_106,W_102)
| ~ product(Xg_105,X_104,Y_106,Z_103) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_633,plain,
! [Z_109] :
( ( a = Z_109 )
| ~ product(g1,a,b,Z_109) ),
inference(resolution,[status(thm)],[c_526,c_575]) ).
tff(c_637,plain,
b = a,
inference(resolution,[status(thm)],[c_537,c_633]) ).
tff(c_644,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_514,c_637]) ).
tff(c_645,plain,
identity_for(g1) = b,
inference(splitRight,[status(thm)],[c_130]) ).
tff(c_657,plain,
! [X_5] : product(g1,X_5,b,X_5),
inference(superposition,[status(thm),theory(equality)],[c_645,c_6]) ).
tff(c_42,plain,
product(g1,b,b,a),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_751,plain,
! [Xg_127,X_126,W_124,Y_128,Z_125] :
( ( Z_125 = W_124 )
| ~ product(Xg_127,X_126,Y_128,W_124)
| ~ product(Xg_127,X_126,Y_128,Z_125) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_813,plain,
! [Z_132] :
( ( a = Z_132 )
| ~ product(g1,b,b,Z_132) ),
inference(resolution,[status(thm)],[c_42,c_751]) ).
tff(c_821,plain,
b = a,
inference(resolution,[status(thm)],[c_657,c_813]) ).
tff(c_835,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_514,c_821]) ).
tff(c_836,plain,
d3 = b,
inference(splitRight,[status(thm)],[c_137]) ).
tff(c_849,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_96,c_54,c_836,c_52,c_54,c_138,c_506,c_64]) ).
tff(c_850,plain,
d1 = b,
inference(splitRight,[status(thm)],[c_135]) ).
tff(c_851,plain,
d1 != a,
inference(splitRight,[status(thm)],[c_135]) ).
tff(c_859,plain,
b != a,
inference(demodulation,[status(thm),theory(equality)],[c_850,c_851]) ).
tff(c_99,plain,
! [X_5] : product(g2,X_5,c,X_5),
inference(superposition,[status(thm),theory(equality)],[c_92,c_6]) ).
tff(c_1282,plain,
d2 = a,
inference(splitLeft,[status(thm)],[c_136]) ).
tff(c_50,plain,
product(g2,d,d,c),
inference(cnfTransformation,[status(thm)],[f_146]) ).
tff(c_882,plain,
identity_for(g1) = a,
inference(splitLeft,[status(thm)],[c_130]) ).
tff(c_892,plain,
! [X_5] : product(g1,X_5,a,X_5),
inference(superposition,[status(thm),theory(equality)],[c_882,c_6]) ).
tff(c_871,plain,
d2 = a,
inference(splitLeft,[status(thm)],[c_136]) ).
tff(c_860,plain,
d3 = a,
inference(splitLeft,[status(thm)],[c_137]) ).
tff(c_852,plain,
product(g1,b,d2,d3),
inference(demodulation,[status(thm),theory(equality)],[c_850,c_62]) ).
tff(c_878,plain,
product(g1,b,a,a),
inference(demodulation,[status(thm),theory(equality)],[c_871,c_860,c_852]) ).
tff(c_1017,plain,
! [Z_152,W_151,Xg_154,Y_155,X_153] :
( ( Z_152 = W_151 )
| ~ product(Xg_154,X_153,Y_155,W_151)
| ~ product(Xg_154,X_153,Y_155,Z_152) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_1078,plain,
! [Z_158] :
( ( a = Z_158 )
| ~ product(g1,b,a,Z_158) ),
inference(resolution,[status(thm)],[c_878,c_1017]) ).
tff(c_1082,plain,
b = a,
inference(resolution,[status(thm)],[c_892,c_1078]) ).
tff(c_1089,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_859,c_1082]) ).
tff(c_1090,plain,
identity_for(g1) = b,
inference(splitRight,[status(thm)],[c_130]) ).
tff(c_1108,plain,
! [X_5] : product(g1,X_5,b,X_5),
inference(superposition,[status(thm),theory(equality)],[c_1090,c_6]) ).
tff(c_1196,plain,
! [Z_174,W_173,Y_177,Xg_176,X_175] :
( ( Z_174 = W_173 )
| ~ product(Xg_176,X_175,Y_177,W_173)
| ~ product(Xg_176,X_175,Y_177,Z_174) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_1253,plain,
! [Z_178] :
( ( b = Z_178 )
| ~ product(g1,a,b,Z_178) ),
inference(resolution,[status(thm)],[c_38,c_1196]) ).
tff(c_1257,plain,
b = a,
inference(resolution,[status(thm)],[c_1108,c_1253]) ).
tff(c_1264,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_859,c_1257]) ).
tff(c_1265,plain,
d2 = b,
inference(splitRight,[status(thm)],[c_136]) ).
tff(c_1267,plain,
~ product(g2,d,an_isomorphism(d2),c),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_54,c_850,c_860,c_64]) ).
tff(c_1268,plain,
~ product(g2,d,an_isomorphism(b),c),
inference(demodulation,[status(thm),theory(equality)],[c_1265,c_1267]) ).
tff(c_1272,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_50,c_54,c_1268]) ).
tff(c_1273,plain,
d3 = b,
inference(splitRight,[status(thm)],[c_137]) ).
tff(c_1298,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_99,c_52,c_1282,c_54,c_1273,c_54,c_850,c_64]) ).
tff(c_1299,plain,
d2 = b,
inference(splitRight,[status(thm)],[c_136]) ).
tff(c_1308,plain,
product(g1,b,b,b),
inference(demodulation,[status(thm),theory(equality)],[c_1299,c_1273,c_852]) ).
tff(c_1398,plain,
! [W_199,Xg_202,Y_203,X_201,Z_200] :
( ( Z_200 = W_199 )
| ~ product(Xg_202,X_201,Y_203,W_199)
| ~ product(Xg_202,X_201,Y_203,Z_200) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_1469,plain,
! [Z_204] :
( ( a = Z_204 )
| ~ product(g1,b,b,Z_204) ),
inference(resolution,[status(thm)],[c_42,c_1398]) ).
tff(c_1472,plain,
b = a,
inference(resolution,[status(thm)],[c_1308,c_1469]) ).
tff(c_1479,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_859,c_1472]) ).
tff(c_1480,plain,
identity_for(g2) = d,
inference(splitRight,[status(thm)],[c_87]) ).
tff(c_1481,plain,
identity_for(g2) != c,
inference(splitRight,[status(thm)],[c_87]) ).
tff(c_1496,plain,
d != c,
inference(demodulation,[status(thm),theory(equality)],[c_1480,c_1481]) ).
tff(c_1485,plain,
! [X_3] : product(g2,d,X_3,X_3),
inference(superposition,[status(thm),theory(equality)],[c_1480,c_4]) ).
tff(c_48,plain,
product(g2,d,c,d),
inference(cnfTransformation,[status(thm)],[f_145]) ).
tff(c_1674,plain,
! [Y_232,Xg_231,W_228,X_230,Z_229] :
( ( Z_229 = W_228 )
| ~ product(Xg_231,X_230,Y_232,W_228)
| ~ product(Xg_231,X_230,Y_232,Z_229) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_1735,plain,
! [Z_234] :
( ( d = Z_234 )
| ~ product(g2,d,c,Z_234) ),
inference(resolution,[status(thm)],[c_48,c_1674]) ).
tff(c_1739,plain,
d = c,
inference(resolution,[status(thm)],[c_1485,c_1735]) ).
tff(c_1746,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1496,c_1739]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP025-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.07/0.13 % 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
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 22:12:07 EDT 2023
% 0.14/0.35 % CPUTime :
% 5.01/2.22 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.01/2.23
% 5.01/2.23 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.01/2.27
% 5.01/2.27 Inference rules
% 5.01/2.27 ----------------------
% 5.01/2.27 #Ref : 0
% 5.01/2.27 #Sup : 408
% 5.01/2.27 #Fact : 0
% 5.01/2.27 #Define : 0
% 5.01/2.27 #Split : 25
% 5.01/2.27 #Chain : 0
% 5.01/2.27 #Close : 0
% 5.01/2.27
% 5.01/2.27 Ordering : KBO
% 5.01/2.27
% 5.01/2.27 Simplification rules
% 5.01/2.27 ----------------------
% 5.01/2.27 #Subsume : 6
% 5.01/2.27 #Demod : 244
% 5.01/2.27 #Tautology : 179
% 5.01/2.27 #SimpNegUnit : 9
% 5.01/2.27 #BackRed : 24
% 5.01/2.27
% 5.01/2.27 #Partial instantiations: 0
% 5.01/2.27 #Strategies tried : 1
% 5.01/2.27
% 5.01/2.27 Timing (in seconds)
% 5.01/2.27 ----------------------
% 5.01/2.28 Preprocessing : 0.49
% 5.01/2.28 Parsing : 0.25
% 5.01/2.28 CNF conversion : 0.03
% 5.01/2.28 Main loop : 0.71
% 5.01/2.28 Inferencing : 0.26
% 5.01/2.28 Reduction : 0.21
% 5.01/2.28 Demodulation : 0.16
% 5.01/2.28 BG Simplification : 0.03
% 5.01/2.28 Subsumption : 0.14
% 5.01/2.28 Abstraction : 0.02
% 5.01/2.28 MUC search : 0.00
% 5.01/2.28 Cooper : 0.00
% 5.01/2.28 Total : 1.27
% 5.01/2.28 Index Insertion : 0.00
% 5.01/2.28 Index Deletion : 0.00
% 5.01/2.28 Index Matching : 0.00
% 5.01/2.28 BG Taut test : 0.00
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