TSTP Solution File: LCL116-2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL116-2 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n025.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 10:47:25 EDT 2023
% Result : Unsatisfiable 10.21s 3.52s
% Output : CNFRefutation 10.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 10
% Syntax : Number of formulae : 85 ( 80 unt; 5 typ; 0 def)
% Number of atoms : 80 ( 79 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 143 (; 143 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ implies > #nlpp > not > truth > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(truth,type,
truth: $i ).
tff(a,type,
a: $i ).
tff(b,type,
b: $i ).
tff(not,type,
not: $i > $i ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff(f_51,axiom,
! [X] : ( implies(truth,X) = X ),
file(unknown,unknown) ).
tff(f_53,axiom,
! [X,Y,Z] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
file(unknown,unknown) ).
tff(f_55,axiom,
! [X,Y] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
file(unknown,unknown) ).
tff(f_57,axiom,
! [X,Y] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
file(unknown,unknown) ).
tff(f_61,axiom,
implies(not(a),implies(b,not(implies(b,a)))) != truth,
file(unknown,unknown) ).
tff(c_2,plain,
! [X_1] : ( implies(truth,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_187,plain,
! [X_17,Y_18,Z_19] : ( implies(implies(X_17,Y_18),implies(implies(Y_18,Z_19),implies(X_17,Z_19))) = truth ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_308,plain,
! [X_1,Z_19] : ( implies(X_1,implies(implies(X_1,Z_19),implies(truth,Z_19))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_187]) ).
tff(c_408,plain,
! [X_21,Z_22] : ( implies(X_21,implies(implies(X_21,Z_22),Z_22)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_308]) ).
tff(c_439,plain,
! [Z_22] : ( implies(implies(truth,Z_22),Z_22) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_408,c_2]) ).
tff(c_503,plain,
! [Z_22] : ( implies(Z_22,Z_22) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_439]) ).
tff(c_46,plain,
! [Y_13,X_14] : ( implies(implies(Y_13,X_14),X_14) = implies(implies(X_14,Y_13),Y_13) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_79,plain,
! [X_1] : ( implies(implies(X_1,truth),truth) = implies(X_1,X_1) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_46]) ).
tff(c_571,plain,
! [X_24] : ( implies(implies(X_24,truth),truth) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_503,c_79]) ).
tff(c_326,plain,
! [X_1,Z_19] : ( implies(X_1,implies(implies(X_1,Z_19),Z_19)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_308]) ).
tff(c_656,plain,
! [X_25] : ( implies(X_25,truth) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_571,c_326]) ).
tff(c_4,plain,
! [X_2,Y_3,Z_4] : ( implies(implies(X_2,Y_3),implies(implies(Y_3,Z_4),implies(X_2,Z_4))) = truth ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_670,plain,
! [Z_4,X_25] : ( implies(truth,implies(implies(truth,Z_4),implies(X_25,Z_4))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_656,c_4]) ).
tff(c_725,plain,
! [Z_4,X_25] : ( implies(Z_4,implies(X_25,Z_4)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_670]) ).
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_57]) ).
tff(c_298,plain,
! [X_17,X_7,Y_8] : ( implies(implies(X_17,implies(not(X_7),not(Y_8))),implies(truth,implies(X_17,implies(Y_8,X_7)))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_187]) ).
tff(c_860,plain,
! [X_28,X_29,Y_30] : ( implies(implies(X_28,implies(not(X_29),not(Y_30))),implies(X_28,implies(Y_30,X_29))) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_298]) ).
tff(c_1017,plain,
! [Y_31,X_32] : ( implies(truth,implies(not(Y_31),implies(Y_31,X_32))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_725,c_860]) ).
tff(c_1034,plain,
! [Y_31,X_32] : ( implies(truth,implies(truth,implies(not(Y_31),implies(Y_31,X_32)))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_1017,c_326]) ).
tff(c_1125,plain,
! [Y_33,X_34] : ( implies(not(Y_33),implies(Y_33,X_34)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_1034]) ).
tff(c_1208,plain,
! [X_1] : ( implies(not(truth),X_1) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1125]) ).
tff(c_20,plain,
! [X_10,Y_11] : ( implies(implies(not(X_10),not(Y_11)),implies(Y_11,X_10)) = truth ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_33,plain,
! [X_1] : ( implies(implies(not(X_1),not(truth)),X_1) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_20]) ).
tff(c_1232,plain,
! [X_35] : ( implies(not(truth),X_35) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1125]) ).
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_55]) ).
tff(c_1288,plain,
! [X_35] : ( implies(implies(X_35,not(truth)),not(truth)) = implies(truth,X_35) ),
inference(superposition,[status(thm),theory(equality)],[c_1232,c_6]) ).
tff(c_1349,plain,
! [X_36] : ( implies(implies(X_36,not(truth)),not(truth)) = X_36 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1288]) ).
tff(c_1389,plain,
not(not(truth)) = truth,
inference(superposition,[status(thm),theory(equality)],[c_1349,c_33]) ).
tff(c_1334,plain,
! [X_35] : ( implies(implies(X_35,not(truth)),not(truth)) = X_35 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1288]) ).
tff(c_4246,plain,
! [Y_62,X_63,Z_64] : ( implies(truth,implies(implies(implies(Y_62,X_63),Z_64),implies(implies(not(X_63),not(Y_62)),Z_64))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_187]) ).
tff(c_4423,plain,
! [X_35] : ( implies(truth,implies(X_35,implies(implies(not(not(truth)),not(X_35)),not(truth)))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_1334,c_4246]) ).
tff(c_4858,plain,
! [X_66] : ( implies(X_66,implies(not(X_66),not(truth))) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_1389,c_4423]) ).
tff(c_4950,plain,
! [X_66] : ( implies(implies(implies(not(X_66),not(truth)),X_66),X_66) = implies(truth,implies(not(X_66),not(truth))) ),
inference(superposition,[status(thm),theory(equality)],[c_4858,c_6]) ).
tff(c_5040,plain,
! [X_67] : ( implies(not(X_67),not(truth)) = X_67 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_33,c_2,c_4950]) ).
tff(c_5137,plain,
! [X_67] : ( implies(implies(not(truth),not(X_67)),not(X_67)) = implies(X_67,not(truth)) ),
inference(superposition,[status(thm),theory(equality)],[c_5040,c_6]) ).
tff(c_5190,plain,
! [X_67] : ( implies(X_67,not(truth)) = not(X_67) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1208,c_5137]) ).
tff(c_6455,plain,
! [Y_76,X_77,Y_78] : ( implies(implies(implies(Y_76,X_77),Y_78),implies(implies(Y_78,X_77),implies(implies(X_77,Y_76),Y_76))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_187]) ).
tff(c_6732,plain,
! [X_1,Y_78] : ( implies(implies(implies(X_1,not(truth)),Y_78),implies(implies(Y_78,not(truth)),implies(truth,X_1))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_1208,c_6455]) ).
tff(c_6968,plain,
! [X_1,Y_78] : ( implies(implies(not(X_1),Y_78),implies(not(Y_78),X_1)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_5190,c_5190,c_2,c_6732]) ).
tff(c_13134,plain,
! [X_115,Y_116] : ( implies(implies(not(X_115),Y_116),implies(not(Y_116),X_115)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_5190,c_5190,c_2,c_6732]) ).
tff(c_13315,plain,
! [Y_116,X_115] : ( implies(implies(implies(not(Y_116),X_115),implies(not(X_115),Y_116)),implies(not(X_115),Y_116)) = implies(truth,implies(not(Y_116),X_115)) ),
inference(superposition,[status(thm),theory(equality)],[c_13134,c_6]) ).
tff(c_13526,plain,
! [Y_116,X_115] : ( implies(not(Y_116),X_115) = implies(not(X_115),Y_116) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6968,c_2,c_13315]) ).
tff(c_325,plain,
! [X_17,X_7,Y_8] : ( implies(implies(X_17,implies(not(X_7),not(Y_8))),implies(X_17,implies(Y_8,X_7))) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_298]) ).
tff(c_3665,plain,
! [X_57,Y_58] : ( implies(truth,implies(not(not(X_57)),implies(Y_58,X_57))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_1125,c_325]) ).
tff(c_743,plain,
! [Z_26,X_27] : ( implies(Z_26,implies(X_27,Z_26)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_670]) ).
tff(c_772,plain,
! [X_27,Z_26] : ( implies(implies(implies(X_27,Z_26),Z_26),Z_26) = implies(truth,implies(X_27,Z_26)) ),
inference(superposition,[status(thm),theory(equality)],[c_743,c_6]) ).
tff(c_830,plain,
! [X_27,Z_26] : ( implies(implies(implies(X_27,Z_26),Z_26),Z_26) = implies(X_27,Z_26) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_772]) ).
tff(c_3694,plain,
! [X_57,Y_58] : ( implies(implies(truth,implies(not(not(X_57)),implies(Y_58,X_57))),implies(not(not(X_57)),implies(Y_58,X_57))) = implies(truth,implies(not(not(X_57)),implies(Y_58,X_57))) ),
inference(superposition,[status(thm),theory(equality)],[c_3665,c_830]) ).
tff(c_3885,plain,
! [X_59,Y_60] : ( implies(not(not(X_59)),implies(Y_60,X_59)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_503,c_2,c_2,c_3694]) ).
tff(c_4052,plain,
! [X_1] : ( implies(not(not(X_1)),X_1) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_3885]) ).
tff(c_4427,plain,
! [X_63] : ( implies(truth,implies(implies(implies(truth,X_63),not(truth)),not(X_63))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_1334,c_4246]) ).
tff(c_4598,plain,
! [X_63] : ( implies(implies(X_63,not(truth)),not(X_63)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_4427]) ).
tff(c_5801,plain,
! [X_71] : ( implies(X_71,not(not(X_71))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_5040,c_4598]) ).
tff(c_5888,plain,
! [X_71] : ( implies(implies(not(not(X_71)),X_71),X_71) = implies(truth,not(not(X_71))) ),
inference(superposition,[status(thm),theory(equality)],[c_5801,c_6]) ).
tff(c_5943,plain,
! [X_71] : ( not(not(X_71)) = X_71 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4052,c_2,c_5888]) ).
tff(c_14001,plain,
! [Y_119,X_120] : ( implies(not(Y_119),X_120) = implies(not(X_120),Y_119) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6968,c_2,c_13315]) ).
tff(c_15065,plain,
! [Y_123,X_124] : ( implies(not(Y_123),not(X_124)) = implies(X_124,Y_123) ),
inference(superposition,[status(thm),theory(equality)],[c_5943,c_14001]) ).
tff(c_15269,plain,
! [X_71,X_124] : ( implies(X_71,not(X_124)) = implies(X_124,not(X_71)) ),
inference(superposition,[status(thm),theory(equality)],[c_5943,c_15065]) ).
tff(c_5022,plain,
! [X_66] : ( implies(not(X_66),not(truth)) = X_66 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_33,c_2,c_4950]) ).
tff(c_760,plain,
! [X_2,Z_26,X_27] : ( implies(implies(X_2,Z_26),implies(truth,implies(X_2,implies(X_27,Z_26)))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_743,c_4]) ).
tff(c_2441,plain,
! [X_46,Z_47,X_48] : ( implies(implies(X_46,Z_47),implies(X_46,implies(X_48,Z_47))) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_760]) ).
tff(c_3033,plain,
! [Z_51,X_52,X_53] : ( implies(truth,implies(Z_51,implies(X_52,implies(X_53,Z_51)))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_725,c_2441]) ).
tff(c_3056,plain,
! [Z_51,X_52,X_53] : ( implies(implies(truth,implies(Z_51,implies(X_52,implies(X_53,Z_51)))),implies(Z_51,implies(X_52,implies(X_53,Z_51)))) = implies(truth,implies(Z_51,implies(X_52,implies(X_53,Z_51)))) ),
inference(superposition,[status(thm),theory(equality)],[c_3033,c_830]) ).
tff(c_3338,plain,
! [Z_54,X_55,X_56] : ( implies(Z_54,implies(X_55,implies(X_56,Z_54))) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_503,c_2,c_2,c_3056]) ).
tff(c_8867,plain,
! [Z_92,X_93,X_94] : ( implies(Z_92,implies(implies(implies(X_93,Z_92),X_94),X_94)) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_3338]) ).
tff(c_276,plain,
! [X_17,Y_6,X_5] : ( implies(implies(X_17,implies(Y_6,X_5)),implies(implies(implies(X_5,Y_6),Y_6),implies(X_17,X_5))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_187]) ).
tff(c_8938,plain,
! [X_94,X_93,Z_92] : ( implies(truth,implies(implies(implies(X_94,implies(implies(X_93,Z_92),X_94)),implies(implies(X_93,Z_92),X_94)),implies(Z_92,X_94))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_8867,c_276]) ).
tff(c_11850,plain,
! [X_108,Z_109,X_110] : ( implies(implies(implies(X_108,Z_109),X_110),implies(Z_109,X_110)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_830,c_2,c_6,c_8938]) ).
tff(c_12176,plain,
! [X_108,X_66] : ( implies(implies(implies(X_108,not(X_66)),not(truth)),X_66) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_5022,c_11850]) ).
tff(c_12468,plain,
! [X_111,X_112] : ( implies(not(implies(X_111,not(X_112))),X_112) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_5190,c_12176]) ).
tff(c_12705,plain,
! [X_112,Y_6] : ( implies(not(implies(implies(not(X_112),Y_6),Y_6)),X_112) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_12468]) ).
tff(c_15071,plain,
! [X_124,Y_123] : ( implies(not(implies(implies(X_124,Y_123),not(X_124))),Y_123) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_15065,c_12705]) ).
tff(c_23739,plain,
! [Y_123,X_124] : ( implies(not(Y_123),implies(X_124,not(implies(X_124,Y_123)))) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_13526,c_15269,c_15071]) ).
tff(c_10,plain,
implies(not(a),implies(b,not(implies(b,a)))) != truth,
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_23742,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_23739,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL116-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.36 % Computer : n025.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Thu Aug 3 14:15:04 EDT 2023
% 0.13/0.36 % CPUTime :
% 10.21/3.52 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.21/3.53
% 10.21/3.53 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.21/3.57
% 10.21/3.57 Inference rules
% 10.21/3.57 ----------------------
% 10.21/3.57 #Ref : 0
% 10.21/3.57 #Sup : 5857
% 10.21/3.57 #Fact : 0
% 10.21/3.57 #Define : 0
% 10.21/3.57 #Split : 0
% 10.21/3.57 #Chain : 0
% 10.21/3.57 #Close : 0
% 10.21/3.57
% 10.21/3.57 Ordering : KBO
% 10.21/3.57
% 10.21/3.57 Simplification rules
% 10.21/3.57 ----------------------
% 10.21/3.57 #Subsume : 5
% 10.21/3.57 #Demod : 8415
% 10.21/3.57 #Tautology : 4287
% 10.21/3.57 #SimpNegUnit : 0
% 10.21/3.57 #BackRed : 20
% 10.21/3.57
% 10.21/3.57 #Partial instantiations: 0
% 10.21/3.57 #Strategies tried : 1
% 10.21/3.57
% 10.21/3.57 Timing (in seconds)
% 10.21/3.57 ----------------------
% 10.21/3.58 Preprocessing : 0.40
% 10.21/3.58 Parsing : 0.21
% 10.21/3.58 CNF conversion : 0.02
% 10.21/3.58 Main loop : 2.07
% 10.21/3.58 Inferencing : 0.51
% 10.21/3.58 Reduction : 1.13
% 10.21/3.58 Demodulation : 1.01
% 10.21/3.58 BG Simplification : 0.04
% 10.21/3.58 Subsumption : 0.28
% 10.21/3.58 Abstraction : 0.07
% 10.21/3.58 MUC search : 0.00
% 10.21/3.58 Cooper : 0.00
% 10.21/3.58 Total : 2.54
% 10.21/3.58 Index Insertion : 0.00
% 10.21/3.58 Index Deletion : 0.00
% 10.21/3.58 Index Matching : 0.00
% 10.21/3.58 BG Taut test : 0.00
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