TSTP Solution File: GRP039-5 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP039-5 : 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 : n012.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 6.38s 2.54s
% Output : CNFRefutation 6.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 22
% Syntax : Number of formulae : 70 ( 39 unt; 9 typ; 0 def)
% Number of atoms : 98 ( 36 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 63 ( 26 ~; 37 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 4 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 48 (; 48 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ 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(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_146,axiom,
~ subgroup_member(d),
file(unknown,unknown) ).
tff(f_144,axiom,
multiply(a,c) = d,
file(unknown,unknown) ).
tff(f_118,axiom,
! [X,Y,Z] :
( ~ subgroup_member(X)
| ~ subgroup_member(Y)
| ( multiply(X,Y) != Z )
| subgroup_member(Z) ),
file(unknown,unknown) ).
tff(f_142,axiom,
subgroup_member(b),
file(unknown,unknown) ).
tff(f_123,axiom,
! [X] : ( multiply(X,identity) = X ),
file(unknown,unknown) ).
tff(f_73,axiom,
! [X] : ( multiply(inverse(X),X) = identity ),
file(unknown,unknown) ).
tff(f_143,axiom,
multiply(b,inverse(a)) = c,
file(unknown,unknown) ).
tff(f_76,axiom,
! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_69,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_140,axiom,
! [X,Y] :
( subgroup_member(X)
| subgroup_member(Y)
| ( multiply(X,element_in_O2(X,Y)) = Y ) ),
file(unknown,unknown) ).
tff(f_125,axiom,
! [X] : ( multiply(X,inverse(X)) = identity ),
file(unknown,unknown) ).
tff(f_134,axiom,
! [X,Y] :
( subgroup_member(X)
| subgroup_member(Y)
| subgroup_member(element_in_O2(X,Y)) ),
file(unknown,unknown) ).
tff(f_107,axiom,
! [X] :
( ~ subgroup_member(X)
| subgroup_member(inverse(X)) ),
file(unknown,unknown) ).
tff(c_28,plain,
~ subgroup_member(d),
inference(cnfTransformation,[status(thm)],[f_146]) ).
tff(c_26,plain,
multiply(a,c) = d,
inference(cnfTransformation,[status(thm)],[f_144]) ).
tff(c_117,plain,
! [X_23,Y_24] :
( subgroup_member(multiply(X_23,Y_24))
| ~ subgroup_member(Y_24)
| ~ subgroup_member(X_23) ),
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_135,plain,
( subgroup_member(d)
| ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_117]) ).
tff(c_144,plain,
( ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(negUnitSimplification,[status(thm)],[c_28,c_135]) ).
tff(c_145,plain,
~ subgroup_member(a),
inference(splitLeft,[status(thm)],[c_144]) ).
tff(c_22,plain,
subgroup_member(b),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_12,plain,
! [X_10] : ( multiply(X_10,identity) = X_10 ),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_4,plain,
! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_24,plain,
multiply(b,inverse(a)) = c,
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_146,plain,
! [X_25,Y_26,Z_27] : ( multiply(multiply(X_25,Y_26),Z_27) = multiply(X_25,multiply(Y_26,Z_27)) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_599,plain,
! [Z_38] : ( multiply(b,multiply(inverse(a),Z_38)) = multiply(c,Z_38) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_146]) ).
tff(c_633,plain,
multiply(c,a) = multiply(b,identity),
inference(superposition,[status(thm),theory(equality)],[c_4,c_599]) ).
tff(c_649,plain,
multiply(c,a) = b,
inference(demodulation,[status(thm),theory(equality)],[c_12,c_633]) ).
tff(c_2,plain,
! [X_1] : ( multiply(identity,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_175,plain,
! [X_2,Z_27] : ( multiply(inverse(X_2),multiply(X_2,Z_27)) = multiply(identity,Z_27) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_146]) ).
tff(c_201,plain,
! [X_2,Z_27] : ( multiply(inverse(X_2),multiply(X_2,Z_27)) = Z_27 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_175]) ).
tff(c_658,plain,
multiply(inverse(c),b) = a,
inference(superposition,[status(thm),theory(equality)],[c_649,c_201]) ).
tff(c_10,plain,
! [X_7,Y_8] :
( subgroup_member(multiply(X_7,Y_8))
| ~ subgroup_member(Y_8)
| ~ subgroup_member(X_7) ),
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_682,plain,
( subgroup_member(a)
| ~ subgroup_member(b)
| ~ subgroup_member(inverse(c)) ),
inference(superposition,[status(thm),theory(equality)],[c_658,c_10]) ).
tff(c_688,plain,
( subgroup_member(a)
| ~ subgroup_member(inverse(c)) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_682]) ).
tff(c_689,plain,
~ subgroup_member(inverse(c)),
inference(negUnitSimplification,[status(thm)],[c_145,c_688]) ).
tff(c_6,plain,
! [X_3,Y_4,Z_5] : ( multiply(multiply(X_3,Y_4),Z_5) = multiply(X_3,multiply(Y_4,Z_5)) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_211,plain,
! [X_28,Y_29] :
( ( multiply(X_28,element_in_O2(X_28,Y_29)) = Y_29 )
| subgroup_member(Y_29)
| subgroup_member(X_28) ),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_3051,plain,
! [X_67,Y_68,Y_69] :
( ( multiply(X_67,multiply(Y_68,element_in_O2(multiply(X_67,Y_68),Y_69))) = Y_69 )
| subgroup_member(Y_69)
| subgroup_member(multiply(X_67,Y_68)) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_211]) ).
tff(c_195,plain,
! [Z_27] : ( multiply(a,multiply(c,Z_27)) = multiply(d,Z_27) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_146]) ).
tff(c_3131,plain,
! [Y_69] :
( ( multiply(d,element_in_O2(multiply(a,c),Y_69)) = Y_69 )
| subgroup_member(Y_69)
| subgroup_member(multiply(a,c)) ),
inference(superposition,[status(thm),theory(equality)],[c_3051,c_195]) ).
tff(c_3337,plain,
! [Y_69] :
( ( multiply(d,element_in_O2(d,Y_69)) = Y_69 )
| subgroup_member(Y_69)
| subgroup_member(d) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_26,c_3131]) ).
tff(c_3412,plain,
! [Y_70] :
( ( multiply(d,element_in_O2(d,Y_70)) = Y_70 )
| subgroup_member(Y_70) ),
inference(negUnitSimplification,[status(thm)],[c_28,c_3337]) ).
tff(c_5271,plain,
! [Y_95] :
( ( multiply(inverse(d),Y_95) = element_in_O2(d,Y_95) )
| subgroup_member(Y_95) ),
inference(superposition,[status(thm),theory(equality)],[c_3412,c_201]) ).
tff(c_14,plain,
! [X_11] : ( multiply(X_11,inverse(X_11)) = identity ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_442,plain,
! [Z_36] : ( multiply(a,multiply(c,Z_36)) = multiply(d,Z_36) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_146]) ).
tff(c_469,plain,
multiply(d,inverse(c)) = multiply(a,identity),
inference(superposition,[status(thm),theory(equality)],[c_14,c_442]) ).
tff(c_477,plain,
multiply(d,inverse(c)) = a,
inference(demodulation,[status(thm),theory(equality)],[c_12,c_469]) ).
tff(c_482,plain,
multiply(inverse(d),a) = inverse(c),
inference(superposition,[status(thm),theory(equality)],[c_477,c_201]) ).
tff(c_5367,plain,
( ( element_in_O2(d,a) = inverse(c) )
| subgroup_member(a) ),
inference(superposition,[status(thm),theory(equality)],[c_5271,c_482]) ).
tff(c_5473,plain,
element_in_O2(d,a) = inverse(c),
inference(negUnitSimplification,[status(thm)],[c_145,c_5367]) ).
tff(c_18,plain,
! [X_12,Y_13] :
( subgroup_member(element_in_O2(X_12,Y_13))
| subgroup_member(Y_13)
| subgroup_member(X_12) ),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_5532,plain,
( subgroup_member(inverse(c))
| subgroup_member(a)
| subgroup_member(d) ),
inference(superposition,[status(thm),theory(equality)],[c_5473,c_18]) ).
tff(c_5542,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_145,c_689,c_5532]) ).
tff(c_5544,plain,
subgroup_member(a),
inference(splitRight,[status(thm)],[c_144]) ).
tff(c_8,plain,
! [X_6] :
( subgroup_member(inverse(X_6))
| ~ subgroup_member(X_6) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_5543,plain,
~ subgroup_member(c),
inference(splitRight,[status(thm)],[c_144]) ).
tff(c_120,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a))
| ~ subgroup_member(b) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_117]) ).
tff(c_137,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_120]) ).
tff(c_5605,plain,
~ subgroup_member(inverse(a)),
inference(negUnitSimplification,[status(thm)],[c_5543,c_137]) ).
tff(c_5608,plain,
~ subgroup_member(a),
inference(resolution,[status(thm)],[c_8,c_5605]) ).
tff(c_5612,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5544,c_5608]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP039-5 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % 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 : n012.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 22:06:52 EDT 2023
% 0.14/0.35 % CPUTime :
% 6.38/2.54 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.38/2.56
% 6.38/2.56 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.38/2.60
% 6.38/2.60 Inference rules
% 6.38/2.60 ----------------------
% 6.38/2.60 #Ref : 0
% 6.38/2.60 #Sup : 1358
% 6.38/2.60 #Fact : 0
% 6.38/2.60 #Define : 0
% 6.38/2.60 #Split : 4
% 6.38/2.60 #Chain : 0
% 6.38/2.60 #Close : 0
% 6.38/2.60
% 6.38/2.60 Ordering : KBO
% 6.38/2.60
% 6.38/2.60 Simplification rules
% 6.38/2.60 ----------------------
% 6.38/2.60 #Subsume : 261
% 6.38/2.60 #Demod : 1239
% 6.38/2.60 #Tautology : 651
% 6.38/2.60 #SimpNegUnit : 162
% 6.38/2.60 #BackRed : 7
% 6.38/2.60
% 6.38/2.60 #Partial instantiations: 0
% 6.38/2.60 #Strategies tried : 1
% 6.38/2.60
% 6.38/2.60 Timing (in seconds)
% 6.38/2.60 ----------------------
% 6.38/2.60 Preprocessing : 0.47
% 6.38/2.60 Parsing : 0.23
% 6.38/2.60 CNF conversion : 0.02
% 6.38/2.60 Main loop : 1.03
% 6.38/2.60 Inferencing : 0.36
% 6.38/2.60 Reduction : 0.39
% 6.38/2.60 Demodulation : 0.30
% 6.38/2.60 BG Simplification : 0.04
% 6.38/2.60 Subsumption : 0.16
% 6.38/2.60 Abstraction : 0.04
% 6.38/2.60 MUC search : 0.00
% 6.38/2.60 Cooper : 0.00
% 6.38/2.60 Total : 1.56
% 6.38/2.60 Index Insertion : 0.00
% 6.38/2.60 Index Deletion : 0.00
% 6.38/2.60 Index Matching : 0.00
% 6.38/2.60 BG Taut test : 0.00
%------------------------------------------------------------------------------