TSTP Solution File: GRP039-2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP039-2 : 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 : n008.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 6.06s 2.48s
% Output : CNFRefutation 6.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 22
% Syntax : Number of formulae : 78 ( 47 unt; 9 typ; 0 def)
% Number of atoms : 106 ( 44 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 ( 2 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 : 57 (; 57 !; 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_148,axiom,
~ subgroup_member(d),
file(unknown,unknown) ).
tff(f_146,axiom,
multiply(a,c) = d,
file(unknown,unknown) ).
tff(f_122,axiom,
! [X,Y,Z] :
( ~ subgroup_member(X)
| ~ subgroup_member(Y)
| ( multiply(X,Y) != Z )
| subgroup_member(Z) ),
file(unknown,unknown) ).
tff(f_144,axiom,
subgroup_member(b),
file(unknown,unknown) ).
tff(f_127,axiom,
! [X] : ( multiply(X,identity) = X ),
file(unknown,unknown) ).
tff(f_129,axiom,
! [X] : ( multiply(X,inverse(X)) = identity ),
file(unknown,unknown) ).
tff(f_73,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_80,axiom,
! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_145,axiom,
multiply(b,inverse(a)) = c,
file(unknown,unknown) ).
tff(f_77,axiom,
! [X] : ( multiply(inverse(X),X) = identity ),
file(unknown,unknown) ).
tff(f_142,axiom,
! [X,Y] :
( subgroup_member(X)
| subgroup_member(Y)
| ( multiply(X,element_in_O2(X,Y)) = Y ) ),
file(unknown,unknown) ).
tff(f_136,axiom,
! [X,Y] :
( subgroup_member(X)
| subgroup_member(Y)
| subgroup_member(element_in_O2(X,Y)) ),
file(unknown,unknown) ).
tff(f_111,axiom,
! [X] :
( ~ subgroup_member(X)
| subgroup_member(inverse(X)) ),
file(unknown,unknown) ).
tff(c_26,plain,
~ subgroup_member(d),
inference(cnfTransformation,[status(thm)],[f_148]) ).
tff(c_24,plain,
multiply(a,c) = d,
inference(cnfTransformation,[status(thm)],[f_146]) ).
tff(c_112,plain,
! [X_21,Y_22] :
( subgroup_member(multiply(X_21,Y_22))
| ~ subgroup_member(Y_22)
| ~ subgroup_member(X_21) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_130,plain,
( subgroup_member(d)
| ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_112]) ).
tff(c_133,plain,
( ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(negUnitSimplification,[status(thm)],[c_26,c_130]) ).
tff(c_134,plain,
~ subgroup_member(a),
inference(splitLeft,[status(thm)],[c_133]) ).
tff(c_20,plain,
subgroup_member(b),
inference(cnfTransformation,[status(thm)],[f_144]) ).
tff(c_12,plain,
! [X_10] : ( multiply(X_10,identity) = X_10 ),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_14,plain,
! [X_11] : ( multiply(X_11,inverse(X_11)) = identity ),
inference(cnfTransformation,[status(thm)],[f_129]) ).
tff(c_2,plain,
! [X_1] : ( multiply(identity,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_217,plain,
! [X_29,Y_30,Z_31] : ( multiply(multiply(X_29,Y_30),Z_31) = multiply(X_29,multiply(Y_30,Z_31)) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_243,plain,
! [X_11,Z_31] : ( multiply(X_11,multiply(inverse(X_11),Z_31)) = multiply(identity,Z_31) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_217]) ).
tff(c_277,plain,
! [X_32,Z_33] : ( multiply(X_32,multiply(inverse(X_32),Z_33)) = Z_33 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_243]) ).
tff(c_313,plain,
! [X_32] : ( inverse(inverse(X_32)) = multiply(X_32,identity) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_277]) ).
tff(c_332,plain,
! [X_32] : ( inverse(inverse(X_32)) = X_32 ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_313]) ).
tff(c_22,plain,
multiply(b,inverse(a)) = c,
inference(cnfTransformation,[status(thm)],[f_145]) ).
tff(c_4,plain,
! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_253,plain,
! [X_2,Z_31] : ( multiply(inverse(X_2),multiply(X_2,Z_31)) = multiply(identity,Z_31) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_217]) ).
tff(c_422,plain,
! [X_38,Z_39] : ( multiply(inverse(X_38),multiply(X_38,Z_39)) = Z_39 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_253]) ).
tff(c_461,plain,
multiply(inverse(b),c) = inverse(a),
inference(superposition,[status(thm),theory(equality)],[c_22,c_422]) ).
tff(c_613,plain,
! [X_41,Y_42] : ( multiply(X_41,multiply(Y_42,inverse(multiply(X_41,Y_42)))) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_217]) ).
tff(c_676,plain,
multiply(inverse(b),multiply(c,inverse(inverse(a)))) = identity,
inference(superposition,[status(thm),theory(equality)],[c_461,c_613]) ).
tff(c_751,plain,
multiply(inverse(b),multiply(c,a)) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_332,c_676]) ).
tff(c_273,plain,
! [X_2,Z_31] : ( multiply(inverse(X_2),multiply(X_2,Z_31)) = Z_31 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_253]) ).
tff(c_822,plain,
multiply(inverse(inverse(b)),identity) = multiply(c,a),
inference(superposition,[status(thm),theory(equality)],[c_751,c_273]) ).
tff(c_835,plain,
multiply(c,a) = b,
inference(demodulation,[status(thm),theory(equality)],[c_12,c_332,c_822]) ).
tff(c_852,plain,
multiply(inverse(c),b) = a,
inference(superposition,[status(thm),theory(equality)],[c_835,c_273]) ).
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_122]) ).
tff(c_951,plain,
( subgroup_member(a)
| ~ subgroup_member(b)
| ~ subgroup_member(inverse(c)) ),
inference(superposition,[status(thm),theory(equality)],[c_852,c_10]) ).
tff(c_958,plain,
( subgroup_member(a)
| ~ subgroup_member(inverse(c)) ),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_951]) ).
tff(c_959,plain,
~ subgroup_member(inverse(c)),
inference(negUnitSimplification,[status(thm)],[c_134,c_958]) ).
tff(c_337,plain,
! [X_34,Y_35] :
( ( multiply(X_34,element_in_O2(X_34,Y_35)) = Y_35 )
| subgroup_member(Y_35)
| subgroup_member(X_34) ),
inference(cnfTransformation,[status(thm)],[f_142]) ).
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_80]) ).
tff(c_2929,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_337,c_6]) ).
tff(c_266,plain,
! [Z_31] : ( multiply(a,multiply(c,Z_31)) = multiply(d,Z_31) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_217]) ).
tff(c_3001,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_2929,c_266]) ).
tff(c_3192,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_24,c_24,c_3001]) ).
tff(c_3260,plain,
! [Y_72] :
( ( multiply(d,element_in_O2(d,Y_72)) = Y_72 )
| subgroup_member(Y_72) ),
inference(negUnitSimplification,[status(thm)],[c_26,c_3192]) ).
tff(c_5253,plain,
! [Y_98] :
( ( multiply(inverse(d),Y_98) = element_in_O2(d,Y_98) )
| subgroup_member(Y_98) ),
inference(superposition,[status(thm),theory(equality)],[c_3260,c_273]) ).
tff(c_542,plain,
! [Z_40] : ( multiply(a,multiply(c,Z_40)) = multiply(d,Z_40) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_217]) ).
tff(c_569,plain,
multiply(d,inverse(c)) = multiply(a,identity),
inference(superposition,[status(thm),theory(equality)],[c_14,c_542]) ).
tff(c_578,plain,
multiply(d,inverse(c)) = a,
inference(demodulation,[status(thm),theory(equality)],[c_12,c_569]) ).
tff(c_583,plain,
multiply(inverse(d),a) = inverse(c),
inference(superposition,[status(thm),theory(equality)],[c_578,c_273]) ).
tff(c_5353,plain,
( ( element_in_O2(d,a) = inverse(c) )
| subgroup_member(a) ),
inference(superposition,[status(thm),theory(equality)],[c_5253,c_583]) ).
tff(c_5464,plain,
element_in_O2(d,a) = inverse(c),
inference(negUnitSimplification,[status(thm)],[c_134,c_5353]) ).
tff(c_16,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_136]) ).
tff(c_5523,plain,
( subgroup_member(inverse(c))
| subgroup_member(a)
| subgroup_member(d) ),
inference(superposition,[status(thm),theory(equality)],[c_5464,c_16]) ).
tff(c_5533,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_26,c_134,c_959,c_5523]) ).
tff(c_5535,plain,
subgroup_member(a),
inference(splitRight,[status(thm)],[c_133]) ).
tff(c_8,plain,
! [X_6] :
( subgroup_member(inverse(X_6))
| ~ subgroup_member(X_6) ),
inference(cnfTransformation,[status(thm)],[f_111]) ).
tff(c_5534,plain,
~ subgroup_member(c),
inference(splitRight,[status(thm)],[c_133]) ).
tff(c_118,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a))
| ~ subgroup_member(b) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_112]) ).
tff(c_132,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_118]) ).
tff(c_5537,plain,
~ subgroup_member(inverse(a)),
inference(negUnitSimplification,[status(thm)],[c_5534,c_132]) ).
tff(c_5540,plain,
~ subgroup_member(a),
inference(resolution,[status(thm)],[c_8,c_5537]) ).
tff(c_5544,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5535,c_5540]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP039-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % 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
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 3 22:23:48 EDT 2023
% 0.12/0.34 % CPUTime :
% 6.06/2.48 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.06/2.50
% 6.06/2.50 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.42/2.53
% 6.42/2.53 Inference rules
% 6.42/2.53 ----------------------
% 6.42/2.53 #Ref : 0
% 6.42/2.53 #Sup : 1343
% 6.42/2.53 #Fact : 0
% 6.42/2.53 #Define : 0
% 6.42/2.53 #Split : 5
% 6.42/2.53 #Chain : 0
% 6.42/2.53 #Close : 0
% 6.42/2.53
% 6.42/2.53 Ordering : KBO
% 6.42/2.53
% 6.42/2.53 Simplification rules
% 6.42/2.53 ----------------------
% 6.42/2.53 #Subsume : 256
% 6.42/2.53 #Demod : 1229
% 6.42/2.53 #Tautology : 653
% 6.42/2.53 #SimpNegUnit : 159
% 6.42/2.53 #BackRed : 9
% 6.42/2.53
% 6.42/2.53 #Partial instantiations: 0
% 6.42/2.53 #Strategies tried : 1
% 6.42/2.53
% 6.42/2.53 Timing (in seconds)
% 6.42/2.53 ----------------------
% 6.42/2.53 Preprocessing : 0.48
% 6.42/2.53 Parsing : 0.25
% 6.42/2.53 CNF conversion : 0.02
% 6.42/2.53 Main loop : 1.02
% 6.42/2.53 Inferencing : 0.37
% 6.42/2.53 Reduction : 0.38
% 6.42/2.53 Demodulation : 0.30
% 6.42/2.53 BG Simplification : 0.03
% 6.42/2.53 Subsumption : 0.16
% 6.42/2.53 Abstraction : 0.04
% 6.42/2.53 MUC search : 0.00
% 6.42/2.53 Cooper : 0.00
% 6.42/2.53 Total : 1.56
% 6.42/2.53 Index Insertion : 0.00
% 6.42/2.53 Index Deletion : 0.00
% 6.42/2.53 Index Matching : 0.00
% 6.42/2.53 BG Taut test : 0.00
%------------------------------------------------------------------------------