TSTP Solution File: LCL268-3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : LCL268-3 : TPTP v8.1.2. Released v2.3.0.
% 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 : n029.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 10:47:51 EDT 2023

% Result   : Unsatisfiable 7.04s 2.71s
% Output   : CNFRefutation 7.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   65 (  30 unt;   8 typ;   0 def)
%            Number of atoms       :   91 (   9 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   70 (  36   ~;  34   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   7   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-2 aty)
%            Number of variables   :  111 (; 111   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ theorem > axiom > or > implies > equivalent > and > #nlpp > not > p

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(theorem,type,
    theorem: $i > $o ).

tff(or,type,
    or: ( $i * $i ) > $i ).

tff(not,type,
    not: $i > $i ).

tff(equivalent,type,
    equivalent: ( $i * $i ) > $i ).

tff(and,type,
    and: ( $i * $i ) > $i ).

tff(axiom,type,
    axiom: $i > $o ).

tff(p,type,
    p: $i ).

tff(implies,type,
    implies: ( $i * $i ) > $i ).

tff(f_48,axiom,
    ! [A,B] : axiom(implies(A,or(B,A))),
    file(unknown,unknown) ).

tff(f_61,axiom,
    ! [X] :
      ( theorem(X)
      | ~ axiom(X) ),
    file(unknown,unknown) ).

tff(f_56,axiom,
    ! [X,Y] : ( implies(X,Y) = or(not(X),Y) ),
    file(unknown,unknown) ).

tff(f_52,axiom,
    ! [A,B,C] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
    file(unknown,unknown) ).

tff(f_69,axiom,
    ! [X,Y] :
      ( theorem(X)
      | ~ theorem(implies(Y,X))
      | ~ theorem(Y) ),
    file(unknown,unknown) ).

tff(f_50,axiom,
    ! [A,B] : axiom(implies(or(A,B),or(B,A))),
    file(unknown,unknown) ).

tff(f_46,axiom,
    ! [A] : axiom(implies(or(A,A),A)),
    file(unknown,unknown) ).

tff(f_119,axiom,
    ! [P,Q] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ),
    file(unknown,unknown) ).

tff(f_96,axiom,
    ! [P,Q] : ( and(P,Q) = not(or(not(P),not(Q))) ),
    file(unknown,unknown) ).

tff(f_123,axiom,
    ~ theorem(equivalent(p,p)),
    file(unknown,unknown) ).

tff(c_4,plain,
    ! [A_2,B_3] : axiom(implies(A_2,or(B_3,A_2))),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_14,plain,
    ! [X_14] :
      ( ~ axiom(X_14)
      | theorem(X_14) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_12,plain,
    ! [X_12,Y_13] : ( or(not(X_12),Y_13) = implies(X_12,Y_13) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_126,plain,
    ! [A_44,B_45,C_46] : axiom(implies(or(A_44,or(B_45,C_46)),or(B_45,or(A_44,C_46)))),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_139,plain,
    ! [X_12,B_45,Y_13] : axiom(implies(or(not(X_12),or(B_45,Y_13)),or(B_45,implies(X_12,Y_13)))),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_126]) ).

tff(c_1043,plain,
    ! [X_154,B_155,Y_156] : axiom(implies(implies(X_154,or(B_155,Y_156)),or(B_155,implies(X_154,Y_156)))),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_139]) ).

tff(c_55,plain,
    ! [Y_31,X_32] :
      ( ~ theorem(Y_31)
      | ~ theorem(implies(Y_31,X_32))
      | theorem(X_32) ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_59,plain,
    ! [Y_31,X_32] :
      ( ~ theorem(Y_31)
      | theorem(X_32)
      | ~ axiom(implies(Y_31,X_32)) ),
    inference(resolution,[status(thm)],[c_14,c_55]) ).

tff(c_1061,plain,
    ! [X_154,B_155,Y_156] :
      ( ~ theorem(implies(X_154,or(B_155,Y_156)))
      | theorem(or(B_155,implies(X_154,Y_156))) ),
    inference(resolution,[status(thm)],[c_1043,c_59]) ).

tff(c_6,plain,
    ! [A_4,B_5] : axiom(implies(or(A_4,B_5),or(B_5,A_4))),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_96,plain,
    ! [Y_38,X_39] :
      ( ~ theorem(Y_38)
      | theorem(X_39)
      | ~ axiom(implies(Y_38,X_39)) ),
    inference(resolution,[status(thm)],[c_14,c_55]) ).

tff(c_115,plain,
    ! [A_2,B_3] :
      ( ~ theorem(A_2)
      | theorem(or(B_3,A_2)) ),
    inference(resolution,[status(thm)],[c_4,c_96]) ).

tff(c_1392,plain,
    ! [A_207,B_208,C_209] :
      ( ~ theorem(or(A_207,or(B_208,C_209)))
      | theorem(or(B_208,or(A_207,C_209))) ),
    inference(resolution,[status(thm)],[c_126,c_59]) ).

tff(c_1553,plain,
    ! [B_231,B_232,C_233] :
      ( theorem(or(B_231,or(B_232,C_233)))
      | ~ theorem(or(B_231,C_233)) ),
    inference(resolution,[status(thm)],[c_115,c_1392]) ).

tff(c_1568,plain,
    ! [X_12,B_232,C_233] :
      ( theorem(implies(X_12,or(B_232,C_233)))
      | ~ theorem(or(not(X_12),C_233)) ),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_1553]) ).

tff(c_1727,plain,
    ! [X_246,B_247,C_248] :
      ( theorem(implies(X_246,or(B_247,C_248)))
      | ~ theorem(implies(X_246,C_248)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_1568]) ).

tff(c_16,plain,
    ! [Y_16,X_15] :
      ( ~ theorem(Y_16)
      | ~ theorem(implies(Y_16,X_15))
      | theorem(X_15) ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_1980,plain,
    ! [X_268,B_269,C_270] :
      ( ~ theorem(X_268)
      | theorem(or(B_269,C_270))
      | ~ theorem(implies(X_268,C_270)) ),
    inference(resolution,[status(thm)],[c_1727,c_16]) ).

tff(c_2157,plain,
    ! [X_281,B_282,C_283] :
      ( ~ theorem(X_281)
      | theorem(or(B_282,C_283))
      | ~ axiom(implies(X_281,C_283)) ),
    inference(resolution,[status(thm)],[c_14,c_1980]) ).

tff(c_2738,plain,
    ! [A_336,B_337,B_338] :
      ( ~ theorem(or(A_336,B_337))
      | theorem(or(B_338,or(B_337,A_336))) ),
    inference(resolution,[status(thm)],[c_6,c_2157]) ).

tff(c_144,plain,
    ! [A_44,B_45,C_46] :
      ( ~ theorem(or(A_44,or(B_45,C_46)))
      | theorem(or(B_45,or(A_44,C_46))) ),
    inference(resolution,[status(thm)],[c_126,c_59]) ).

tff(c_3330,plain,
    ! [B_365,B_366,A_367] :
      ( theorem(or(B_365,or(B_366,A_367)))
      | ~ theorem(or(A_367,B_365)) ),
    inference(resolution,[status(thm)],[c_2738,c_144]) ).

tff(c_2,plain,
    ! [A_1] : axiom(implies(or(A_1,A_1),A_1)),
    inference(cnfTransformation,[status(thm)],[f_46]) ).

tff(c_116,plain,
    ! [A_1] :
      ( ~ theorem(or(A_1,A_1))
      | theorem(A_1) ),
    inference(resolution,[status(thm)],[c_2,c_96]) ).

tff(c_3691,plain,
    ! [B_383,A_384] :
      ( theorem(or(B_383,A_384))
      | ~ theorem(or(A_384,or(B_383,A_384))) ),
    inference(resolution,[status(thm)],[c_3330,c_116]) ).

tff(c_3774,plain,
    ! [X_12,Y_13] :
      ( theorem(or(not(X_12),Y_13))
      | ~ theorem(or(Y_13,implies(X_12,Y_13))) ),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_3691]) ).

tff(c_4137,plain,
    ! [X_416,Y_417] :
      ( theorem(implies(X_416,Y_417))
      | ~ theorem(or(Y_417,implies(X_416,Y_417))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_3774]) ).

tff(c_4335,plain,
    ! [X_425,Y_426] :
      ( theorem(implies(X_425,Y_426))
      | ~ theorem(implies(X_425,or(Y_426,Y_426))) ),
    inference(resolution,[status(thm)],[c_1061,c_4137]) ).

tff(c_4409,plain,
    ! [X_427,Y_428] :
      ( theorem(implies(X_427,Y_428))
      | ~ axiom(implies(X_427,or(Y_428,Y_428))) ),
    inference(resolution,[status(thm)],[c_14,c_4335]) ).

tff(c_4448,plain,
    ! [A_2] : theorem(implies(A_2,A_2)),
    inference(resolution,[status(thm)],[c_4,c_4409]) ).

tff(c_20,plain,
    ! [P_19,Q_20] : ( and(implies(P_19,Q_20),implies(Q_20,P_19)) = equivalent(P_19,Q_20) ),
    inference(cnfTransformation,[status(thm)],[f_119]) ).

tff(c_18,plain,
    ! [P_17,Q_18] : ( not(or(not(P_17),not(Q_18))) = and(P_17,Q_18) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_69,plain,
    ! [P_35,Q_36] : ( not(implies(P_35,not(Q_36))) = and(P_35,Q_36) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_18]) ).

tff(c_78,plain,
    ! [P_35,Q_36,Y_13] : ( implies(implies(P_35,not(Q_36)),Y_13) = or(and(P_35,Q_36),Y_13) ),
    inference(superposition,[status(thm),theory(equality)],[c_69,c_12]) ).

tff(c_31,plain,
    ! [X_25,Y_26] : ( or(not(X_25),Y_26) = implies(X_25,Y_26) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_41,plain,
    ! [X_25] : axiom(implies(implies(X_25,not(X_25)),not(X_25))),
    inference(superposition,[status(thm),theory(equality)],[c_31,c_2]) ).

tff(c_416,plain,
    ! [X_75] : axiom(or(and(X_75,X_75),not(X_75))),
    inference(demodulation,[status(thm),theory(equality)],[c_78,c_41]) ).

tff(c_423,plain,
    ! [Q_20] : axiom(or(equivalent(Q_20,Q_20),not(implies(Q_20,Q_20)))),
    inference(superposition,[status(thm),theory(equality)],[c_20,c_416]) ).

tff(c_48,plain,
    ! [A_29,B_30] : axiom(implies(or(A_29,B_30),or(B_30,A_29))),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_269,plain,
    ! [Y_66,X_67] : axiom(implies(or(Y_66,not(X_67)),implies(X_67,Y_66))),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_48]) ).

tff(c_298,plain,
    ! [Y_70,X_71] :
      ( ~ theorem(or(Y_70,not(X_71)))
      | theorem(implies(X_71,Y_70)) ),
    inference(resolution,[status(thm)],[c_269,c_59]) ).

tff(c_444,plain,
    ! [X_79,Y_80] :
      ( theorem(implies(X_79,Y_80))
      | ~ axiom(or(Y_80,not(X_79))) ),
    inference(resolution,[status(thm)],[c_14,c_298]) ).

tff(c_479,plain,
    ! [Q_83] : theorem(implies(implies(Q_83,Q_83),equivalent(Q_83,Q_83))),
    inference(resolution,[status(thm)],[c_423,c_444]) ).

tff(c_491,plain,
    ! [Q_83] :
      ( ~ theorem(implies(Q_83,Q_83))
      | theorem(equivalent(Q_83,Q_83)) ),
    inference(resolution,[status(thm)],[c_479,c_16]) ).

tff(c_4457,plain,
    ! [Q_83] : theorem(equivalent(Q_83,Q_83)),
    inference(demodulation,[status(thm),theory(equality)],[c_4448,c_491]) ).

tff(c_22,plain,
    ~ theorem(equivalent(p,p)),
    inference(cnfTransformation,[status(thm)],[f_123]) ).

tff(c_4505,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_4457,c_22]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : LCL268-3 : TPTP v8.1.2. Released v2.3.0.
% 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
% 0.14/0.35  % Computer : n029.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 14:13:37 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 7.04/2.71  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.04/2.72  
% 7.04/2.72  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.04/2.76  
% 7.04/2.76  Inference rules
% 7.04/2.76  ----------------------
% 7.04/2.76  #Ref     : 0
% 7.04/2.76  #Sup     : 1072
% 7.04/2.76  #Fact    : 0
% 7.04/2.76  #Define  : 0
% 7.04/2.76  #Split   : 2
% 7.04/2.76  #Chain   : 0
% 7.04/2.76  #Close   : 0
% 7.04/2.76  
% 7.04/2.76  Ordering : KBO
% 7.04/2.76  
% 7.04/2.76  Simplification rules
% 7.04/2.76  ----------------------
% 7.04/2.76  #Subsume      : 412
% 7.04/2.76  #Demod        : 366
% 7.04/2.76  #Tautology    : 83
% 7.04/2.76  #SimpNegUnit  : 0
% 7.04/2.76  #BackRed      : 6
% 7.04/2.76  
% 7.04/2.76  #Partial instantiations: 0
% 7.04/2.76  #Strategies tried      : 1
% 7.04/2.76  
% 7.04/2.76  Timing (in seconds)
% 7.04/2.76  ----------------------
% 7.04/2.76  Preprocessing        : 0.43
% 7.04/2.76  Parsing              : 0.24
% 7.04/2.76  CNF conversion       : 0.02
% 7.04/2.76  Main loop            : 1.27
% 7.04/2.76  Inferencing          : 0.47
% 7.04/2.76  Reduction            : 0.37
% 7.04/2.76  Demodulation         : 0.27
% 7.04/2.76  BG Simplification    : 0.03
% 7.04/2.76  Subsumption          : 0.31
% 7.04/2.76  Abstraction          : 0.04
% 7.04/2.76  MUC search           : 0.00
% 7.04/2.76  Cooper               : 0.00
% 7.04/2.76  Total                : 1.76
% 7.04/2.76  Index Insertion      : 0.00
% 7.04/2.76  Index Deletion       : 0.00
% 7.04/2.76  Index Matching       : 0.00
% 7.04/2.76  BG Taut test         : 0.00
%------------------------------------------------------------------------------