TSTP Solution File: LCL294-3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : LCL294-3 : 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 : n027.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 10:47:53 EDT 2023

% Result   : Unsatisfiable 7.02s 2.70s
% Output   : CNFRefutation 7.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   66 (  33 unt;   9 typ;   0 def)
%            Number of atoms       :   88 (   9 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   65 (  34   ~;  31   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    5 (   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    :    7 (   7 usr;   2 con; 0-2 aty)
%            Number of variables   :  110 (; 110   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ theorem > axiom > or > implies > equivalent > 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(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(implies(p,q),or(not(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_169,plain,
    ! [A_51,B_52,C_53] : axiom(implies(or(A_51,or(B_52,C_53)),or(B_52,or(A_51,C_53)))),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_179,plain,
    ! [X_12,B_52,C_53] : axiom(implies(implies(X_12,or(B_52,C_53)),or(B_52,or(not(X_12),C_53)))),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_169]) ).

tff(c_945,plain,
    ! [X_138,B_139,C_140] : axiom(implies(implies(X_138,or(B_139,C_140)),or(B_139,implies(X_138,C_140)))),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_179]) ).

tff(c_74,plain,
    ! [Y_33,X_34] :
      ( ~ theorem(Y_33)
      | ~ theorem(implies(Y_33,X_34))
      | theorem(X_34) ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_78,plain,
    ! [Y_33,X_34] :
      ( ~ theorem(Y_33)
      | theorem(X_34)
      | ~ axiom(implies(Y_33,X_34)) ),
    inference(resolution,[status(thm)],[c_14,c_74]) ).

tff(c_963,plain,
    ! [X_138,B_139,C_140] :
      ( ~ theorem(implies(X_138,or(B_139,C_140)))
      | theorem(or(B_139,implies(X_138,C_140))) ),
    inference(resolution,[status(thm)],[c_945,c_78]) ).

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_88,plain,
    ! [Y_37,X_38] :
      ( ~ theorem(Y_37)
      | theorem(X_38)
      | ~ axiom(implies(Y_37,X_38)) ),
    inference(resolution,[status(thm)],[c_14,c_74]) ).

tff(c_104,plain,
    ! [A_2,B_3] :
      ( ~ theorem(A_2)
      | theorem(or(B_3,A_2)) ),
    inference(resolution,[status(thm)],[c_4,c_88]) ).

tff(c_186,plain,
    ! [A_51,X_12,C_53] : axiom(implies(or(A_51,or(not(X_12),C_53)),implies(X_12,or(A_51,C_53)))),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_169]) ).

tff(c_591,plain,
    ! [A_90,X_91,C_92] : axiom(implies(or(A_90,implies(X_91,C_92)),implies(X_91,or(A_90,C_92)))),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_186]) ).

tff(c_1440,plain,
    ! [A_216,X_217,C_218] :
      ( ~ theorem(or(A_216,implies(X_217,C_218)))
      | theorem(implies(X_217,or(A_216,C_218))) ),
    inference(resolution,[status(thm)],[c_591,c_78]) ).

tff(c_1504,plain,
    ! [X_225,B_226,C_227] :
      ( theorem(implies(X_225,or(B_226,C_227)))
      | ~ theorem(implies(X_225,C_227)) ),
    inference(resolution,[status(thm)],[c_104,c_1440]) ).

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_1522,plain,
    ! [X_228,B_229,C_230] :
      ( ~ theorem(X_228)
      | theorem(or(B_229,C_230))
      | ~ theorem(implies(X_228,C_230)) ),
    inference(resolution,[status(thm)],[c_1504,c_16]) ).

tff(c_1713,plain,
    ! [X_249,B_250,C_251] :
      ( ~ theorem(X_249)
      | theorem(or(B_250,C_251))
      | ~ axiom(implies(X_249,C_251)) ),
    inference(resolution,[status(thm)],[c_14,c_1522]) ).

tff(c_2716,plain,
    ! [A_342,B_343,B_344] :
      ( ~ theorem(or(A_342,B_343))
      | theorem(or(B_344,or(B_343,A_342))) ),
    inference(resolution,[status(thm)],[c_6,c_1713]) ).

tff(c_187,plain,
    ! [A_51,B_52,C_53] :
      ( ~ theorem(or(A_51,or(B_52,C_53)))
      | theorem(or(B_52,or(A_51,C_53))) ),
    inference(resolution,[status(thm)],[c_169,c_78]) ).

tff(c_2816,plain,
    ! [B_352,B_353,A_354] :
      ( theorem(or(B_352,or(B_353,A_354)))
      | ~ theorem(or(A_354,B_352)) ),
    inference(resolution,[status(thm)],[c_2716,c_187]) ).

tff(c_3917,plain,
    ! [B_413,X_414,Y_415] :
      ( theorem(or(B_413,implies(X_414,Y_415)))
      | ~ theorem(or(Y_415,B_413)) ),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_2816]) ).

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

tff(c_103,plain,
    ! [A_1] :
      ( ~ theorem(or(A_1,A_1))
      | theorem(A_1) ),
    inference(resolution,[status(thm)],[c_2,c_88]) ).

tff(c_4000,plain,
    ! [X_419,Y_420] :
      ( theorem(implies(X_419,Y_420))
      | ~ theorem(or(Y_420,implies(X_419,Y_420))) ),
    inference(resolution,[status(thm)],[c_3917,c_103]) ).

tff(c_4217,plain,
    ! [X_429,C_430] :
      ( theorem(implies(X_429,C_430))
      | ~ theorem(implies(X_429,or(C_430,C_430))) ),
    inference(resolution,[status(thm)],[c_963,c_4000]) ).

tff(c_4322,plain,
    ! [X_433,C_434] :
      ( theorem(implies(X_433,C_434))
      | ~ axiom(implies(X_433,or(C_434,C_434))) ),
    inference(resolution,[status(thm)],[c_14,c_4217]) ).

tff(c_4362,plain,
    ! [A_2] : theorem(implies(A_2,A_2)),
    inference(resolution,[status(thm)],[c_4,c_4322]) ).

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_56,plain,
    ! [P_31,Q_32] : ( not(implies(P_31,not(Q_32))) = and(P_31,Q_32) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_18]) ).

tff(c_65,plain,
    ! [P_31,Q_32,Y_13] : ( implies(implies(P_31,not(Q_32)),Y_13) = or(and(P_31,Q_32),Y_13) ),
    inference(superposition,[status(thm),theory(equality)],[c_56,c_12]) ).

tff(c_28,plain,
    ! [X_25,Y_26] : ( or(not(X_25),Y_26) = implies(X_25,Y_26) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_35,plain,
    ! [X_25] : axiom(implies(implies(X_25,not(X_25)),not(X_25))),
    inference(superposition,[status(thm),theory(equality)],[c_28,c_2]) ).

tff(c_417,plain,
    ! [X_75] : axiom(or(and(X_75,X_75),not(X_75))),
    inference(demodulation,[status(thm),theory(equality)],[c_65,c_35]) ).

tff(c_421,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_417]) ).

tff(c_45,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_270,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_45]) ).

tff(c_299,plain,
    ! [Y_70,X_71] :
      ( ~ theorem(or(Y_70,not(X_71)))
      | theorem(implies(X_71,Y_70)) ),
    inference(resolution,[status(thm)],[c_270,c_78]) ).

tff(c_445,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_299]) ).

tff(c_480,plain,
    ! [Q_83] : theorem(implies(implies(Q_83,Q_83),equivalent(Q_83,Q_83))),
    inference(resolution,[status(thm)],[c_421,c_445]) ).

tff(c_492,plain,
    ! [Q_83] :
      ( ~ theorem(implies(Q_83,Q_83))
      | theorem(equivalent(Q_83,Q_83)) ),
    inference(resolution,[status(thm)],[c_480,c_16]) ).

tff(c_4370,plain,
    ! [Q_83] : theorem(equivalent(Q_83,Q_83)),
    inference(demodulation,[status(thm),theory(equality)],[c_4362,c_492]) ).

tff(c_22,plain,
    ~ theorem(equivalent(implies(p,q),or(not(p),q))),
    inference(cnfTransformation,[status(thm)],[f_123]) ).

tff(c_24,plain,
    ~ theorem(equivalent(implies(p,q),implies(p,q))),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_22]) ).

tff(c_4414,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_4370,c_24]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : LCL294-3 : 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
% 0.13/0.34  % Computer : n027.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 14:00:53 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 7.02/2.70  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.02/2.71  
% 7.02/2.71  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.18/2.74  
% 7.18/2.74  Inference rules
% 7.18/2.74  ----------------------
% 7.18/2.74  #Ref     : 0
% 7.18/2.74  #Sup     : 1054
% 7.18/2.74  #Fact    : 0
% 7.18/2.74  #Define  : 0
% 7.18/2.74  #Split   : 1
% 7.18/2.74  #Chain   : 0
% 7.18/2.74  #Close   : 0
% 7.18/2.74  
% 7.18/2.74  Ordering : KBO
% 7.18/2.74  
% 7.18/2.74  Simplification rules
% 7.18/2.74  ----------------------
% 7.18/2.74  #Subsume      : 398
% 7.18/2.74  #Demod        : 375
% 7.18/2.74  #Tautology    : 86
% 7.18/2.74  #SimpNegUnit  : 0
% 7.18/2.74  #BackRed      : 6
% 7.18/2.74  
% 7.18/2.74  #Partial instantiations: 0
% 7.18/2.74  #Strategies tried      : 1
% 7.18/2.74  
% 7.18/2.74  Timing (in seconds)
% 7.18/2.74  ----------------------
% 7.18/2.74  Preprocessing        : 0.45
% 7.18/2.74  Parsing              : 0.25
% 7.18/2.74  CNF conversion       : 0.02
% 7.18/2.74  Main loop            : 1.24
% 7.18/2.75  Inferencing          : 0.48
% 7.18/2.75  Reduction            : 0.35
% 7.18/2.75  Demodulation         : 0.25
% 7.18/2.75  BG Simplification    : 0.03
% 7.18/2.75  Subsumption          : 0.28
% 7.18/2.75  Abstraction          : 0.04
% 7.18/2.75  MUC search           : 0.00
% 7.18/2.75  Cooper               : 0.00
% 7.18/2.75  Total                : 1.74
% 7.18/2.75  Index Insertion      : 0.00
% 7.18/2.75  Index Deletion       : 0.00
% 7.18/2.75  Index Matching       : 0.00
% 7.18/2.75  BG Taut test         : 0.00
%------------------------------------------------------------------------------