%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : COL013-1 : 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 : 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 10:34:49 EDT 2023

% Result   : Unsatisfiable 2.03s 1.51s
% Output   : CNFRefutation 2.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   10 (   6 unt;   4 typ;   0 def)
%            Number of atoms       :    6 (   5 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    3 (   3   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   3 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    2 (   1   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :    7 (;   7   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ apply > #nlpp > s > l > combinator

%Foreground sorts:

%Background operators:

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

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

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

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

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

tff(f_33,axiom,
    ! [Y] : ( Y != apply(combinator,Y) ),
    file(unknown,unknown) ).

tff(c_8,plain,
    ! [X_8,Y_9] : ( apply(apply(l,X_8),Y_9) = apply(X_8,apply(Y_9,Y_9)) ),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_6,plain,
    ! [Y_6] : ( apply(combinator,Y_6) != Y_6 ),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_26,plain,
    ! [Y_9] : ( apply(apply(l,combinator),Y_9) != apply(Y_9,Y_9) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_6]) ).

tff(c_48,plain,
    $false,
    inference(reflexivity,[status(thm),theory(equality)],[c_26]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : COL013-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % 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
% 0.13/0.34  % 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 18:37:08 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 2.03/1.51  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.03/1.51  
% 2.03/1.51  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.44/1.54  
% 2.44/1.54  Inference rules
% 2.44/1.54  ----------------------
% 2.44/1.54  #Ref     : 1
% 2.44/1.54  #Sup     : 9
% 2.44/1.54  #Fact    : 0
% 2.44/1.54  #Define  : 0
% 2.44/1.54  #Split   : 0
% 2.44/1.54  #Chain   : 0
% 2.44/1.54  #Close   : 0
% 2.44/1.54  
% 2.44/1.54  Ordering : KBO
% 2.44/1.54  
% 2.44/1.54  Simplification rules
% 2.44/1.54  ----------------------
% 2.44/1.54  #Subsume      : 0
% 2.44/1.54  #Demod        : 0
% 2.44/1.54  #Tautology    : 4
% 2.44/1.54  #SimpNegUnit  : 0
% 2.44/1.54  #BackRed      : 0
% 2.44/1.54  
% 2.44/1.54  #Partial instantiations: 0
% 2.44/1.54  #Strategies tried      : 1
% 2.44/1.54  
% 2.44/1.54  Timing (in seconds)
% 2.44/1.54  ----------------------
% 2.44/1.55  Preprocessing        : 0.36
% 2.44/1.55  Parsing              : 0.19
% 2.44/1.55  CNF conversion       : 0.02
% 2.44/1.55  Main loop            : 0.14
% 2.44/1.55  Inferencing          : 0.06
% 2.44/1.55  Reduction            : 0.03
% 2.44/1.55  Demodulation         : 0.03
% 2.44/1.55  BG Simplification    : 0.01
% 2.44/1.55  Subsumption          : 0.03
% 2.44/1.55  Abstraction          : 0.01
% 2.44/1.55  MUC search           : 0.00
% 2.44/1.55  Cooper               : 0.00
% 2.44/1.55  Total                : 0.54
% 2.44/1.55  Index Insertion      : 0.00
% 2.44/1.55  Index Deletion       : 0.00
% 2.44/1.55  Index Matching       : 0.00
% 2.44/1.55  BG Taut test         : 0.00
%------------------------------------------------------------------------------