TSTP Solution File: LCL158-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL158-1 : 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 : n010.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 10:47:30 EDT 2023
% Result : Unsatisfiable 6.68s 2.78s
% Output : CNFRefutation 6.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 24
% Syntax : Number of formulae : 102 ( 93 unt; 9 typ; 0 def)
% Number of atoms : 93 ( 92 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 11 ( 6 >; 5 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 123 (; 123 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ xor > or > implies > and_star > and > #nlpp > not > x > truth > falsehood
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(truth,type,
truth: $i ).
tff(x,type,
x: $i ).
tff(falsehood,type,
falsehood: $i ).
tff(xor,type,
xor: ( $i * $i ) > $i ).
tff(or,type,
or: ( $i * $i ) > $i ).
tff(not,type,
not: $i > $i ).
tff(and_star,type,
and_star: ( $i * $i ) > $i ).
tff(and,type,
and: ( $i * $i ) > $i ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff(f_129,axiom,
not(truth) = falsehood,
file(unknown,unknown) ).
tff(f_81,axiom,
! [X,Y] : ( or(X,Y) = implies(not(X),Y) ),
file(unknown,unknown) ).
tff(f_48,axiom,
! [X] : ( implies(truth,X) = X ),
file(unknown,unknown) ).
tff(f_50,axiom,
! [X,Y,Z] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
file(unknown,unknown) ).
tff(f_87,axiom,
! [X,Y] : ( and(X,Y) = not(or(not(X),not(Y))) ),
file(unknown,unknown) ).
tff(f_85,axiom,
! [X,Y] : ( or(X,Y) = or(Y,X) ),
file(unknown,unknown) ).
tff(f_54,axiom,
! [X,Y] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
file(unknown,unknown) ).
tff(f_52,axiom,
! [X,Y] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
file(unknown,unknown) ).
tff(f_89,axiom,
! [X,Y,Z] : ( and(and(X,Y),Z) = and(X,and(Y,Z)) ),
file(unknown,unknown) ).
tff(f_91,axiom,
! [X,Y] : ( and(X,Y) = and(Y,X) ),
file(unknown,unknown) ).
tff(f_118,axiom,
! [X,Y] : ( xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) ),
file(unknown,unknown) ).
tff(f_120,axiom,
! [X,Y] : ( xor(X,Y) = xor(Y,X) ),
file(unknown,unknown) ).
tff(f_122,axiom,
! [X,Y] : ( and_star(X,Y) = not(or(not(X),not(Y))) ),
file(unknown,unknown) ).
tff(f_127,axiom,
! [X,Y] : ( and_star(X,Y) = and_star(Y,X) ),
file(unknown,unknown) ).
tff(f_133,axiom,
and_star(xor(truth,x),x) != falsehood,
file(unknown,unknown) ).
tff(c_32,plain,
not(truth) = falsehood,
inference(cnfTransformation,[status(thm)],[f_129]) ).
tff(c_10,plain,
! [X_9,Y_10] : ( implies(not(X_9),Y_10) = or(X_9,Y_10) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_2,plain,
! [X_1] : ( implies(truth,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_1142,plain,
! [X_72,Y_73,Z_74] : ( implies(implies(X_72,Y_73),implies(implies(Y_73,Z_74),implies(X_72,Z_74))) = truth ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_1308,plain,
! [Y_73,X_1] : ( implies(implies(truth,Y_73),implies(implies(Y_73,X_1),X_1)) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1142]) ).
tff(c_1480,plain,
! [Y_76,X_77] : ( implies(Y_76,implies(implies(Y_76,X_77),X_77)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1308]) ).
tff(c_1518,plain,
! [X_77] : ( implies(implies(truth,X_77),X_77) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_1480,c_2]) ).
tff(c_1597,plain,
! [X_78] : ( implies(X_78,X_78) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1518]) ).
tff(c_1735,plain,
! [X_80] : ( or(X_80,not(X_80)) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_1597]) ).
tff(c_16,plain,
! [X_16,Y_17] : ( not(or(not(X_16),not(Y_17))) = and(X_16,Y_17) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_1763,plain,
! [X_16] : ( and(X_16,not(X_16)) = not(truth) ),
inference(superposition,[status(thm),theory(equality)],[c_1735,c_16]) ).
tff(c_1799,plain,
! [X_16] : ( and(X_16,not(X_16)) = falsehood ),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_1763]) ).
tff(c_14,plain,
! [Y_15,X_14] : ( or(Y_15,X_14) = or(X_14,Y_15) ),
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_163,plain,
! [X_43,Y_44] : ( implies(not(X_43),Y_44) = or(X_43,Y_44) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_172,plain,
! [Y_44] : ( or(truth,Y_44) = implies(falsehood,Y_44) ),
inference(superposition,[status(thm),theory(equality)],[c_32,c_163]) ).
tff(c_8,plain,
! [X_7,Y_8] : ( implies(implies(not(X_7),not(Y_8)),implies(Y_8,X_7)) = truth ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_305,plain,
! [X_50,Y_51] : ( implies(or(X_50,not(Y_51)),implies(Y_51,X_50)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_8]) ).
tff(c_339,plain,
! [X_1] : ( implies(or(X_1,not(truth)),X_1) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_305]) ).
tff(c_347,plain,
! [X_52] : ( implies(or(X_52,falsehood),X_52) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_339]) ).
tff(c_358,plain,
implies(implies(falsehood,falsehood),truth) = truth,
inference(superposition,[status(thm),theory(equality)],[c_172,c_347]) ).
tff(c_175,plain,
! [Y_45] : ( or(truth,Y_45) = implies(falsehood,Y_45) ),
inference(superposition,[status(thm),theory(equality)],[c_32,c_163]) ).
tff(c_191,plain,
! [Y_15] : ( or(Y_15,truth) = implies(falsehood,Y_15) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_175]) ).
tff(c_402,plain,
! [Y_54,X_55] : ( implies(implies(Y_54,X_55),X_55) = implies(implies(X_55,Y_54),Y_54) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_480,plain,
! [X_56] : ( implies(implies(X_56,truth),truth) = implies(X_56,X_56) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_402]) ).
tff(c_505,plain,
! [X_9] : ( or(X_9,not(X_9)) = implies(implies(not(X_9),truth),truth) ),
inference(superposition,[status(thm),theory(equality)],[c_480,c_10]) ).
tff(c_1063,plain,
! [X_71] : ( or(X_71,not(X_71)) = implies(implies(falsehood,X_71),truth) ),
inference(demodulation,[status(thm),theory(equality)],[c_191,c_10,c_505]) ).
tff(c_362,plain,
! [X_14] : ( implies(or(falsehood,X_14),X_14) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_347]) ).
tff(c_1089,plain,
implies(implies(implies(falsehood,falsehood),truth),not(falsehood)) = truth,
inference(superposition,[status(thm),theory(equality)],[c_1063,c_362]) ).
tff(c_1136,plain,
not(falsehood) = truth,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_358,c_1089]) ).
tff(c_1370,plain,
! [Y_10] : ( or(falsehood,Y_10) = implies(truth,Y_10) ),
inference(superposition,[status(thm),theory(equality)],[c_1136,c_10]) ).
tff(c_1424,plain,
! [Y_75] : ( or(falsehood,Y_75) = Y_75 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1370]) ).
tff(c_1471,plain,
! [X_14] : ( or(X_14,falsehood) = X_14 ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_1424]) ).
tff(c_1584,plain,
! [X_77] : ( implies(X_77,X_77) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1518]) ).
tff(c_441,plain,
! [X_1] : ( implies(implies(X_1,truth),truth) = implies(X_1,X_1) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_402]) ).
tff(c_1928,plain,
! [X_84] : ( implies(implies(X_84,truth),truth) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_1584,c_441]) ).
tff(c_1330,plain,
! [Y_73,X_1] : ( implies(Y_73,implies(implies(Y_73,X_1),X_1)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1308]) ).
tff(c_2015,plain,
! [X_85] : ( implies(X_85,truth) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_1928,c_1330]) ).
tff(c_2059,plain,
! [X_9] : ( or(X_9,truth) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_2015,c_10]) ).
tff(c_2247,plain,
! [Y_90] : ( implies(falsehood,Y_90) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2059,c_191]) ).
tff(c_6,plain,
! [Y_6,X_5] : ( implies(implies(Y_6,X_5),X_5) = implies(implies(X_5,Y_6),Y_6) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_2279,plain,
! [Y_90] : ( implies(implies(Y_90,falsehood),falsehood) = implies(truth,Y_90) ),
inference(superposition,[status(thm),theory(equality)],[c_2247,c_6]) ).
tff(c_3018,plain,
! [Y_101] : ( implies(implies(Y_101,falsehood),falsehood) = Y_101 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2279]) ).
tff(c_3088,plain,
! [X_9] : ( implies(or(X_9,falsehood),falsehood) = not(X_9) ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_3018]) ).
tff(c_3111,plain,
! [X_9] : ( implies(X_9,falsehood) = not(X_9) ),
inference(demodulation,[status(thm),theory(equality)],[c_1471,c_3088]) ).
tff(c_2104,plain,
! [Y_15] : ( implies(falsehood,Y_15) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2059,c_191]) ).
tff(c_198,plain,
! [X_46,Y_47] : ( not(or(not(X_46),not(Y_47))) = and(X_46,Y_47) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_225,plain,
! [Y_47,X_46] : ( not(or(not(Y_47),not(X_46))) = and(X_46,Y_47) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_198]) ).
tff(c_1349,plain,
! [Y_47] : ( not(or(not(Y_47),truth)) = and(falsehood,Y_47) ),
inference(superposition,[status(thm),theory(equality)],[c_1136,c_225]) ).
tff(c_1376,plain,
! [Y_47] : ( not(implies(falsehood,not(Y_47))) = and(falsehood,Y_47) ),
inference(demodulation,[status(thm),theory(equality)],[c_172,c_14,c_1349]) ).
tff(c_7369,plain,
! [Y_47] : ( and(falsehood,Y_47) = falsehood ),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_2104,c_1376]) ).
tff(c_7370,plain,
! [Y_155] : ( and(falsehood,Y_155) = falsehood ),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_2104,c_1376]) ).
tff(c_692,plain,
! [X_61,Y_62,Z_63] : ( and(and(X_61,Y_62),Z_63) = and(X_61,and(Y_62,Z_63)) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_20,plain,
! [Y_22,X_21] : ( and(Y_22,X_21) = and(X_21,Y_22) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_701,plain,
! [Z_63,X_61,Y_62] : ( and(Z_63,and(X_61,Y_62)) = and(X_61,and(Y_62,Z_63)) ),
inference(superposition,[status(thm),theory(equality)],[c_692,c_20]) ).
tff(c_7375,plain,
! [Y_155,Z_63] : ( and(falsehood,and(Y_155,Z_63)) = and(Z_63,falsehood) ),
inference(superposition,[status(thm),theory(equality)],[c_7370,c_701]) ).
tff(c_7436,plain,
! [Z_63] : ( and(Z_63,falsehood) = falsehood ),
inference(demodulation,[status(thm),theory(equality)],[c_7369,c_7375]) ).
tff(c_2304,plain,
! [Y_90] : ( implies(implies(Y_90,falsehood),falsehood) = Y_90 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2279]) ).
tff(c_3226,plain,
! [Y_103] : ( not(not(Y_103)) = Y_103 ),
inference(demodulation,[status(thm),theory(equality)],[c_3111,c_3111,c_2304]) ).
tff(c_3268,plain,
! [Y_103,Y_10] : ( or(not(Y_103),Y_10) = implies(Y_103,Y_10) ),
inference(superposition,[status(thm),theory(equality)],[c_3226,c_10]) ).
tff(c_3113,plain,
! [Y_90] : ( not(not(Y_90)) = Y_90 ),
inference(demodulation,[status(thm),theory(equality)],[c_3111,c_3111,c_2304]) ).
tff(c_1383,plain,
! [Y_10] : ( or(falsehood,Y_10) = Y_10 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1370]) ).
tff(c_228,plain,
! [Y_47] : ( not(or(falsehood,not(Y_47))) = and(truth,Y_47) ),
inference(superposition,[status(thm),theory(equality)],[c_32,c_198]) ).
tff(c_1422,plain,
! [Y_47] : ( not(not(Y_47)) = and(truth,Y_47) ),
inference(demodulation,[status(thm),theory(equality)],[c_1383,c_228]) ).
tff(c_3224,plain,
! [Y_47] : ( and(truth,Y_47) = Y_47 ),
inference(demodulation,[status(thm),theory(equality)],[c_3113,c_1422]) ).
tff(c_919,plain,
! [X_68,Y_69] : ( or(and(X_68,not(Y_69)),and(not(X_68),Y_69)) = xor(X_68,Y_69) ),
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_981,plain,
! [X_68] : ( or(and(X_68,falsehood),and(not(X_68),truth)) = xor(X_68,truth) ),
inference(superposition,[status(thm),theory(equality)],[c_32,c_919]) ).
tff(c_992,plain,
! [X_68] : ( or(and(X_68,falsehood),and(truth,not(X_68))) = xor(X_68,truth) ),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_981]) ).
tff(c_8119,plain,
! [X_164] : ( xor(X_164,truth) = not(X_164) ),
inference(demodulation,[status(thm),theory(equality)],[c_3111,c_7436,c_3268,c_14,c_3224,c_992]) ).
tff(c_24,plain,
! [Y_26,X_25] : ( xor(Y_26,X_25) = xor(X_25,Y_26) ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_8133,plain,
! [X_164] : ( xor(truth,X_164) = not(X_164) ),
inference(superposition,[status(thm),theory(equality)],[c_8119,c_24]) ).
tff(c_26,plain,
! [X_27,Y_28] : ( not(or(not(X_27),not(Y_28))) = and_star(X_27,Y_28) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_36,plain,
! [X_27,Y_28] : ( and_star(X_27,Y_28) = and(X_27,Y_28) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_26]) ).
tff(c_30,plain,
! [Y_33,X_32] : ( and_star(Y_33,X_32) = and_star(X_32,Y_33) ),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_34,plain,
and_star(xor(truth,x),x) != falsehood,
inference(cnfTransformation,[status(thm)],[f_133]) ).
tff(c_35,plain,
and_star(x,xor(truth,x)) != falsehood,
inference(demodulation,[status(thm),theory(equality)],[c_30,c_34]) ).
tff(c_38,plain,
and(x,xor(truth,x)) != falsehood,
inference(demodulation,[status(thm),theory(equality)],[c_36,c_35]) ).
tff(c_8162,plain,
and(x,not(x)) != falsehood,
inference(demodulation,[status(thm),theory(equality)],[c_8133,c_38]) ).
tff(c_8165,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1799,c_8162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL158-1 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.13 % 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 : n010.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 13:20:29 EDT 2023
% 0.13/0.35 % CPUTime :
% 6.68/2.78 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.68/2.79
% 6.68/2.79 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.68/2.83
% 6.68/2.83 Inference rules
% 6.68/2.83 ----------------------
% 6.68/2.83 #Ref : 0
% 6.68/2.83 #Sup : 2022
% 6.68/2.83 #Fact : 0
% 6.68/2.83 #Define : 0
% 6.68/2.83 #Split : 0
% 6.68/2.83 #Chain : 0
% 6.68/2.83 #Close : 0
% 6.68/2.83
% 6.68/2.83 Ordering : KBO
% 6.68/2.83
% 6.68/2.83 Simplification rules
% 6.68/2.83 ----------------------
% 6.68/2.83 #Subsume : 47
% 6.68/2.83 #Demod : 2031
% 6.68/2.83 #Tautology : 1308
% 6.68/2.83 #SimpNegUnit : 0
% 6.68/2.83 #BackRed : 21
% 6.68/2.83
% 6.68/2.83 #Partial instantiations: 0
% 6.68/2.83 #Strategies tried : 1
% 6.68/2.83
% 6.68/2.83 Timing (in seconds)
% 6.68/2.83 ----------------------
% 6.68/2.83 Preprocessing : 0.48
% 6.68/2.83 Parsing : 0.25
% 6.68/2.83 CNF conversion : 0.02
% 6.68/2.84 Main loop : 1.26
% 6.68/2.84 Inferencing : 0.38
% 6.68/2.84 Reduction : 0.57
% 6.68/2.84 Demodulation : 0.48
% 6.68/2.84 BG Simplification : 0.04
% 6.68/2.84 Subsumption : 0.18
% 6.68/2.84 Abstraction : 0.05
% 6.68/2.84 MUC search : 0.00
% 6.68/2.84 Cooper : 0.00
% 6.68/2.84 Total : 1.80
% 6.68/2.84 Index Insertion : 0.00
% 6.68/2.84 Index Deletion : 0.00
% 6.68/2.84 Index Matching : 0.00
% 6.68/2.84 BG Taut test : 0.00
%------------------------------------------------------------------------------