TSTP Solution File: GRP126-2.004 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP126-2.004 : TPTP v8.1.2. Released v1.2.0.
% 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 : n006.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 10:39:58 EDT 2023
% Result : Unsatisfiable 6.02s 2.41s
% Output : CNFRefutation 6.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 28
% Syntax : Number of formulae : 112 ( 60 unt; 9 typ; 0 def)
% Number of atoms : 204 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 170 ( 69 ~; 101 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 5 >; 5 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 71 (; 71 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > next > greater > equalish > group_element > #nlpp > e_4 > e_3 > e_2 > e_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(group_element,type,
group_element: $i > $o ).
tff(greater,type,
greater: ( $i * $i ) > $o ).
tff(e_2,type,
e_2: $i ).
tff(product,type,
product: ( $i * $i * $i ) > $o ).
tff(next,type,
next: ( $i * $i ) > $o ).
tff(e_4,type,
e_4: $i ).
tff(e_3,type,
e_3: $i ).
tff(equalish,type,
equalish: ( $i * $i ) > $o ).
tff(e_1,type,
e_1: $i ).
tff(f_75,axiom,
~ equalish(e_4,e_3),
file(unknown,unknown) ).
tff(f_73,axiom,
~ equalish(e_4,e_2),
file(unknown,unknown) ).
tff(f_63,axiom,
~ equalish(e_2,e_4),
file(unknown,unknown) ).
tff(f_55,axiom,
~ equalish(e_1,e_3),
file(unknown,unknown) ).
tff(f_71,axiom,
~ equalish(e_4,e_1),
file(unknown,unknown) ).
tff(f_57,axiom,
~ equalish(e_1,e_4),
file(unknown,unknown) ).
tff(f_48,axiom,
group_element(e_1),
file(unknown,unknown) ).
tff(f_51,axiom,
group_element(e_4),
file(unknown,unknown) ).
tff(f_89,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(X,Y,e_1)
| product(X,Y,e_2)
| product(X,Y,e_3)
| product(X,Y,e_4) ),
file(unknown,unknown) ).
tff(f_115,axiom,
! [X] : product(X,X,X),
file(unknown,unknown) ).
tff(f_105,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_31,axiom,
next(e_2,e_3),
file(unknown,unknown) ).
tff(f_50,axiom,
group_element(e_3),
file(unknown,unknown) ).
tff(f_69,axiom,
~ equalish(e_3,e_4),
file(unknown,unknown) ).
tff(f_113,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_123,axiom,
! [X,Y,Z1,Z2] :
( ~ product(X,Y,Z1)
| ~ product(Y,X,Z2)
| product(Z1,Z2,Y) ),
file(unknown,unknown) ).
tff(f_97,axiom,
! [X,Y,W,Z] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_38,axiom,
greater(e_4,e_3),
file(unknown,unknown) ).
tff(f_47,axiom,
! [X,Y,X1] :
( ~ product(X,e_1,Y)
| ~ next(X,X1)
| ~ greater(Y,X1) ),
file(unknown,unknown) ).
tff(c_52,plain,
~ equalish(e_4,e_3),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_50,plain,
~ equalish(e_4,e_2),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_40,plain,
~ equalish(e_2,e_4),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_32,plain,
~ equalish(e_1,e_3),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_48,plain,
~ equalish(e_4,e_1),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_34,plain,
~ equalish(e_1,e_4),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_22,plain,
group_element(e_1),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_28,plain,
group_element(e_4),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_130,plain,
! [X_58,Y_59] :
( product(X_58,Y_59,e_4)
| product(X_58,Y_59,e_3)
| product(X_58,Y_59,e_2)
| product(X_58,Y_59,e_1)
| ~ group_element(Y_59)
| ~ group_element(X_58) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_62,plain,
! [X_18] : product(X_18,X_18,X_18),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_111,plain,
! [W_46,Z_47,X_48,Y_49] :
( equalish(W_46,Z_47)
| ~ product(X_48,Z_47,Y_49)
| ~ product(X_48,W_46,Y_49) ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_114,plain,
! [W_46,X_18] :
( equalish(W_46,X_18)
| ~ product(X_18,W_46,X_18) ),
inference(resolution,[status(thm)],[c_62,c_111]) ).
tff(c_137,plain,
! [Y_59] :
( equalish(Y_59,e_4)
| product(e_4,Y_59,e_3)
| product(e_4,Y_59,e_2)
| product(e_4,Y_59,e_1)
| ~ group_element(Y_59)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_130,c_114]) ).
tff(c_169,plain,
! [Y_59] :
( equalish(Y_59,e_4)
| product(e_4,Y_59,e_3)
| product(e_4,Y_59,e_2)
| product(e_4,Y_59,e_1)
| ~ group_element(Y_59) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_137]) ).
tff(c_4,plain,
next(e_2,e_3),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_26,plain,
group_element(e_3),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_54,plain,
! [X_4,Y_5] :
( product(X_4,Y_5,e_4)
| product(X_4,Y_5,e_3)
| product(X_4,Y_5,e_2)
| product(X_4,Y_5,e_1)
| ~ group_element(Y_5)
| ~ group_element(X_4) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_46,plain,
~ equalish(e_3,e_4),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_187,plain,
! [Y_60] :
( equalish(Y_60,e_4)
| product(e_4,Y_60,e_3)
| product(e_4,Y_60,e_2)
| product(e_4,Y_60,e_1)
| ~ group_element(Y_60) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_137]) ).
tff(c_87,plain,
! [W_29,Z_30,Y_31,X_32] :
( equalish(W_29,Z_30)
| ~ product(Z_30,Y_31,X_32)
| ~ product(W_29,Y_31,X_32) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_90,plain,
! [W_29,X_18] :
( equalish(W_29,X_18)
| ~ product(W_29,X_18,X_18) ),
inference(resolution,[status(thm)],[c_62,c_87]) ).
tff(c_208,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_187,c_90]) ).
tff(c_231,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_208]) ).
tff(c_232,plain,
( product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_46,c_52,c_231]) ).
tff(c_238,plain,
product(e_4,e_3,e_1),
inference(splitLeft,[status(thm)],[c_232]) ).
tff(c_64,plain,
! [Z1_21,Z2_22,Y_20,X_19] :
( product(Z1_21,Z2_22,Y_20)
| ~ product(Y_20,X_19,Z2_22)
| ~ product(X_19,Y_20,Z1_21) ),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_295,plain,
! [Z1_67] :
( product(Z1_67,e_1,e_4)
| ~ product(e_3,e_4,Z1_67) ),
inference(resolution,[status(thm)],[c_238,c_64]) ).
tff(c_298,plain,
( product(e_4,e_1,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_54,c_295]) ).
tff(c_301,plain,
( product(e_4,e_1,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_28,c_298]) ).
tff(c_314,plain,
product(e_3,e_4,e_1),
inference(splitLeft,[status(thm)],[c_301]) ).
tff(c_257,plain,
! [Z1_21] :
( product(Z1_21,e_1,e_4)
| ~ product(e_3,e_4,Z1_21) ),
inference(resolution,[status(thm)],[c_238,c_64]) ).
tff(c_325,plain,
product(e_1,e_1,e_4),
inference(resolution,[status(thm)],[c_314,c_257]) ).
tff(c_100,plain,
! [W_39,Z_40,X_41,Y_42] :
( equalish(W_39,Z_40)
| ~ product(X_41,Y_42,Z_40)
| ~ product(X_41,Y_42,W_39) ),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_103,plain,
! [W_39,X_18] :
( equalish(W_39,X_18)
| ~ product(X_18,X_18,W_39) ),
inference(resolution,[status(thm)],[c_62,c_100]) ).
tff(c_342,plain,
equalish(e_4,e_1),
inference(resolution,[status(thm)],[c_325,c_103]) ).
tff(c_368,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_48,c_342]) ).
tff(c_369,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_4,e_3)
| product(e_4,e_1,e_4) ),
inference(splitRight,[status(thm)],[c_301]) ).
tff(c_423,plain,
product(e_4,e_1,e_4),
inference(splitLeft,[status(thm)],[c_369]) ).
tff(c_430,plain,
equalish(e_1,e_4),
inference(resolution,[status(thm)],[c_423,c_114]) ).
tff(c_457,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_34,c_430]) ).
tff(c_458,plain,
( product(e_3,e_4,e_3)
| product(e_3,e_4,e_2) ),
inference(splitRight,[status(thm)],[c_369]) ).
tff(c_466,plain,
product(e_3,e_4,e_2),
inference(splitLeft,[status(thm)],[c_458]) ).
tff(c_507,plain,
product(e_2,e_1,e_4),
inference(resolution,[status(thm)],[c_466,c_257]) ).
tff(c_18,plain,
greater(e_4,e_3),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_66,plain,
! [Y_24,X1_25,X_26] :
( ~ greater(Y_24,X1_25)
| ~ next(X_26,X1_25)
| ~ product(X_26,e_1,Y_24) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_81,plain,
! [X_26] :
( ~ next(X_26,e_3)
| ~ product(X_26,e_1,e_4) ),
inference(resolution,[status(thm)],[c_18,c_66]) ).
tff(c_529,plain,
~ next(e_2,e_3),
inference(resolution,[status(thm)],[c_507,c_81]) ).
tff(c_551,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_529]) ).
tff(c_552,plain,
product(e_3,e_4,e_3),
inference(splitRight,[status(thm)],[c_458]) ).
tff(c_558,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_552,c_114]) ).
tff(c_571,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_558]) ).
tff(c_572,plain,
product(e_4,e_3,e_2),
inference(splitRight,[status(thm)],[c_232]) ).
tff(c_631,plain,
! [Z1_81] :
( product(Z1_81,e_2,e_4)
| ~ product(e_3,e_4,Z1_81) ),
inference(resolution,[status(thm)],[c_572,c_64]) ).
tff(c_634,plain,
( product(e_4,e_2,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_54,c_631]) ).
tff(c_637,plain,
( product(e_4,e_2,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_28,c_634]) ).
tff(c_992,plain,
product(e_3,e_4,e_1),
inference(splitLeft,[status(thm)],[c_637]) ).
tff(c_1306,plain,
! [Z1_102] :
( product(Z1_102,e_1,e_3)
| ~ product(e_4,e_3,Z1_102) ),
inference(resolution,[status(thm)],[c_992,c_64]) ).
tff(c_1321,plain,
product(e_2,e_1,e_3),
inference(resolution,[status(thm)],[c_572,c_1306]) ).
tff(c_60,plain,
! [W_14,Z_17,Y_15,X_16] :
( equalish(W_14,Z_17)
| ~ product(Z_17,Y_15,X_16)
| ~ product(W_14,Y_15,X_16) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_1480,plain,
! [W_108] :
( equalish(W_108,e_2)
| ~ product(W_108,e_1,e_3) ),
inference(resolution,[status(thm)],[c_1321,c_60]) ).
tff(c_1493,plain,
( equalish(e_4,e_2)
| equalish(e_1,e_4)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_169,c_1480]) ).
tff(c_1502,plain,
( equalish(e_4,e_2)
| equalish(e_1,e_4)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_1493]) ).
tff(c_1503,plain,
( product(e_4,e_1,e_2)
| product(e_4,e_1,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_34,c_50,c_1502]) ).
tff(c_1547,plain,
product(e_4,e_1,e_1),
inference(splitLeft,[status(thm)],[c_1503]) ).
tff(c_1560,plain,
equalish(e_4,e_1),
inference(resolution,[status(thm)],[c_1547,c_90]) ).
tff(c_1576,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_48,c_1560]) ).
tff(c_1577,plain,
product(e_4,e_1,e_2),
inference(splitRight,[status(thm)],[c_1503]) ).
tff(c_58,plain,
! [W_11,Z_13,X_10,Y_12] :
( equalish(W_11,Z_13)
| ~ product(X_10,Z_13,Y_12)
| ~ product(X_10,W_11,Y_12) ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_584,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product(e_4,W_11,e_2) ),
inference(resolution,[status(thm)],[c_572,c_58]) ).
tff(c_1591,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_1577,c_584]) ).
tff(c_1613,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_1591]) ).
tff(c_1614,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_4,e_3)
| product(e_4,e_2,e_4) ),
inference(splitRight,[status(thm)],[c_637]) ).
tff(c_1616,plain,
product(e_4,e_2,e_4),
inference(splitLeft,[status(thm)],[c_1614]) ).
tff(c_1676,plain,
equalish(e_2,e_4),
inference(resolution,[status(thm)],[c_1616,c_114]) ).
tff(c_1697,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_40,c_1676]) ).
tff(c_1698,plain,
( product(e_3,e_4,e_3)
| product(e_3,e_4,e_2) ),
inference(splitRight,[status(thm)],[c_1614]) ).
tff(c_1706,plain,
product(e_3,e_4,e_2),
inference(splitLeft,[status(thm)],[c_1698]) ).
tff(c_583,plain,
! [Z1_21] :
( product(Z1_21,e_2,e_4)
| ~ product(e_3,e_4,Z1_21) ),
inference(resolution,[status(thm)],[c_572,c_64]) ).
tff(c_1809,plain,
product(e_2,e_2,e_4),
inference(resolution,[status(thm)],[c_1706,c_583]) ).
tff(c_1826,plain,
equalish(e_4,e_2),
inference(resolution,[status(thm)],[c_1809,c_103]) ).
tff(c_1843,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_50,c_1826]) ).
tff(c_1844,plain,
product(e_3,e_4,e_3),
inference(splitRight,[status(thm)],[c_1698]) ).
tff(c_1850,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_1844,c_114]) ).
tff(c_1863,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_1850]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP126-2.004 : TPTP v8.1.2. Released v1.2.0.
% 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
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 22:07:29 EDT 2023
% 0.19/0.35 % CPUTime :
% 6.02/2.41 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.02/2.44
% 6.02/2.44 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.32/2.48
% 6.32/2.48 Inference rules
% 6.32/2.48 ----------------------
% 6.32/2.48 #Ref : 0
% 6.32/2.48 #Sup : 369
% 6.32/2.48 #Fact : 0
% 6.32/2.48 #Define : 0
% 6.32/2.48 #Split : 12
% 6.32/2.48 #Chain : 0
% 6.32/2.48 #Close : 0
% 6.32/2.48
% 6.32/2.48 Ordering : KBO
% 6.32/2.48
% 6.32/2.48 Simplification rules
% 6.32/2.48 ----------------------
% 6.32/2.48 #Subsume : 24
% 6.32/2.48 #Demod : 279
% 6.32/2.48 #Tautology : 108
% 6.32/2.48 #SimpNegUnit : 92
% 6.32/2.48 #BackRed : 0
% 6.32/2.48
% 6.32/2.48 #Partial instantiations: 0
% 6.32/2.48 #Strategies tried : 1
% 6.32/2.48
% 6.32/2.48 Timing (in seconds)
% 6.32/2.48 ----------------------
% 6.32/2.48 Preprocessing : 0.47
% 6.32/2.48 Parsing : 0.26
% 6.32/2.48 CNF conversion : 0.03
% 6.32/2.48 Main loop : 0.89
% 6.32/2.48 Inferencing : 0.31
% 6.32/2.48 Reduction : 0.25
% 6.32/2.48 Demodulation : 0.16
% 6.32/2.48 BG Simplification : 0.04
% 6.32/2.48 Subsumption : 0.25
% 6.32/2.48 Abstraction : 0.03
% 6.32/2.49 MUC search : 0.00
% 6.32/2.49 Cooper : 0.00
% 6.32/2.49 Total : 1.45
% 6.32/2.49 Index Insertion : 0.00
% 6.32/2.49 Index Deletion : 0.00
% 6.32/2.49 Index Matching : 0.00
% 6.32/2.49 BG Taut test : 0.00
%------------------------------------------------------------------------------