TSTP Solution File: LCL109-3 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL109-3 : 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 : n026.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 10:47:23 EDT 2023
% Result : Unsatisfiable 195.70s 170.04s
% Output : CNFRefutation 195.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 72 ( 38 unt; 5 typ; 0 def)
% Number of atoms : 97 ( 96 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 64 ( 34 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 6 ( 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 : 123 (; 123 !; 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_70,axiom,
! [X,Y] : ( implies(X,implies(Y,X)) = truth ),
file(unknown,unknown) ).
tff(f_54,axiom,
! [X,Y] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
file(unknown,unknown) ).
tff(f_50,axiom,
! [X] : ( implies(truth,X) = X ),
file(unknown,unknown) ).
tff(f_79,axiom,
! [X,Y,Z] : ( implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)) ),
file(unknown,unknown) ).
tff(f_77,axiom,
! [X,Y,Z] : ( implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))) = truth ),
file(unknown,unknown) ).
tff(f_83,axiom,
! [X] : ( not(not(X)) = X ),
file(unknown,unknown) ).
tff(f_85,axiom,
! [X,Y] : ( implies(not(X),not(Y)) = implies(Y,X) ),
file(unknown,unknown) ).
tff(f_75,axiom,
! [X,Y,Z] :
( ( implies(X,Y) != implies(Y,Z) )
| ( implies(X,Z) = truth ) ),
file(unknown,unknown) ).
tff(f_66,axiom,
! [X,Y] :
( ( implies(X,Y) != implies(Y,X) )
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_81,axiom,
! [X] : ( implies(X,not(truth)) = not(X) ),
file(unknown,unknown) ).
tff(f_87,axiom,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
file(unknown,unknown) ).
tff(c_16,plain,
! [X_13,Y_14] : ( implies(X_13,implies(Y_14,X_13)) = truth ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
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_54]) ).
tff(c_2,plain,
! [X_1] : ( implies(truth,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_526,plain,
! [Y_50,X_51] : ( implies(implies(Y_50,X_51),X_51) = implies(implies(X_51,Y_50),Y_50) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_628,plain,
! [Y_14,X_13] : ( implies(implies(implies(Y_14,X_13),X_13),X_13) = implies(truth,implies(Y_14,X_13)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_526]) ).
tff(c_3936,plain,
! [Y_93,X_94] : ( implies(implies(implies(Y_93,X_94),X_94),X_94) = implies(Y_93,X_94) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_628]) ).
tff(c_4147,plain,
! [Y_6,X_5] : ( implies(implies(implies(Y_6,X_5),X_5),Y_6) = implies(X_5,Y_6) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_3936]) ).
tff(c_22,plain,
! [Y_22,X_21,Z_23] : ( implies(Y_22,implies(X_21,Z_23)) = implies(X_21,implies(Y_22,Z_23)) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_20,plain,
! [X_18,Y_19,Z_20] : ( implies(implies(X_18,Y_19),implies(implies(Z_20,X_18),implies(Z_20,Y_19))) = truth ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_1669,plain,
! [X_67,Y_68,Z_69] : ( implies(implies(X_67,Y_68),implies(Z_69,implies(implies(Z_69,X_67),Y_68))) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_20]) ).
tff(c_1827,plain,
! [Y_6,X_5,Z_69] : ( implies(implies(implies(Y_6,X_5),X_5),implies(Z_69,implies(implies(Z_69,implies(X_5,Y_6)),Y_6))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_1669]) ).
tff(c_26,plain,
! [X_25] : ( not(not(X_25)) = X_25 ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_285,plain,
! [X_39,Y_40] : ( implies(not(X_39),not(Y_40)) = implies(Y_40,X_39) ),
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_301,plain,
! [Y_40,X_39] : ( implies(not(Y_40),implies(Y_40,X_39)) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_285,c_16]) ).
tff(c_28,plain,
! [X_26,Y_27] : ( implies(not(X_26),not(Y_27)) = implies(Y_27,X_26) ),
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_396,plain,
! [X_43,Z_44,Y_45] :
( ( implies(X_43,Z_44) = truth )
| ( implies(Y_45,Z_44) != implies(X_43,Y_45) ) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_14886,plain,
! [X_197,Z_198,Y_199] :
( ( implies(not(X_197),Z_198) = truth )
| ( implies(not(Y_199),Z_198) != implies(Y_199,X_197) ) ),
inference(superposition,[status(thm),theory(equality)],[c_28,c_396]) ).
tff(c_15012,plain,
! [Y_40,X_39,Z_198] :
( ( implies(not(implies(Y_40,X_39)),Z_198) = truth )
| ( implies(not(not(Y_40)),Z_198) != truth ) ),
inference(superposition,[status(thm),theory(equality)],[c_301,c_14886]) ).
tff(c_15079,plain,
! [Y_40,X_39,Z_198] :
( ( implies(not(implies(Y_40,X_39)),Z_198) = truth )
| ( implies(Y_40,Z_198) != truth ) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_15012]) ).
tff(c_573,plain,
! [Y_50,X_51] : ( implies(Y_50,implies(implies(Y_50,X_51),X_51)) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_526,c_16]) ).
tff(c_76342,plain,
! [Y_449,X_450] : ( implies(implies(implies(Y_449,X_450),X_450),Y_449) = implies(X_450,Y_449) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_3936]) ).
tff(c_12,plain,
! [Y_11,X_10] :
( ( Y_11 = X_10 )
| ( implies(Y_11,X_10) != implies(X_10,Y_11) ) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_77075,plain,
! [Y_449,X_450] :
( ( implies(implies(Y_449,X_450),X_450) = Y_449 )
| ( implies(Y_449,implies(implies(Y_449,X_450),X_450)) != implies(X_450,Y_449) ) ),
inference(superposition,[status(thm),theory(equality)],[c_76342,c_12]) ).
tff(c_77620,plain,
! [Y_449,X_450] :
( ( implies(implies(Y_449,X_450),X_450) = Y_449 )
| ( implies(X_450,Y_449) != truth ) ),
inference(demodulation,[status(thm),theory(equality)],[c_573,c_77075]) ).
tff(c_24,plain,
! [X_24] : ( implies(X_24,not(truth)) = not(X_24) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_410,plain,
! [X_43,X_24] :
( ( implies(X_43,not(truth)) = truth )
| ( implies(X_43,X_24) != not(X_24) ) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_396]) ).
tff(c_427,plain,
! [X_43,X_24] :
( ( not(X_43) = truth )
| ( implies(X_43,X_24) != not(X_24) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_410]) ).
tff(c_466681,plain,
! [Y_1068,X_1069] :
( ( not(implies(implies(Y_1068,X_1069),X_1069)) = truth )
| ( implies(Y_1068,X_1069) != not(X_1069) ) ),
inference(superposition,[status(thm),theory(equality)],[c_3936,c_427]) ).
tff(c_3278,plain,
! [X_84,X_83] : ( implies(not(X_84),X_83) = implies(not(X_83),X_84) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_285]) ).
tff(c_416,plain,
! [Z_44,X_1] :
( ( implies(truth,Z_44) = truth )
| ( implies(X_1,Z_44) != X_1 ) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_396]) ).
tff(c_430,plain,
! [Z_44,X_1] :
( ( truth = Z_44 )
| ( implies(X_1,Z_44) != X_1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_416]) ).
tff(c_3850,plain,
! [X_91,X_92] :
( ( truth = X_91 )
| ( implies(not(X_91),X_92) != not(X_92) ) ),
inference(superposition,[status(thm),theory(equality)],[c_3278,c_430]) ).
tff(c_3915,plain,
! [X_91,Y_14] :
( ( truth = X_91 )
| ( not(implies(Y_14,not(X_91))) != truth ) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_3850]) ).
tff(c_467501,plain,
! [X_91,Y_1068] :
( ( truth = X_91 )
| ( implies(Y_1068,not(X_91)) != not(not(X_91)) ) ),
inference(superposition,[status(thm),theory(equality)],[c_466681,c_3915]) ).
tff(c_469013,plain,
! [X_1070,Y_1071] :
( ( truth = X_1070 )
| ( implies(Y_1071,not(X_1070)) != X_1070 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_467501]) ).
tff(c_470016,plain,
! [Y_1074] :
( ( truth = Y_1074 )
| ( implies(not(Y_1074),Y_1074) != truth ) ),
inference(superposition,[status(thm),theory(equality)],[c_77620,c_469013]) ).
tff(c_661034,plain,
! [Y_1422,X_1423] :
( ( implies(Y_1422,X_1423) = truth )
| ( implies(Y_1422,implies(Y_1422,X_1423)) != truth ) ),
inference(superposition,[status(thm),theory(equality)],[c_15079,c_470016]) ).
tff(c_661411,plain,
! [Y_6,X_5] : ( implies(implies(implies(Y_6,X_5),X_5),implies(implies(implies(implies(Y_6,X_5),X_5),implies(X_5,Y_6)),Y_6)) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_1827,c_661034]) ).
tff(c_662337,plain,
! [X_1424,Y_1425] : ( implies(implies(implies(X_1424,Y_1425),X_1424),X_1424) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4147,c_22,c_4147,c_22,c_661411]) ).
tff(c_83390,plain,
! [Y_466,X_467] :
( ( implies(implies(Y_466,X_467),X_467) = Y_466 )
| ( implies(X_467,Y_466) != truth ) ),
inference(demodulation,[status(thm),theory(equality)],[c_573,c_77075]) ).
tff(c_131,plain,
! [X_33,Y_34] : ( implies(X_33,implies(Y_34,X_33)) = truth ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_171,plain,
! [X_35] : ( implies(not(truth),not(X_35)) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_131]) ).
tff(c_194,plain,
! [X_25] : ( implies(not(truth),X_25) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_171]) ).
tff(c_252,plain,
! [Y_37,X_38] :
( ( Y_37 = X_38 )
| ( implies(Y_37,X_38) != implies(X_38,Y_37) ) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_264,plain,
! [X_24] :
( ( not(truth) = X_24 )
| ( implies(not(truth),X_24) != not(X_24) ) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_252]) ).
tff(c_341,plain,
! [X_41] :
( ( not(truth) = X_41 )
| ( not(X_41) != truth ) ),
inference(demodulation,[status(thm),theory(equality)],[c_194,c_264]) ).
tff(c_345,plain,
! [X_42] :
( ( not(truth) = not(X_42) )
| ( truth != X_42 ) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_341]) ).
tff(c_359,plain,
! [X_26,X_42] :
( ( implies(not(X_26),not(truth)) = implies(X_42,X_26) )
| ( truth != X_42 ) ),
inference(superposition,[status(thm),theory(equality)],[c_345,c_28]) ).
tff(c_386,plain,
! [X_42,X_26] :
( ( implies(X_42,X_26) = X_26 )
| ( truth != X_42 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_24,c_359]) ).
tff(c_84121,plain,
! [Y_466,X_467] :
( ( Y_466 = X_467 )
| ( implies(Y_466,X_467) != truth )
| ( implies(X_467,Y_466) != truth ) ),
inference(superposition,[status(thm),theory(equality)],[c_83390,c_386]) ).
tff(c_663049,plain,
! [X_1424,Y_1425] :
( ( implies(implies(X_1424,Y_1425),X_1424) = X_1424 )
| ( implies(X_1424,implies(implies(X_1424,Y_1425),X_1424)) != truth ) ),
inference(superposition,[status(thm),theory(equality)],[c_662337,c_84121]) ).
tff(c_665850,plain,
! [X_1424,Y_1425] : ( implies(implies(X_1424,Y_1425),X_1424) = X_1424 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_663049]) ).
tff(c_30,plain,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_31,plain,
implies(b,implies(implies(b,implies(implies(a,b),a)),a)) != truth,
inference(demodulation,[status(thm),theory(equality)],[c_22,c_22,c_30]) ).
tff(c_666523,plain,
implies(b,implies(implies(b,a),a)) != truth,
inference(demodulation,[status(thm),theory(equality)],[c_665850,c_31]) ).
tff(c_666528,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_6,c_666523]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL109-3 : 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
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 14:15:16 EDT 2023
% 0.13/0.35 % CPUTime :
% 195.70/170.04 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 195.74/170.05
% 195.74/170.05 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 195.74/170.09
% 195.74/170.09 Inference rules
% 195.74/170.09 ----------------------
% 195.74/170.09 #Ref : 51
% 195.74/170.09 #Sup : 178116
% 195.74/170.09 #Fact : 0
% 195.74/170.09 #Define : 0
% 195.74/170.09 #Split : 2
% 195.74/170.09 #Chain : 0
% 195.74/170.09 #Close : 0
% 195.74/170.09
% 195.74/170.09 Ordering : KBO
% 195.74/170.09
% 195.74/170.09 Simplification rules
% 195.74/170.09 ----------------------
% 195.74/170.09 #Subsume : 70416
% 195.74/170.09 #Demod : 145852
% 195.74/170.09 #Tautology : 40307
% 195.74/170.09 #SimpNegUnit : 1443
% 195.74/170.09 #BackRed : 28
% 195.74/170.09
% 195.74/170.09 #Partial instantiations: 0
% 195.74/170.09 #Strategies tried : 1
% 195.74/170.09
% 195.74/170.09 Timing (in seconds)
% 195.74/170.09 ----------------------
% 195.74/170.09 Preprocessing : 0.46
% 195.74/170.10 Parsing : 0.22
% 195.74/170.10 CNF conversion : 0.02
% 195.74/170.10 Main loop : 168.53
% 195.74/170.10 Inferencing : 7.07
% 195.74/170.10 Reduction : 105.75
% 195.74/170.10 Demodulation : 95.92
% 195.74/170.10 BG Simplification : 0.78
% 195.74/170.10 Subsumption : 43.71
% 195.74/170.10 Abstraction : 1.57
% 195.74/170.10 MUC search : 0.00
% 195.74/170.10 Cooper : 0.00
% 195.74/170.10 Total : 169.06
% 195.74/170.10 Index Insertion : 0.00
% 195.74/170.10 Index Deletion : 0.00
% 195.74/170.10 Index Matching : 0.00
% 195.74/170.10 BG Taut test : 0.00
%------------------------------------------------------------------------------