TSTP Solution File: GRP123-4.003 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP123-4.003 : 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/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 : n004.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 10:39:54 EDT 2023
% Result : Unsatisfiable 4.42s 1.99s
% Output : CNFRefutation 4.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 20
% Syntax : Number of formulae : 58 ( 21 unt; 6 typ; 0 def)
% Number of atoms : 131 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 139 ( 60 ~; 79 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 68 (; 68 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > equalish > group_element > #nlpp > e_3 > e_2 > e_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(group_element,type,
group_element: $i > $o ).
tff(e_2,type,
e_2: $i ).
tff(product,type,
product: ( $i * $i * $i ) > $o ).
tff(e_3,type,
e_3: $i ).
tff(equalish,type,
equalish: ( $i * $i ) > $o ).
tff(e_1,type,
e_1: $i ).
tff(f_64,axiom,
~ equalish(e_1,e_2),
file(unknown,unknown) ).
tff(f_66,axiom,
~ equalish(e_1,e_3),
file(unknown,unknown) ).
tff(f_60,axiom,
group_element(e_1),
file(unknown,unknown) ).
tff(f_112,axiom,
! [X] : product(X,X,X),
file(unknown,unknown) ).
tff(f_62,axiom,
group_element(e_3),
file(unknown,unknown) ).
tff(f_86,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(X,Y,e_1)
| product(X,Y,e_2)
| product(X,Y,e_3) ),
file(unknown,unknown) ).
tff(f_102,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_74,axiom,
~ equalish(e_3,e_2),
file(unknown,unknown) ).
tff(f_70,axiom,
~ equalish(e_2,e_3),
file(unknown,unknown) ).
tff(f_61,axiom,
group_element(e_2),
file(unknown,unknown) ).
tff(f_59,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(X,e_1,Y)
| product(X,e_2,Y)
| product(X,e_3,Y) ),
file(unknown,unknown) ).
tff(f_110,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_94,axiom,
! [X,Y,W,Z] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_126,axiom,
! [Y1,X1,Z2,Y2,X2,Z1] :
( ~ product(X1,Y1,Z1)
| ~ product(X2,Y2,Z1)
| ~ product(Z2,Y1,X1)
| ~ product(Z2,Y2,X2)
| equalish(X1,X2) ),
file(unknown,unknown) ).
tff(c_12,plain,
~ equalish(e_1,e_2),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_14,plain,
~ equalish(e_1,e_3),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_6,plain,
group_element(e_1),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_32,plain,
! [X_19] : product(X_19,X_19,X_19),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_10,plain,
group_element(e_3),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_68,plain,
! [X_52,Y_53] :
( product(X_52,Y_53,e_3)
| product(X_52,Y_53,e_2)
| product(X_52,Y_53,e_1)
| ~ group_element(Y_53)
| ~ group_element(X_52) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_48,plain,
! [W_40,Z_41,X_42,Y_43] :
( equalish(W_40,Z_41)
| ~ product(X_42,Z_41,Y_43)
| ~ product(X_42,W_40,Y_43) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_51,plain,
! [W_40,X_19] :
( equalish(W_40,X_19)
| ~ product(X_19,W_40,X_19) ),
inference(resolution,[status(thm)],[c_32,c_48]) ).
tff(c_78,plain,
! [Y_53] :
( equalish(Y_53,e_3)
| product(e_3,Y_53,e_2)
| product(e_3,Y_53,e_1)
| ~ group_element(Y_53)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_68,c_51]) ).
tff(c_91,plain,
! [Y_53] :
( equalish(Y_53,e_3)
| product(e_3,Y_53,e_2)
| product(e_3,Y_53,e_1)
| ~ group_element(Y_53) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_78]) ).
tff(c_22,plain,
~ equalish(e_3,e_2),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_18,plain,
~ equalish(e_2,e_3),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_8,plain,
group_element(e_2),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_265,plain,
! [X_61,Y_62] :
( product(X_61,e_3,Y_62)
| product(X_61,e_2,Y_62)
| product(X_61,e_1,Y_62)
| ~ group_element(Y_62)
| ~ group_element(X_61) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_38,plain,
! [W_33,Z_34,Y_35,X_36] :
( equalish(W_33,Z_34)
| ~ product(Z_34,Y_35,X_36)
| ~ product(W_33,Y_35,X_36) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_41,plain,
! [W_33,X_19] :
( equalish(W_33,X_19)
| ~ product(W_33,X_19,X_19) ),
inference(resolution,[status(thm)],[c_32,c_38]) ).
tff(c_281,plain,
! [X_61] :
( equalish(X_61,e_3)
| product(X_61,e_2,e_3)
| product(X_61,e_1,e_3)
| ~ group_element(e_3)
| ~ group_element(X_61) ),
inference(resolution,[status(thm)],[c_265,c_41]) ).
tff(c_473,plain,
! [X_75] :
( equalish(X_75,e_3)
| product(X_75,e_2,e_3)
| product(X_75,e_1,e_3)
| ~ group_element(X_75) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_281]) ).
tff(c_58,plain,
! [W_46,Z_47,X_48,Y_49] :
( equalish(W_46,Z_47)
| ~ product(X_48,Y_49,Z_47)
| ~ product(X_48,Y_49,W_46) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_61,plain,
! [W_46,X_19] :
( equalish(W_46,X_19)
| ~ product(X_19,X_19,W_46) ),
inference(resolution,[status(thm)],[c_32,c_58]) ).
tff(c_494,plain,
( equalish(e_3,e_2)
| equalish(e_2,e_3)
| product(e_2,e_1,e_3)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_473,c_61]) ).
tff(c_521,plain,
( equalish(e_3,e_2)
| equalish(e_2,e_3)
| product(e_2,e_1,e_3) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_494]) ).
tff(c_522,plain,
product(e_2,e_1,e_3),
inference(negUnitSimplification,[status(thm)],[c_18,c_22,c_521]) ).
tff(c_530,plain,
! [Y1_76,X2_81,X1_79,Z1_80,Z2_77,Y2_78] :
( equalish(X1_79,X2_81)
| ~ product(Z2_77,Y2_78,X2_81)
| ~ product(Z2_77,Y1_76,X1_79)
| ~ product(X2_81,Y2_78,Z1_80)
| ~ product(X1_79,Y1_76,Z1_80) ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_917,plain,
! [X1_90,X_91,Y1_92,Z1_93] :
( equalish(X1_90,X_91)
| ~ product(X_91,Y1_92,X1_90)
| ~ product(X_91,X_91,Z1_93)
| ~ product(X1_90,Y1_92,Z1_93) ),
inference(resolution,[status(thm)],[c_32,c_530]) ).
tff(c_927,plain,
! [Z1_93] :
( equalish(e_3,e_2)
| ~ product(e_2,e_2,Z1_93)
| ~ product(e_3,e_1,Z1_93) ),
inference(resolution,[status(thm)],[c_522,c_917]) ).
tff(c_981,plain,
! [Z1_94] :
( ~ product(e_2,e_2,Z1_94)
| ~ product(e_3,e_1,Z1_94) ),
inference(negUnitSimplification,[status(thm)],[c_22,c_927]) ).
tff(c_993,plain,
( ~ product(e_2,e_2,e_2)
| equalish(e_1,e_3)
| product(e_3,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_91,c_981]) ).
tff(c_1012,plain,
( equalish(e_1,e_3)
| product(e_3,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_32,c_993]) ).
tff(c_1013,plain,
product(e_3,e_1,e_1),
inference(negUnitSimplification,[status(thm)],[c_14,c_1012]) ).
tff(c_201,plain,
! [Y_59] :
( equalish(Y_59,e_3)
| product(e_3,Y_59,e_2)
| product(e_3,Y_59,e_1)
| ~ group_element(Y_59) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_78]) ).
tff(c_213,plain,
( equalish(e_3,e_2)
| equalish(e_2,e_3)
| product(e_3,e_2,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_201,c_41]) ).
tff(c_224,plain,
( equalish(e_3,e_2)
| equalish(e_2,e_3)
| product(e_3,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_213]) ).
tff(c_225,plain,
product(e_3,e_2,e_1),
inference(negUnitSimplification,[status(thm)],[c_18,c_22,c_224]) ).
tff(c_28,plain,
! [W_12,Z_14,X_11,Y_13] :
( equalish(W_12,Z_14)
| ~ product(X_11,Z_14,Y_13)
| ~ product(X_11,W_12,Y_13) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_234,plain,
! [W_12] :
( equalish(W_12,e_2)
| ~ product(e_3,W_12,e_1) ),
inference(resolution,[status(thm)],[c_225,c_28]) ).
tff(c_1031,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[c_1013,c_234]) ).
tff(c_1050,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12,c_1031]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP123-4.003 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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
% 0.16/0.34 % Computer : n004.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Thu Aug 3 22:01:56 EDT 2023
% 0.16/0.34 % CPUTime :
% 4.42/1.99 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.42/2.00
% 4.42/2.00 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.42/2.03
% 4.42/2.03 Inference rules
% 4.42/2.03 ----------------------
% 4.42/2.03 #Ref : 0
% 4.42/2.03 #Sup : 198
% 4.42/2.03 #Fact : 0
% 4.42/2.03 #Define : 0
% 4.42/2.03 #Split : 0
% 4.42/2.03 #Chain : 0
% 4.42/2.03 #Close : 0
% 4.42/2.03
% 4.42/2.03 Ordering : KBO
% 4.42/2.03
% 4.42/2.03 Simplification rules
% 4.42/2.03 ----------------------
% 4.42/2.03 #Subsume : 4
% 4.42/2.03 #Demod : 147
% 4.42/2.03 #Tautology : 66
% 4.42/2.03 #SimpNegUnit : 61
% 4.42/2.03 #BackRed : 0
% 4.42/2.03
% 4.42/2.03 #Partial instantiations: 0
% 4.42/2.03 #Strategies tried : 1
% 4.42/2.03
% 4.42/2.03 Timing (in seconds)
% 4.42/2.03 ----------------------
% 4.42/2.03 Preprocessing : 0.44
% 4.42/2.03 Parsing : 0.24
% 4.42/2.03 CNF conversion : 0.03
% 4.42/2.03 Main loop : 0.53
% 4.42/2.03 Inferencing : 0.20
% 4.42/2.04 Reduction : 0.13
% 4.42/2.04 Demodulation : 0.09
% 4.42/2.04 BG Simplification : 0.03
% 4.42/2.04 Subsumption : 0.15
% 4.42/2.04 Abstraction : 0.02
% 4.42/2.04 MUC search : 0.00
% 4.42/2.04 Cooper : 0.00
% 4.42/2.04 Total : 1.02
% 4.42/2.04 Index Insertion : 0.00
% 4.42/2.04 Index Deletion : 0.00
% 4.42/2.04 Index Matching : 0.00
% 4.42/2.04 BG Taut test : 0.00
%------------------------------------------------------------------------------