TSTP Solution File: LCL236-3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : LCL236-3 : 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/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 : n016.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 10:47:45 EDT 2023

% Result   : Unsatisfiable 5.94s 2.47s
% Output   : CNFRefutation 6.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   59 (  26 unt;   8 typ;   0 def)
%            Number of atoms       :   83 (   6 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   69 (  37   ~;  32   |;   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  :    9 (   6   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :  100 (; 100   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ theorem > axiom > or > implies > and > #nlpp > not > q > 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(q,type,
    q: $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_96,axiom,
    ! [P,Q] : ( and(P,Q) = not(or(not(P),not(Q))) ),
    file(unknown,unknown) ).

tff(f_100,axiom,
    ~ theorem(implies(or(not(p),not(q)),not(and(p,q)))),
    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_82,plain,
    ! [A_34,B_35,C_36] : axiom(implies(or(A_34,or(B_35,C_36)),or(B_35,or(A_34,C_36)))),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_92,plain,
    ! [X_12,B_35,Y_13] : axiom(implies(or(not(X_12),or(B_35,Y_13)),or(B_35,implies(X_12,Y_13)))),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_82]) ).

tff(c_752,plain,
    ! [X_114,B_115,Y_116] : axiom(implies(implies(X_114,or(B_115,Y_116)),or(B_115,implies(X_114,Y_116)))),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_92]) ).

tff(c_68,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_72,plain,
    ! [Y_31,X_32] :
      ( ~ theorem(Y_31)
      | theorem(X_32)
      | ~ axiom(implies(Y_31,X_32)) ),
    inference(resolution,[status(thm)],[c_14,c_68]) ).

tff(c_770,plain,
    ! [X_114,B_115,Y_116] :
      ( ~ theorem(implies(X_114,or(B_115,Y_116)))
      | theorem(or(B_115,implies(X_114,Y_116))) ),
    inference(resolution,[status(thm)],[c_752,c_72]) ).

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_101,plain,
    ! [Y_37,X_38] :
      ( ~ theorem(Y_37)
      | theorem(X_38)
      | ~ axiom(implies(Y_37,X_38)) ),
    inference(resolution,[status(thm)],[c_14,c_68]) ).

tff(c_125,plain,
    ! [A_2,B_3] :
      ( ~ theorem(A_2)
      | theorem(or(B_3,A_2)) ),
    inference(resolution,[status(thm)],[c_4,c_101]) ).

tff(c_8,plain,
    ! [A_6,B_7,C_8] : axiom(implies(or(A_6,or(B_7,C_8)),or(B_7,or(A_6,C_8)))),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_959,plain,
    ! [A_139,B_140,C_141] :
      ( ~ theorem(or(A_139,or(B_140,C_141)))
      | theorem(or(B_140,or(A_139,C_141))) ),
    inference(resolution,[status(thm)],[c_8,c_101]) ).

tff(c_1088,plain,
    ! [B_160,B_161,C_162] :
      ( theorem(or(B_160,or(B_161,C_162)))
      | ~ theorem(or(B_160,C_162)) ),
    inference(resolution,[status(thm)],[c_125,c_959]) ).

tff(c_1103,plain,
    ! [X_12,B_161,C_162] :
      ( theorem(implies(X_12,or(B_161,C_162)))
      | ~ theorem(or(not(X_12),C_162)) ),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_1088]) ).

tff(c_1237,plain,
    ! [X_172,B_173,C_174] :
      ( theorem(implies(X_172,or(B_173,C_174)))
      | ~ theorem(implies(X_172,C_174)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_1103]) ).

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_1289,plain,
    ! [X_181,B_182,C_183] :
      ( ~ theorem(X_181)
      | theorem(or(B_182,C_183))
      | ~ theorem(implies(X_181,C_183)) ),
    inference(resolution,[status(thm)],[c_1237,c_16]) ).

tff(c_1606,plain,
    ! [X_209,B_210,C_211] :
      ( ~ theorem(X_209)
      | theorem(or(B_210,C_211))
      | ~ axiom(implies(X_209,C_211)) ),
    inference(resolution,[status(thm)],[c_14,c_1289]) ).

tff(c_2111,plain,
    ! [A_264,B_265,B_266] :
      ( ~ theorem(or(A_264,B_265))
      | theorem(or(B_266,or(B_265,A_264))) ),
    inference(resolution,[status(thm)],[c_6,c_1606]) ).

tff(c_120,plain,
    ! [A_6,B_7,C_8] :
      ( ~ theorem(or(A_6,or(B_7,C_8)))
      | theorem(or(B_7,or(A_6,C_8))) ),
    inference(resolution,[status(thm)],[c_8,c_101]) ).

tff(c_2318,plain,
    ! [B_281,B_282,A_283] :
      ( theorem(or(B_281,or(B_282,A_283)))
      | ~ theorem(or(A_283,B_281)) ),
    inference(resolution,[status(thm)],[c_2111,c_120]) ).

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

tff(c_124,plain,
    ! [A_1] :
      ( ~ theorem(or(A_1,A_1))
      | theorem(A_1) ),
    inference(resolution,[status(thm)],[c_2,c_101]) ).

tff(c_2637,plain,
    ! [B_315,A_316] :
      ( theorem(or(B_315,A_316))
      | ~ theorem(or(A_316,or(B_315,A_316))) ),
    inference(resolution,[status(thm)],[c_2318,c_124]) ).

tff(c_2732,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_2637]) ).

tff(c_2774,plain,
    ! [X_320,Y_321] :
      ( theorem(implies(X_320,Y_321))
      | ~ theorem(or(Y_321,implies(X_320,Y_321))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_2732]) ).

tff(c_3164,plain,
    ! [X_339,Y_340] :
      ( theorem(implies(X_339,Y_340))
      | ~ theorem(implies(X_339,or(Y_340,Y_340))) ),
    inference(resolution,[status(thm)],[c_770,c_2774]) ).

tff(c_3269,plain,
    ! [X_343,Y_344] :
      ( theorem(implies(X_343,Y_344))
      | ~ axiom(implies(X_343,or(Y_344,Y_344))) ),
    inference(resolution,[status(thm)],[c_14,c_3164]) ).

tff(c_3309,plain,
    ! [A_2] : theorem(implies(A_2,A_2)),
    inference(resolution,[status(thm)],[c_4,c_3269]) ).

tff(c_61,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_234,plain,
    ! [X_55,Y_56] : axiom(implies(implies(X_55,Y_56),or(Y_56,not(X_55)))),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_61]) ).

tff(c_245,plain,
    ! [X_55,Y_56] :
      ( ~ theorem(implies(X_55,Y_56))
      | theorem(or(Y_56,not(X_55))) ),
    inference(resolution,[status(thm)],[c_234,c_72]) ).

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_43,plain,
    ! [P_27,Q_28] : ( not(implies(P_27,not(Q_28))) = and(P_27,Q_28) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_18]) ).

tff(c_52,plain,
    ! [P_27,Q_28,Y_13] : ( implies(implies(P_27,not(Q_28)),Y_13) = or(and(P_27,Q_28),Y_13) ),
    inference(superposition,[status(thm),theory(equality)],[c_43,c_12]) ).

tff(c_20,plain,
    ~ theorem(implies(or(not(p),not(q)),not(and(p,q)))),
    inference(cnfTransformation,[status(thm)],[f_100]) ).

tff(c_22,plain,
    ~ theorem(implies(implies(p,not(q)),not(and(p,q)))),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_20]) ).

tff(c_388,plain,
    ~ theorem(or(and(p,q),not(and(p,q)))),
    inference(demodulation,[status(thm),theory(equality)],[c_52,c_22]) ).

tff(c_524,plain,
    ~ theorem(implies(and(p,q),and(p,q))),
    inference(resolution,[status(thm)],[c_245,c_388]) ).

tff(c_3312,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_3309,c_524]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : LCL236-3 : TPTP v8.1.2. Released v2.3.0.
% 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
% 0.16/0.34  % Computer : n016.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
% 0.16/0.35  % CPULimit : 300
% 0.16/0.35  % WCLimit  : 300
% 0.16/0.35  % DateTime : Thu Aug  3 14:28:22 EDT 2023
% 0.16/0.35  % CPUTime  : 
% 5.94/2.47  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.94/2.48  
% 5.94/2.48  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.20/2.51  
% 6.20/2.51  Inference rules
% 6.20/2.51  ----------------------
% 6.20/2.51  #Ref     : 0
% 6.20/2.51  #Sup     : 779
% 6.20/2.51  #Fact    : 0
% 6.20/2.51  #Define  : 0
% 6.20/2.51  #Split   : 1
% 6.20/2.51  #Chain   : 0
% 6.20/2.51  #Close   : 0
% 6.20/2.51  
% 6.20/2.51  Ordering : KBO
% 6.20/2.51  
% 6.20/2.51  Simplification rules
% 6.20/2.51  ----------------------
% 6.20/2.51  #Subsume      : 339
% 6.20/2.51  #Demod        : 197
% 6.20/2.51  #Tautology    : 53
% 6.20/2.51  #SimpNegUnit  : 0
% 6.20/2.51  #BackRed      : 7
% 6.20/2.51  
% 6.20/2.51  #Partial instantiations: 0
% 6.20/2.51  #Strategies tried      : 1
% 6.20/2.51  
% 6.20/2.51  Timing (in seconds)
% 6.20/2.51  ----------------------
% 6.20/2.51  Preprocessing        : 0.43
% 6.20/2.52  Parsing              : 0.24
% 6.20/2.52  CNF conversion       : 0.02
% 6.20/2.52  Main loop            : 1.02
% 6.20/2.52  Inferencing          : 0.41
% 6.20/2.52  Reduction            : 0.27
% 6.20/2.52  Demodulation         : 0.19
% 6.20/2.52  BG Simplification    : 0.03
% 6.20/2.52  Subsumption          : 0.23
% 6.20/2.52  Abstraction          : 0.03
% 6.20/2.52  MUC search           : 0.00
% 6.20/2.52  Cooper               : 0.00
% 6.20/2.52  Total                : 1.51
% 6.20/2.52  Index Insertion      : 0.00
% 6.20/2.52  Index Deletion       : 0.00
% 6.20/2.52  Index Matching       : 0.00
% 6.20/2.52  BG Taut test         : 0.00
%------------------------------------------------------------------------------