TSTP Solution File: COL074-3 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : COL074-3 : TPTP v8.1.2. Released v1.2.0.
% 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 : n005.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 10:35:00 EDT 2023

% Result   : Unsatisfiable 3.04s 1.90s
% Output   : CNFRefutation 3.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   41 (  27 unt;  11 typ;   0 def)
%            Number of atoms       :   33 (  31 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    5 (   2   ~;   3   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   8 con; 0-2 aty)
%            Number of variables   :   13 (;  13   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ pair > n > apply > #nlpp > s > projection2 > projection1 > k_projection2 > k_projection1 > k > eq > abstraction

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(apply,type,
    apply: ( $i * $i ) > $i ).

tff(k_projection2,type,
    k_projection2: $i ).

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

tff(k_projection1,type,
    k_projection1: $i ).

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

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

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

tff(projection1,type,
    projection1: $i ).

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

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

tff(projection2,type,
    projection2: $i ).

tff(f_57,axiom,
    projection1 != projection2,
    file(unknown,unknown) ).

tff(f_46,axiom,
    ! [X] : ( apply(eq,pair(X,X)) = projection1 ),
    file(unknown,unknown) ).

tff(f_60,axiom,
    apply(k,projection2) = k_projection2,
    file(unknown,unknown) ).

tff(f_59,axiom,
    apply(k,projection1) = k_projection1,
    file(unknown,unknown) ).

tff(f_30,axiom,
    ! [X,Y] : ( apply(apply(k,X),Y) = X ),
    file(unknown,unknown) ).

tff(f_61,axiom,
    s = apply(eq,pair(apply(k,s),apply(k,projection2))),
    file(unknown,unknown) ).

tff(f_50,axiom,
    ! [X,Y] :
      ( ( X = Y )
      | ( apply(eq,pair(X,Y)) = projection2 ) ),
    file(unknown,unknown) ).

tff(c_20,plain,
    projection2 != projection1,
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_14,plain,
    ! [X_14] : ( apply(eq,pair(X_14,X_14)) = projection1 ),
    inference(cnfTransformation,[status(thm)],[f_46]) ).

tff(c_24,plain,
    apply(k,projection2) = k_projection2,
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_22,plain,
    apply(k,projection1) = k_projection1,
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_36,plain,
    ! [X_19,Y_20] : ( apply(apply(k,X_19),Y_20) = X_19 ),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_45,plain,
    ! [Y_20] : ( apply(k_projection1,Y_20) = projection1 ),
    inference(superposition,[status(thm),theory(equality)],[c_22,c_36]) ).

tff(c_26,plain,
    apply(eq,pair(apply(k,s),apply(k,projection2))) = s,
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_27,plain,
    apply(eq,pair(apply(k,s),k_projection2)) = s,
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_26]) ).

tff(c_16,plain,
    ! [X_15,Y_16] :
      ( ( apply(eq,pair(X_15,Y_16)) = projection2 )
      | ( Y_16 = X_15 ) ),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_143,plain,
    ( ( s = projection2 )
    | ( apply(k,s) = k_projection2 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_27,c_16]) ).

tff(c_150,plain,
    apply(k,s) = k_projection2,
    inference(splitLeft,[status(thm)],[c_143]) ).

tff(c_151,plain,
    apply(eq,pair(k_projection2,k_projection2)) = s,
    inference(demodulation,[status(thm),theory(equality)],[c_150,c_27]) ).

tff(c_152,plain,
    s = projection1,
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_151]) ).

tff(c_161,plain,
    apply(k,projection1) = k_projection2,
    inference(demodulation,[status(thm),theory(equality)],[c_152,c_150]) ).

tff(c_162,plain,
    k_projection2 = k_projection1,
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_161]) ).

tff(c_48,plain,
    ! [Y_20] : ( apply(k_projection2,Y_20) = projection2 ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_36]) ).

tff(c_196,plain,
    ! [Y_20] : ( apply(k_projection1,Y_20) = projection2 ),
    inference(demodulation,[status(thm),theory(equality)],[c_162,c_48]) ).

tff(c_198,plain,
    projection2 = projection1,
    inference(demodulation,[status(thm),theory(equality)],[c_45,c_196]) ).

tff(c_200,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_20,c_198]) ).

tff(c_201,plain,
    s = projection2,
    inference(splitRight,[status(thm)],[c_143]) ).

tff(c_203,plain,
    apply(eq,pair(apply(k,projection2),k_projection2)) = projection2,
    inference(demodulation,[status(thm),theory(equality)],[c_201,c_201,c_27]) ).

tff(c_204,plain,
    projection2 = projection1,
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_24,c_203]) ).

tff(c_206,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_20,c_204]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem  : COL074-3 : TPTP v8.1.2. Released v1.2.0.
% 0.13/0.14  % 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
% 0.14/0.35  % Computer : n005.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 18:06:56 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 3.04/1.90  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.04/1.91  
% 3.04/1.91  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.04/1.93  
% 3.04/1.93  Inference rules
% 3.04/1.93  ----------------------
% 3.04/1.93  #Ref     : 1
% 3.04/1.93  #Sup     : 44
% 3.04/1.93  #Fact    : 0
% 3.04/1.93  #Define  : 0
% 3.04/1.93  #Split   : 1
% 3.04/1.93  #Chain   : 0
% 3.04/1.93  #Close   : 0
% 3.04/1.93  
% 3.04/1.93  Ordering : KBO
% 3.04/1.93  
% 3.04/1.93  Simplification rules
% 3.04/1.93  ----------------------
% 3.04/1.93  #Subsume      : 0
% 3.04/1.93  #Demod        : 15
% 3.04/1.93  #Tautology    : 33
% 3.04/1.93  #SimpNegUnit  : 4
% 3.04/1.93  #BackRed      : 5
% 3.04/1.93  
% 3.04/1.93  #Partial instantiations: 0
% 3.04/1.93  #Strategies tried      : 1
% 3.04/1.93  
% 3.04/1.93  Timing (in seconds)
% 3.04/1.93  ----------------------
% 3.04/1.94  Preprocessing        : 0.49
% 3.04/1.94  Parsing              : 0.26
% 3.04/1.94  CNF conversion       : 0.02
% 3.04/1.94  Main loop            : 0.25
% 3.04/1.94  Inferencing          : 0.10
% 3.04/1.94  Reduction            : 0.08
% 3.04/1.94  Demodulation         : 0.06
% 3.04/1.94  BG Simplification    : 0.01
% 3.04/1.94  Subsumption          : 0.05
% 3.04/1.94  Abstraction          : 0.01
% 3.04/1.94  MUC search           : 0.00
% 3.04/1.94  Cooper               : 0.00
% 3.04/1.94  Total                : 0.78
% 3.04/1.94  Index Insertion      : 0.00
% 3.04/1.94  Index Deletion       : 0.00
% 3.04/1.94  Index Matching       : 0.00
% 3.04/1.94  BG Taut test         : 0.00
%------------------------------------------------------------------------------