TSTP Solution File: GRP039-7 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP039-7 : TPTP v8.1.2. Bugfixed v1.0.1.
% 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 : n019.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 6.28s 2.52s
% Output : CNFRefutation 6.28s
% 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_153,axiom,
~ subgroup_member(d),
file(unknown,unknown) ).
tff(f_151,axiom,
multiply(a,c) = d,
file(unknown,unknown) ).
tff(f_121,axiom,
! [X,Y,Z] :
( ~ subgroup_member(X)
| ~ subgroup_member(Y)
| ( multiply(X,Y) != Z )
| subgroup_member(Z) ),
file(unknown,unknown) ).
tff(f_149,axiom,
subgroup_member(b),
file(unknown,unknown) ).
tff(f_126,axiom,
! [X] : ( multiply(X,identity) = X ),
file(unknown,unknown) ).
tff(f_76,axiom,
! [X] : ( multiply(inverse(X),X) = identity ),
file(unknown,unknown) ).
tff(f_150,axiom,
multiply(b,inverse(a)) = c,
file(unknown,unknown) ).
tff(f_79,axiom,
! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_72,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_147,axiom,
! [X,Y] :
( subgroup_member(X)
| subgroup_member(Y)
| ( multiply(X,element_in_O2(X,Y)) = Y ) ),
file(unknown,unknown) ).
tff(f_128,axiom,
! [X] : ( multiply(X,inverse(X)) = identity ),
file(unknown,unknown) ).
tff(f_141,axiom,
! [X,Y] :
( subgroup_member(X)
| subgroup_member(Y)
| subgroup_member(element_in_O2(X,Y)) ),
file(unknown,unknown) ).
tff(f_110,axiom,
! [X] :
( ~ subgroup_member(X)
| subgroup_member(inverse(X)) ),
file(unknown,unknown) ).
tff(c_32,plain,
~ subgroup_member(d),
inference(cnfTransformation,[status(thm)],[f_153]) ).
tff(c_30,plain,
multiply(a,c) = d,
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_166,plain,
! [X_24,Y_25] :
( subgroup_member(multiply(X_24,Y_25))
| ~ subgroup_member(Y_25)
| ~ subgroup_member(X_24) ),
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_181,plain,
( subgroup_member(d)
| ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(superposition,[status(thm),theory(equality)],[c_30,c_166]) ).
tff(c_191,plain,
( ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(negUnitSimplification,[status(thm)],[c_32,c_181]) ).
tff(c_195,plain,
~ subgroup_member(a),
inference(splitLeft,[status(thm)],[c_191]) ).
tff(c_26,plain,
subgroup_member(b),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_12,plain,
! [X_10] : ( multiply(X_10,identity) = X_10 ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_4,plain,
! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_28,plain,
multiply(b,inverse(a)) = c,
inference(cnfTransformation,[status(thm)],[f_150]) ).
tff(c_197,plain,
! [X_28,Y_29,Z_30] : ( multiply(multiply(X_28,Y_29),Z_30) = multiply(X_28,multiply(Y_29,Z_30)) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_590,plain,
! [Z_40] : ( multiply(b,multiply(inverse(a),Z_40)) = multiply(c,Z_40) ),
inference(superposition,[status(thm),theory(equality)],[c_28,c_197]) ).
tff(c_624,plain,
multiply(c,a) = multiply(b,identity),
inference(superposition,[status(thm),theory(equality)],[c_4,c_590]) ).
tff(c_640,plain,
multiply(c,a) = b,
inference(demodulation,[status(thm),theory(equality)],[c_12,c_624]) ).
tff(c_2,plain,
! [X_1] : ( multiply(identity,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_226,plain,
! [X_2,Z_30] : ( multiply(inverse(X_2),multiply(X_2,Z_30)) = multiply(identity,Z_30) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_197]) ).
tff(c_252,plain,
! [X_2,Z_30] : ( multiply(inverse(X_2),multiply(X_2,Z_30)) = Z_30 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_226]) ).
tff(c_649,plain,
multiply(inverse(c),b) = a,
inference(superposition,[status(thm),theory(equality)],[c_640,c_252]) ).
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_121]) ).
tff(c_673,plain,
( subgroup_member(a)
| ~ subgroup_member(b)
| ~ subgroup_member(inverse(c)) ),
inference(superposition,[status(thm),theory(equality)],[c_649,c_10]) ).
tff(c_679,plain,
( subgroup_member(a)
| ~ subgroup_member(inverse(c)) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_673]) ).
tff(c_680,plain,
~ subgroup_member(inverse(c)),
inference(negUnitSimplification,[status(thm)],[c_195,c_679]) ).
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_79]) ).
tff(c_397,plain,
! [X_35,Y_36] :
( ( multiply(X_35,element_in_O2(X_35,Y_36)) = Y_36 )
| subgroup_member(Y_36)
| subgroup_member(X_35) ),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_3121,plain,
! [X_69,Y_70,Y_71] :
( ( multiply(X_69,multiply(Y_70,element_in_O2(multiply(X_69,Y_70),Y_71))) = Y_71 )
| subgroup_member(Y_71)
| subgroup_member(multiply(X_69,Y_70)) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_397]) ).
tff(c_243,plain,
! [Z_30] : ( multiply(a,multiply(c,Z_30)) = multiply(d,Z_30) ),
inference(superposition,[status(thm),theory(equality)],[c_30,c_197]) ).
tff(c_3201,plain,
! [Y_71] :
( ( multiply(d,element_in_O2(multiply(a,c),Y_71)) = Y_71 )
| subgroup_member(Y_71)
| subgroup_member(multiply(a,c)) ),
inference(superposition,[status(thm),theory(equality)],[c_3121,c_243]) ).
tff(c_3413,plain,
! [Y_71] :
( ( multiply(d,element_in_O2(d,Y_71)) = Y_71 )
| subgroup_member(Y_71)
| subgroup_member(d) ),
inference(demodulation,[status(thm),theory(equality)],[c_30,c_30,c_3201]) ).
tff(c_3491,plain,
! [Y_72] :
( ( multiply(d,element_in_O2(d,Y_72)) = Y_72 )
| subgroup_member(Y_72) ),
inference(negUnitSimplification,[status(thm)],[c_32,c_3413]) ).
tff(c_4816,plain,
! [Y_93] :
( ( multiply(inverse(d),Y_93) = element_in_O2(d,Y_93) )
| subgroup_member(Y_93) ),
inference(superposition,[status(thm),theory(equality)],[c_3491,c_252]) ).
tff(c_14,plain,
! [X_11] : ( multiply(X_11,inverse(X_11)) = identity ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_520,plain,
! [Z_39] : ( multiply(a,multiply(c,Z_39)) = multiply(d,Z_39) ),
inference(superposition,[status(thm),theory(equality)],[c_30,c_197]) ).
tff(c_547,plain,
multiply(d,inverse(c)) = multiply(a,identity),
inference(superposition,[status(thm),theory(equality)],[c_14,c_520]) ).
tff(c_556,plain,
multiply(d,inverse(c)) = a,
inference(demodulation,[status(thm),theory(equality)],[c_12,c_547]) ).
tff(c_561,plain,
multiply(inverse(d),a) = inverse(c),
inference(superposition,[status(thm),theory(equality)],[c_556,c_252]) ).
tff(c_4916,plain,
( ( element_in_O2(d,a) = inverse(c) )
| subgroup_member(a) ),
inference(superposition,[status(thm),theory(equality)],[c_4816,c_561]) ).
tff(c_5020,plain,
element_in_O2(d,a) = inverse(c),
inference(negUnitSimplification,[status(thm)],[c_195,c_4916]) ).
tff(c_22,plain,
! [X_13,Y_14] :
( subgroup_member(element_in_O2(X_13,Y_14))
| subgroup_member(Y_14)
| subgroup_member(X_13) ),
inference(cnfTransformation,[status(thm)],[f_141]) ).
tff(c_5212,plain,
( subgroup_member(inverse(c))
| subgroup_member(a)
| subgroup_member(d) ),
inference(superposition,[status(thm),theory(equality)],[c_5020,c_22]) ).
tff(c_5222,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_195,c_680,c_5212]) ).
tff(c_5224,plain,
subgroup_member(a),
inference(splitRight,[status(thm)],[c_191]) ).
tff(c_8,plain,
! [X_6] :
( subgroup_member(inverse(X_6))
| ~ subgroup_member(X_6) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_5223,plain,
~ subgroup_member(c),
inference(splitRight,[status(thm)],[c_191]) ).
tff(c_169,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a))
| ~ subgroup_member(b) ),
inference(superposition,[status(thm),theory(equality)],[c_28,c_166]) ).
tff(c_186,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_169]) ).
tff(c_5225,plain,
~ subgroup_member(inverse(a)),
inference(negUnitSimplification,[status(thm)],[c_5223,c_186]) ).
tff(c_5228,plain,
~ subgroup_member(a),
inference(resolution,[status(thm)],[c_8,c_5225]) ).
tff(c_5232,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5224,c_5228]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP039-7 : TPTP v8.1.2. Bugfixed v1.0.1.
% 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
% 0.15/0.36 % Computer : n019.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 22:00:46 EDT 2023
% 0.15/0.36 % CPUTime :
% 6.28/2.52 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.28/2.53
% 6.28/2.53 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.28/2.56
% 6.28/2.56 Inference rules
% 6.28/2.56 ----------------------
% 6.28/2.56 #Ref : 0
% 6.28/2.56 #Sup : 1265
% 6.28/2.56 #Fact : 0
% 6.28/2.56 #Define : 0
% 6.63/2.56 #Split : 4
% 6.63/2.56 #Chain : 0
% 6.63/2.56 #Close : 0
% 6.63/2.56
% 6.63/2.56 Ordering : KBO
% 6.63/2.56
% 6.63/2.56 Simplification rules
% 6.63/2.56 ----------------------
% 6.63/2.56 #Subsume : 250
% 6.63/2.56 #Demod : 1119
% 6.63/2.56 #Tautology : 603
% 6.63/2.56 #SimpNegUnit : 159
% 6.63/2.56 #BackRed : 4
% 6.63/2.56
% 6.63/2.56 #Partial instantiations: 0
% 6.63/2.56 #Strategies tried : 1
% 6.63/2.56
% 6.63/2.56 Timing (in seconds)
% 6.63/2.56 ----------------------
% 6.63/2.57 Preprocessing : 0.47
% 6.63/2.57 Parsing : 0.23
% 6.63/2.57 CNF conversion : 0.02
% 6.63/2.57 Main loop : 1.01
% 6.63/2.57 Inferencing : 0.36
% 6.63/2.57 Reduction : 0.37
% 6.63/2.57 Demodulation : 0.28
% 6.63/2.57 BG Simplification : 0.05
% 6.63/2.57 Subsumption : 0.16
% 6.63/2.57 Abstraction : 0.04
% 6.63/2.57 MUC search : 0.00
% 6.63/2.57 Cooper : 0.00
% 6.63/2.57 Total : 1.54
% 6.63/2.57 Index Insertion : 0.00
% 6.63/2.57 Index Deletion : 0.00
% 6.63/2.57 Index Matching : 0.00
% 6.63/2.57 BG Taut test : 0.00
%------------------------------------------------------------------------------