TSTP Solution File: ALG138+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ALG138+1 : TPTP v8.1.2. Released v2.7.0.
% 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 : 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 10:31:45 EDT 2023

% Result   : Unsatisfiable 6.31s 2.46s
% Output   : CNFRefutation 7.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   12
% Syntax   : Number of formulae    :  134 (  74 unt;   5 typ;   0 def)
%            Number of atoms       :  472 ( 465 equ)
%            Maximal formula atoms :  128 (   3 avg)
%            Number of connectives :  450 ( 107   ~; 240   |; 103   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   49 (   3 avg)
%            Maximal term depth    :    3 (   1 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    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ op > #nlpp > e3 > e2 > e1 > e0

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(e1,type,
    e1: $i ).

tff(e0,type,
    e0: $i ).

tff(e2,type,
    e2: $i ).

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

tff(e3,type,
    e3: $i ).

tff(f_567,axiom,
    ( ( e0 != e1 )
    & ( e0 != e2 )
    & ( e0 != e3 )
    & ( e1 != e2 )
    & ( e1 != e3 )
    & ( e2 != e3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).

tff(f_598,axiom,
    ~ ( ( e0 = op(e2,e1) )
      & ( e3 = op(op(e2,e1),e1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11) ).

tff(f_574,axiom,
    ( ( op(e0,e0) = e0 )
    & ( op(e1,e1) = e1 )
    & ( op(e2,e2) = e2 )
    & ( op(e3,e3) = e3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).

tff(f_550,axiom,
    ( ( op(e0,e0) != op(e1,e0) )
    & ( op(e0,e0) != op(e2,e0) )
    & ( op(e0,e0) != op(e3,e0) )
    & ( op(e1,e0) != op(e2,e0) )
    & ( op(e1,e0) != op(e3,e0) )
    & ( op(e2,e0) != op(e3,e0) )
    & ( op(e0,e1) != op(e1,e1) )
    & ( op(e0,e1) != op(e2,e1) )
    & ( op(e0,e1) != op(e3,e1) )
    & ( op(e1,e1) != op(e2,e1) )
    & ( op(e1,e1) != op(e3,e1) )
    & ( op(e2,e1) != op(e3,e1) )
    & ( op(e0,e2) != op(e1,e2) )
    & ( op(e0,e2) != op(e2,e2) )
    & ( op(e0,e2) != op(e3,e2) )
    & ( op(e1,e2) != op(e2,e2) )
    & ( op(e1,e2) != op(e3,e2) )
    & ( op(e2,e2) != op(e3,e2) )
    & ( op(e0,e3) != op(e1,e3) )
    & ( op(e0,e3) != op(e2,e3) )
    & ( op(e0,e3) != op(e3,e3) )
    & ( op(e1,e3) != op(e2,e3) )
    & ( op(e1,e3) != op(e3,e3) )
    & ( op(e2,e3) != op(e3,e3) )
    & ( op(e0,e0) != op(e0,e1) )
    & ( op(e0,e0) != op(e0,e2) )
    & ( op(e0,e0) != op(e0,e3) )
    & ( op(e0,e1) != op(e0,e2) )
    & ( op(e0,e1) != op(e0,e3) )
    & ( op(e0,e2) != op(e0,e3) )
    & ( op(e1,e0) != op(e1,e1) )
    & ( op(e1,e0) != op(e1,e2) )
    & ( op(e1,e0) != op(e1,e3) )
    & ( op(e1,e1) != op(e1,e2) )
    & ( op(e1,e1) != op(e1,e3) )
    & ( op(e1,e2) != op(e1,e3) )
    & ( op(e2,e0) != op(e2,e1) )
    & ( op(e2,e0) != op(e2,e2) )
    & ( op(e2,e0) != op(e2,e3) )
    & ( op(e2,e1) != op(e2,e2) )
    & ( op(e2,e1) != op(e2,e3) )
    & ( op(e2,e2) != op(e2,e3) )
    & ( op(e3,e0) != op(e3,e1) )
    & ( op(e3,e0) != op(e3,e2) )
    & ( op(e3,e0) != op(e3,e3) )
    & ( op(e3,e1) != op(e3,e2) )
    & ( op(e3,e1) != op(e3,e3) )
    & ( op(e3,e2) != op(e3,e3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).

tff(f_152,axiom,
    ( ( ( op(e0,e0) = e0 )
      | ( op(e0,e0) = e1 )
      | ( op(e0,e0) = e2 )
      | ( op(e0,e0) = e3 ) )
    & ( ( op(e0,e1) = e0 )
      | ( op(e0,e1) = e1 )
      | ( op(e0,e1) = e2 )
      | ( op(e0,e1) = e3 ) )
    & ( ( op(e0,e2) = e0 )
      | ( op(e0,e2) = e1 )
      | ( op(e0,e2) = e2 )
      | ( op(e0,e2) = e3 ) )
    & ( ( op(e0,e3) = e0 )
      | ( op(e0,e3) = e1 )
      | ( op(e0,e3) = e2 )
      | ( op(e0,e3) = e3 ) )
    & ( ( op(e1,e0) = e0 )
      | ( op(e1,e0) = e1 )
      | ( op(e1,e0) = e2 )
      | ( op(e1,e0) = e3 ) )
    & ( ( op(e1,e1) = e0 )
      | ( op(e1,e1) = e1 )
      | ( op(e1,e1) = e2 )
      | ( op(e1,e1) = e3 ) )
    & ( ( op(e1,e2) = e0 )
      | ( op(e1,e2) = e1 )
      | ( op(e1,e2) = e2 )
      | ( op(e1,e2) = e3 ) )
    & ( ( op(e1,e3) = e0 )
      | ( op(e1,e3) = e1 )
      | ( op(e1,e3) = e2 )
      | ( op(e1,e3) = e3 ) )
    & ( ( op(e2,e0) = e0 )
      | ( op(e2,e0) = e1 )
      | ( op(e2,e0) = e2 )
      | ( op(e2,e0) = e3 ) )
    & ( ( op(e2,e1) = e0 )
      | ( op(e2,e1) = e1 )
      | ( op(e2,e1) = e2 )
      | ( op(e2,e1) = e3 ) )
    & ( ( op(e2,e2) = e0 )
      | ( op(e2,e2) = e1 )
      | ( op(e2,e2) = e2 )
      | ( op(e2,e2) = e3 ) )
    & ( ( op(e2,e3) = e0 )
      | ( op(e2,e3) = e1 )
      | ( op(e2,e3) = e2 )
      | ( op(e2,e3) = e3 ) )
    & ( ( op(e3,e0) = e0 )
      | ( op(e3,e0) = e1 )
      | ( op(e3,e0) = e2 )
      | ( op(e3,e0) = e3 ) )
    & ( ( op(e3,e1) = e0 )
      | ( op(e3,e1) = e1 )
      | ( op(e3,e1) = e2 )
      | ( op(e3,e1) = e3 ) )
    & ( ( op(e3,e2) = e0 )
      | ( op(e3,e2) = e1 )
      | ( op(e3,e2) = e2 )
      | ( op(e3,e2) = e3 ) )
    & ( ( op(e3,e3) = e0 )
      | ( op(e3,e3) = e1 )
      | ( op(e3,e3) = e2 )
      | ( op(e3,e3) = e3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).

tff(f_407,axiom,
    ( ( ( op(e0,e0) = e0 )
      | ( op(e0,e1) = e0 )
      | ( op(e0,e2) = e0 )
      | ( op(e0,e3) = e0 ) )
    & ( ( op(e0,e0) = e0 )
      | ( op(e1,e0) = e0 )
      | ( op(e2,e0) = e0 )
      | ( op(e3,e0) = e0 ) )
    & ( ( op(e0,e0) = e1 )
      | ( op(e0,e1) = e1 )
      | ( op(e0,e2) = e1 )
      | ( op(e0,e3) = e1 ) )
    & ( ( op(e0,e0) = e1 )
      | ( op(e1,e0) = e1 )
      | ( op(e2,e0) = e1 )
      | ( op(e3,e0) = e1 ) )
    & ( ( op(e0,e0) = e2 )
      | ( op(e0,e1) = e2 )
      | ( op(e0,e2) = e2 )
      | ( op(e0,e3) = e2 ) )
    & ( ( op(e0,e0) = e2 )
      | ( op(e1,e0) = e2 )
      | ( op(e2,e0) = e2 )
      | ( op(e3,e0) = e2 ) )
    & ( ( op(e0,e0) = e3 )
      | ( op(e0,e1) = e3 )
      | ( op(e0,e2) = e3 )
      | ( op(e0,e3) = e3 ) )
    & ( ( op(e0,e0) = e3 )
      | ( op(e1,e0) = e3 )
      | ( op(e2,e0) = e3 )
      | ( op(e3,e0) = e3 ) )
    & ( ( op(e1,e0) = e0 )
      | ( op(e1,e1) = e0 )
      | ( op(e1,e2) = e0 )
      | ( op(e1,e3) = e0 ) )
    & ( ( op(e0,e1) = e0 )
      | ( op(e1,e1) = e0 )
      | ( op(e2,e1) = e0 )
      | ( op(e3,e1) = e0 ) )
    & ( ( op(e1,e0) = e1 )
      | ( op(e1,e1) = e1 )
      | ( op(e1,e2) = e1 )
      | ( op(e1,e3) = e1 ) )
    & ( ( op(e0,e1) = e1 )
      | ( op(e1,e1) = e1 )
      | ( op(e2,e1) = e1 )
      | ( op(e3,e1) = e1 ) )
    & ( ( op(e1,e0) = e2 )
      | ( op(e1,e1) = e2 )
      | ( op(e1,e2) = e2 )
      | ( op(e1,e3) = e2 ) )
    & ( ( op(e0,e1) = e2 )
      | ( op(e1,e1) = e2 )
      | ( op(e2,e1) = e2 )
      | ( op(e3,e1) = e2 ) )
    & ( ( op(e1,e0) = e3 )
      | ( op(e1,e1) = e3 )
      | ( op(e1,e2) = e3 )
      | ( op(e1,e3) = e3 ) )
    & ( ( op(e0,e1) = e3 )
      | ( op(e1,e1) = e3 )
      | ( op(e2,e1) = e3 )
      | ( op(e3,e1) = e3 ) )
    & ( ( op(e2,e0) = e0 )
      | ( op(e2,e1) = e0 )
      | ( op(e2,e2) = e0 )
      | ( op(e2,e3) = e0 ) )
    & ( ( op(e0,e2) = e0 )
      | ( op(e1,e2) = e0 )
      | ( op(e2,e2) = e0 )
      | ( op(e3,e2) = e0 ) )
    & ( ( op(e2,e0) = e1 )
      | ( op(e2,e1) = e1 )
      | ( op(e2,e2) = e1 )
      | ( op(e2,e3) = e1 ) )
    & ( ( op(e0,e2) = e1 )
      | ( op(e1,e2) = e1 )
      | ( op(e2,e2) = e1 )
      | ( op(e3,e2) = e1 ) )
    & ( ( op(e2,e0) = e2 )
      | ( op(e2,e1) = e2 )
      | ( op(e2,e2) = e2 )
      | ( op(e2,e3) = e2 ) )
    & ( ( op(e0,e2) = e2 )
      | ( op(e1,e2) = e2 )
      | ( op(e2,e2) = e2 )
      | ( op(e3,e2) = e2 ) )
    & ( ( op(e2,e0) = e3 )
      | ( op(e2,e1) = e3 )
      | ( op(e2,e2) = e3 )
      | ( op(e2,e3) = e3 ) )
    & ( ( op(e0,e2) = e3 )
      | ( op(e1,e2) = e3 )
      | ( op(e2,e2) = e3 )
      | ( op(e3,e2) = e3 ) )
    & ( ( op(e3,e0) = e0 )
      | ( op(e3,e1) = e0 )
      | ( op(e3,e2) = e0 )
      | ( op(e3,e3) = e0 ) )
    & ( ( op(e0,e3) = e0 )
      | ( op(e1,e3) = e0 )
      | ( op(e2,e3) = e0 )
      | ( op(e3,e3) = e0 ) )
    & ( ( op(e3,e0) = e1 )
      | ( op(e3,e1) = e1 )
      | ( op(e3,e2) = e1 )
      | ( op(e3,e3) = e1 ) )
    & ( ( op(e0,e3) = e1 )
      | ( op(e1,e3) = e1 )
      | ( op(e2,e3) = e1 )
      | ( op(e3,e3) = e1 ) )
    & ( ( op(e3,e0) = e2 )
      | ( op(e3,e1) = e2 )
      | ( op(e3,e2) = e2 )
      | ( op(e3,e3) = e2 ) )
    & ( ( op(e0,e3) = e2 )
      | ( op(e1,e3) = e2 )
      | ( op(e2,e3) = e2 )
      | ( op(e3,e3) = e2 ) )
    & ( ( op(e3,e0) = e3 )
      | ( op(e3,e1) = e3 )
      | ( op(e3,e2) = e3 )
      | ( op(e3,e3) = e3 ) )
    & ( ( op(e0,e3) = e3 )
      | ( op(e1,e3) = e3 )
      | ( op(e2,e3) = e3 )
      | ( op(e3,e3) = e3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).

tff(f_594,axiom,
    ~ ( ( e0 = op(e1,e2) )
      & ( e3 = op(op(e1,e2),e2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10) ).

tff(c_196,plain,
    e3 != e1,
    inference(cnfTransformation,[status(thm)],[f_567]) ).

tff(c_204,plain,
    e1 != e0,
    inference(cnfTransformation,[status(thm)],[f_567]) ).

tff(c_198,plain,
    e2 != e1,
    inference(cnfTransformation,[status(thm)],[f_567]) ).

tff(c_224,plain,
    ( ( op(op(e2,e1),e1) != e3 )
    | ( op(e2,e1) != e0 ) ),
    inference(cnfTransformation,[status(thm)],[f_598]) ).

tff(c_438,plain,
    op(e2,e1) != e0,
    inference(splitLeft,[status(thm)],[c_224]) ).

tff(c_202,plain,
    e2 != e0,
    inference(cnfTransformation,[status(thm)],[f_567]) ).

tff(c_194,plain,
    e3 != e2,
    inference(cnfTransformation,[status(thm)],[f_567]) ).

tff(c_212,plain,
    op(e0,e0) = e0,
    inference(cnfTransformation,[status(thm)],[f_574]) ).

tff(c_142,plain,
    op(e0,e2) != op(e0,e0),
    inference(cnfTransformation,[status(thm)],[f_550]) ).

tff(c_274,plain,
    op(e0,e2) != e0,
    inference(demodulation,[status(thm),theory(equality)],[c_212,c_142]) ).

tff(c_208,plain,
    op(e2,e2) = e2,
    inference(cnfTransformation,[status(thm)],[f_574]) ).

tff(c_166,plain,
    op(e2,e2) != op(e0,e2),
    inference(cnfTransformation,[status(thm)],[f_550]) ).

tff(c_267,plain,
    op(e0,e2) != e2,
    inference(demodulation,[status(thm),theory(equality)],[c_208,c_166]) ).

tff(c_28,plain,
    ( ( op(e0,e2) = e3 )
    | ( op(e0,e2) = e2 )
    | ( op(e0,e2) = e1 )
    | ( op(e0,e2) = e0 ) ),
    inference(cnfTransformation,[status(thm)],[f_152]) ).

tff(c_352,plain,
    ( ( op(e0,e2) = e3 )
    | ( op(e0,e2) = e1 ) ),
    inference(negUnitSimplification,[status(thm)],[c_274,c_267,c_28]) ).

tff(c_454,plain,
    op(e0,e2) = e1,
    inference(splitLeft,[status(thm)],[c_352]) ).

tff(c_200,plain,
    e3 != e0,
    inference(cnfTransformation,[status(thm)],[f_567]) ).

tff(c_206,plain,
    op(e3,e3) = e3,
    inference(cnfTransformation,[status(thm)],[f_574]) ).

tff(c_152,plain,
    op(e3,e3) != op(e0,e3),
    inference(cnfTransformation,[status(thm)],[f_550]) ).

tff(c_270,plain,
    op(e0,e3) != e3,
    inference(demodulation,[status(thm),theory(equality)],[c_206,c_152]) ).

tff(c_84,plain,
    ( ( op(e0,e3) = e3 )
    | ( op(e0,e2) = e3 )
    | ( op(e0,e1) = e3 )
    | ( op(e0,e0) = e3 ) ),
    inference(cnfTransformation,[status(thm)],[f_407]) ).

tff(c_297,plain,
    ( ( op(e0,e3) = e3 )
    | ( op(e0,e2) = e3 )
    | ( op(e0,e1) = e3 )
    | ( e3 = e0 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_212,c_84]) ).

tff(c_298,plain,
    ( ( op(e0,e2) = e3 )
    | ( op(e0,e1) = e3 ) ),
    inference(negUnitSimplification,[status(thm)],[c_200,c_270,c_297]) ).

tff(c_494,plain,
    ( ( e3 = e1 )
    | ( op(e0,e1) = e3 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_454,c_298]) ).

tff(c_495,plain,
    op(e0,e1) = e3,
    inference(negUnitSimplification,[status(thm)],[c_196,c_494]) ).

tff(c_114,plain,
    op(e2,e2) != op(e2,e1),
    inference(cnfTransformation,[status(thm)],[f_550]) ).

tff(c_280,plain,
    op(e2,e1) != e2,
    inference(demodulation,[status(thm),theory(equality)],[c_208,c_114]) ).

tff(c_210,plain,
    op(e1,e1) = e1,
    inference(cnfTransformation,[status(thm)],[f_574]) ).

tff(c_70,plain,
    ( ( op(e3,e1) = e2 )
    | ( op(e2,e1) = e2 )
    | ( op(e1,e1) = e2 )
    | ( op(e0,e1) = e2 ) ),
    inference(cnfTransformation,[status(thm)],[f_407]) ).

tff(c_311,plain,
    ( ( op(e3,e1) = e2 )
    | ( op(e2,e1) = e2 )
    | ( e2 = e1 )
    | ( op(e0,e1) = e2 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_210,c_70]) ).

tff(c_312,plain,
    ( ( op(e3,e1) = e2 )
    | ( op(e0,e1) = e2 ) ),
    inference(negUnitSimplification,[status(thm)],[c_198,c_280,c_311]) ).

tff(c_526,plain,
    ( ( op(e3,e1) = e2 )
    | ( e3 = e2 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_495,c_312]) ).

tff(c_527,plain,
    op(e3,e1) = e2,
    inference(negUnitSimplification,[status(thm)],[c_194,c_526]) ).

tff(c_144,plain,
    op(e0,e1) != op(e0,e0),
    inference(cnfTransformation,[status(thm)],[f_550]) ).

tff(c_273,plain,
    op(e0,e1) != e0,
    inference(demodulation,[status(thm),theory(equality)],[c_212,c_144]) ).

tff(c_78,plain,
    ( ( op(e3,e1) = e0 )
    | ( op(e2,e1) = e0 )
    | ( op(e1,e1) = e0 )
    | ( op(e0,e1) = e0 ) ),
    inference(cnfTransformation,[status(thm)],[f_407]) ).

tff(c_303,plain,
    ( ( op(e3,e1) = e0 )
    | ( op(e2,e1) = e0 )
    | ( e1 = e0 )
    | ( op(e0,e1) = e0 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_210,c_78]) ).

tff(c_304,plain,
    ( ( op(e3,e1) = e0 )
    | ( op(e2,e1) = e0 ) ),
    inference(negUnitSimplification,[status(thm)],[c_273,c_204,c_303]) ).

tff(c_556,plain,
    ( ( e2 = e0 )
    | ( op(e2,e1) = e0 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_527,c_304]) ).

tff(c_557,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_438,c_202,c_556]) ).

tff(c_558,plain,
    op(e0,e2) = e3,
    inference(splitRight,[status(thm)],[c_352]) ).

tff(c_110,plain,
    op(e2,e3) != op(e2,e2),
    inference(cnfTransformation,[status(thm)],[f_550]) ).

tff(c_281,plain,
    op(e2,e3) != e2,
    inference(demodulation,[status(thm),theory(equality)],[c_208,c_110]) ).

tff(c_38,plain,
    ( ( op(e3,e3) = e2 )
    | ( op(e2,e3) = e2 )
    | ( op(e1,e3) = e2 )
    | ( op(e0,e3) = e2 ) ),
    inference(cnfTransformation,[status(thm)],[f_407]) ).

tff(c_343,plain,
    ( ( e3 = e2 )
    | ( op(e2,e3) = e2 )
    | ( op(e1,e3) = e2 )
    | ( op(e0,e3) = e2 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_206,c_38]) ).

tff(c_344,plain,
    ( ( op(e1,e3) = e2 )
    | ( op(e0,e3) = e2 ) ),
    inference(negUnitSimplification,[status(thm)],[c_281,c_194,c_343]) ).

tff(c_385,plain,
    op(e0,e3) = e2,
    inference(splitLeft,[status(thm)],[c_344]) ).

tff(c_180,plain,
    op(e1,e1) != op(e0,e1),
    inference(cnfTransformation,[status(thm)],[f_550]) ).

tff(c_264,plain,
    op(e0,e1) != e1,
    inference(demodulation,[status(thm),theory(equality)],[c_210,c_180]) ).

tff(c_92,plain,
    ( ( op(e0,e3) = e1 )
    | ( op(e0,e2) = e1 )
    | ( op(e0,e1) = e1 )
    | ( op(e0,e0) = e1 ) ),
    inference(cnfTransformation,[status(thm)],[f_407]) ).

tff(c_289,plain,
    ( ( op(e0,e3) = e1 )
    | ( op(e0,e2) = e1 )
    | ( op(e0,e1) = e1 )
    | ( e1 = e0 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_212,c_92]) ).

tff(c_290,plain,
    ( ( op(e0,e3) = e1 )
    | ( op(e0,e2) = e1 ) ),
    inference(negUnitSimplification,[status(thm)],[c_204,c_264,c_289]) ).

tff(c_596,plain,
    ( ( e2 = e1 )
    | ( e3 = e1 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_558,c_385,c_290]) ).

tff(c_597,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_196,c_198,c_596]) ).

tff(c_599,plain,
    op(e2,e1) = e0,
    inference(splitRight,[status(thm)],[c_224]) ).

tff(c_598,plain,
    op(op(e2,e1),e1) != e3,
    inference(splitRight,[status(thm)],[c_224]) ).

tff(c_611,plain,
    op(e0,e1) != e3,
    inference(demodulation,[status(thm),theory(equality)],[c_599,c_598]) ).

tff(c_625,plain,
    op(e0,e2) = e3,
    inference(negUnitSimplification,[status(thm)],[c_611,c_298]) ).

tff(c_132,plain,
    op(e1,e1) != op(e1,e0),
    inference(cnfTransformation,[status(thm)],[f_550]) ).

tff(c_276,plain,
    op(e1,e0) != e1,
    inference(demodulation,[status(thm),theory(equality)],[c_210,c_132]) ).

tff(c_90,plain,
    ( ( op(e3,e0) = e1 )
    | ( op(e2,e0) = e1 )
    | ( op(e1,e0) = e1 )
    | ( op(e0,e0) = e1 ) ),
    inference(cnfTransformation,[status(thm)],[f_407]) ).

tff(c_291,plain,
    ( ( op(e3,e0) = e1 )
    | ( op(e2,e0) = e1 )
    | ( op(e1,e0) = e1 )
    | ( e1 = e0 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_212,c_90]) ).

tff(c_292,plain,
    ( ( op(e3,e0) = e1 )
    | ( op(e2,e0) = e1 ) ),
    inference(negUnitSimplification,[status(thm)],[c_204,c_276,c_291]) ).

tff(c_399,plain,
    op(e2,e0) = e1,
    inference(splitLeft,[status(thm)],[c_292]) ).

tff(c_116,plain,
    op(e2,e3) != op(e2,e0),
    inference(cnfTransformation,[status(thm)],[f_550]) ).

tff(c_403,plain,
    op(e2,e3) != e1,
    inference(demodulation,[status(thm),theory(equality)],[c_399,c_116]) ).

tff(c_124,plain,
    op(e1,e3) != op(e1,e1),
    inference(cnfTransformation,[status(thm)],[f_550]) ).

tff(c_278,plain,
    op(e1,e3) != e1,
    inference(demodulation,[status(thm),theory(equality)],[c_210,c_124]) ).

tff(c_42,plain,
    ( ( op(e3,e3) = e1 )
    | ( op(e2,e3) = e1 )
    | ( op(e1,e3) = e1 )
    | ( op(e0,e3) = e1 ) ),
    inference(cnfTransformation,[status(thm)],[f_407]) ).

tff(c_339,plain,
    ( ( e3 = e1 )
    | ( op(e2,e3) = e1 )
    | ( op(e1,e3) = e1 )
    | ( op(e0,e3) = e1 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_206,c_42]) ).

tff(c_340,plain,
    ( ( op(e2,e3) = e1 )
    | ( op(e0,e3) = e1 ) ),
    inference(negUnitSimplification,[status(thm)],[c_278,c_196,c_339]) ).

tff(c_424,plain,
    ( ( op(e2,e3) = e1 )
    | ( e2 = e1 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_385,c_340]) ).

tff(c_425,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_198,c_403,c_424]) ).

tff(c_426,plain,
    op(e3,e0) = e1,
    inference(splitRight,[status(thm)],[c_292]) ).

tff(c_106,plain,
    op(e3,e2) != op(e3,e0),
    inference(cnfTransformation,[status(thm)],[f_550]) ).

tff(c_430,plain,
    op(e3,e2) != e1,
    inference(demodulation,[status(thm),theory(equality)],[c_426,c_106]) ).

tff(c_158,plain,
    op(e3,e2) != op(e2,e2),
    inference(cnfTransformation,[status(thm)],[f_550]) ).

tff(c_269,plain,
    op(e3,e2) != e2,
    inference(demodulation,[status(thm),theory(equality)],[c_208,c_158]) ).

tff(c_98,plain,
    op(e3,e3) != op(e3,e2),
    inference(cnfTransformation,[status(thm)],[f_550]) ).

tff(c_284,plain,
    op(e3,e2) != e3,
    inference(demodulation,[status(thm),theory(equality)],[c_206,c_98]) ).

tff(c_4,plain,
    ( ( op(e3,e2) = e3 )
    | ( op(e3,e2) = e2 )
    | ( op(e3,e2) = e1 )
    | ( op(e3,e2) = e0 ) ),
    inference(cnfTransformation,[status(thm)],[f_152]) ).

tff(c_366,plain,
    ( ( op(e3,e2) = e1 )
    | ( op(e3,e2) = e0 ) ),
    inference(negUnitSimplification,[status(thm)],[c_269,c_284,c_4]) ).

tff(c_659,plain,
    op(e3,e2) = e0,
    inference(negUnitSimplification,[status(thm)],[c_430,c_366]) ).

tff(c_126,plain,
    op(e1,e2) != op(e1,e1),
    inference(cnfTransformation,[status(thm)],[f_550]) ).

tff(c_277,plain,
    op(e1,e2) != e1,
    inference(demodulation,[status(thm),theory(equality)],[c_210,c_126]) ).

tff(c_58,plain,
    ( ( op(e3,e2) = e1 )
    | ( op(e2,e2) = e1 )
    | ( op(e1,e2) = e1 )
    | ( op(e0,e2) = e1 ) ),
    inference(cnfTransformation,[status(thm)],[f_407]) ).

tff(c_323,plain,
    ( ( op(e3,e2) = e1 )
    | ( e2 = e1 )
    | ( op(e1,e2) = e1 )
    | ( op(e0,e2) = e1 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_208,c_58]) ).

tff(c_324,plain,
    ( ( op(e3,e2) = e1 )
    | ( op(e0,e2) = e1 ) ),
    inference(negUnitSimplification,[status(thm)],[c_277,c_198,c_323]) ).

tff(c_668,plain,
    ( ( e1 = e0 )
    | ( e3 = e1 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_625,c_659,c_324]) ).

tff(c_669,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_196,c_204,c_668]) ).

tff(c_670,plain,
    op(e1,e3) = e2,
    inference(splitRight,[status(thm)],[c_344]) ).

tff(c_128,plain,
    op(e1,e3) != op(e1,e0),
    inference(cnfTransformation,[status(thm)],[f_550]) ).

tff(c_674,plain,
    op(e1,e0) != e2,
    inference(demodulation,[status(thm),theory(equality)],[c_670,c_128]) ).

tff(c_192,plain,
    op(e1,e0) != op(e0,e0),
    inference(cnfTransformation,[status(thm)],[f_550]) ).

tff(c_261,plain,
    op(e1,e0) != e0,
    inference(demodulation,[status(thm),theory(equality)],[c_212,c_192]) ).

tff(c_80,plain,
    ( ( op(e1,e3) = e0 )
    | ( op(e1,e2) = e0 )
    | ( op(e1,e1) = e0 )
    | ( op(e1,e0) = e0 ) ),
    inference(cnfTransformation,[status(thm)],[f_407]) ).

tff(c_301,plain,
    ( ( op(e1,e3) = e0 )
    | ( op(e1,e2) = e0 )
    | ( e1 = e0 )
    | ( op(e1,e0) = e0 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_210,c_80]) ).

tff(c_302,plain,
    ( ( op(e1,e3) = e0 )
    | ( op(e1,e2) = e0 ) ),
    inference(negUnitSimplification,[status(thm)],[c_261,c_204,c_301]) ).

tff(c_797,plain,
    ( ( e2 = e0 )
    | ( op(e1,e2) = e0 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_670,c_302]) ).

tff(c_798,plain,
    op(e1,e2) = e0,
    inference(negUnitSimplification,[status(thm)],[c_202,c_797]) ).

tff(c_848,plain,
    op(e0,e1) = e3,
    inference(splitLeft,[status(thm)],[c_298]) ).

tff(c_178,plain,
    op(e2,e1) != op(e0,e1),
    inference(cnfTransformation,[status(thm)],[f_550]) ).

tff(c_852,plain,
    op(e2,e1) != e3,
    inference(demodulation,[status(thm),theory(equality)],[c_848,c_178]) ).

tff(c_682,plain,
    op(e2,e0) = e1,
    inference(splitLeft,[status(thm)],[c_292]) ).

tff(c_146,plain,
    op(e3,e3) != op(e2,e3),
    inference(cnfTransformation,[status(thm)],[f_550]) ).

tff(c_272,plain,
    op(e2,e3) != e3,
    inference(demodulation,[status(thm),theory(equality)],[c_206,c_146]) ).

tff(c_52,plain,
    ( ( op(e2,e3) = e3 )
    | ( op(e2,e2) = e3 )
    | ( op(e2,e1) = e3 )
    | ( op(e2,e0) = e3 ) ),
    inference(cnfTransformation,[status(thm)],[f_407]) ).

tff(c_329,plain,
    ( ( op(e2,e3) = e3 )
    | ( e3 = e2 )
    | ( op(e2,e1) = e3 )
    | ( op(e2,e0) = e3 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_208,c_52]) ).

tff(c_330,plain,
    ( ( op(e2,e1) = e3 )
    | ( op(e2,e0) = e3 ) ),
    inference(negUnitSimplification,[status(thm)],[c_194,c_272,c_329]) ).

tff(c_876,plain,
    ( ( op(e2,e1) = e3 )
    | ( e3 = e1 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_682,c_330]) ).

tff(c_877,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_196,c_852,c_876]) ).

tff(c_878,plain,
    op(e0,e2) = e3,
    inference(splitRight,[status(thm)],[c_298]) ).

tff(c_222,plain,
    ( ( op(op(e1,e2),e2) != e3 )
    | ( op(e1,e2) != e0 ) ),
    inference(cnfTransformation,[status(thm)],[f_594]) ).

tff(c_890,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_798,c_878,c_798,c_222]) ).

tff(c_891,plain,
    op(e3,e0) = e1,
    inference(splitRight,[status(thm)],[c_292]) ).

tff(c_118,plain,
    op(e2,e2) != op(e2,e0),
    inference(cnfTransformation,[status(thm)],[f_550]) ).

tff(c_279,plain,
    op(e2,e0) != e2,
    inference(demodulation,[status(thm),theory(equality)],[c_208,c_118]) ).

tff(c_86,plain,
    ( ( op(e3,e0) = e2 )
    | ( op(e2,e0) = e2 )
    | ( op(e1,e0) = e2 )
    | ( op(e0,e0) = e2 ) ),
    inference(cnfTransformation,[status(thm)],[f_407]) ).

tff(c_295,plain,
    ( ( op(e3,e0) = e2 )
    | ( op(e2,e0) = e2 )
    | ( op(e1,e0) = e2 )
    | ( e2 = e0 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_212,c_86]) ).

tff(c_296,plain,
    ( ( op(e3,e0) = e2 )
    | ( op(e1,e0) = e2 ) ),
    inference(negUnitSimplification,[status(thm)],[c_202,c_279,c_295]) ).

tff(c_984,plain,
    ( ( e2 = e1 )
    | ( op(e1,e0) = e2 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_891,c_296]) ).

tff(c_985,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_674,c_198,c_984]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ALG138+1 : TPTP v8.1.2. Released v2.7.0.
% 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 : n029.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 20:36:37 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 6.31/2.46  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.77/2.48  
% 6.77/2.48  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.10/2.54  
% 7.10/2.54  Inference rules
% 7.10/2.54  ----------------------
% 7.10/2.54  #Ref     : 0
% 7.10/2.54  #Sup     : 104
% 7.10/2.54  #Fact    : 0
% 7.10/2.54  #Define  : 0
% 7.10/2.54  #Split   : 17
% 7.10/2.54  #Chain   : 0
% 7.10/2.54  #Close   : 0
% 7.10/2.54  
% 7.10/2.54  Ordering : KBO
% 7.10/2.54  
% 7.10/2.54  Simplification rules
% 7.10/2.54  ----------------------
% 7.10/2.54  #Subsume      : 217
% 7.10/2.54  #Demod        : 411
% 7.10/2.54  #Tautology    : 143
% 7.10/2.54  #SimpNegUnit  : 112
% 7.10/2.54  #BackRed      : 245
% 7.10/2.54  
% 7.10/2.54  #Partial instantiations: 0
% 7.10/2.54  #Strategies tried      : 1
% 7.10/2.54  
% 7.10/2.54  Timing (in seconds)
% 7.10/2.54  ----------------------
% 7.10/2.54  Preprocessing        : 0.71
% 7.10/2.54  Parsing              : 0.38
% 7.10/2.54  CNF conversion       : 0.04
% 7.10/2.54  Main loop            : 0.73
% 7.10/2.54  Inferencing          : 0.15
% 7.10/2.54  Reduction            : 0.24
% 7.10/2.54  Demodulation         : 0.16
% 7.10/2.54  BG Simplification    : 0.05
% 7.10/2.54  Subsumption          : 0.24
% 7.10/2.54  Abstraction          : 0.02
% 7.10/2.54  MUC search           : 0.00
% 7.10/2.54  Cooper               : 0.00
% 7.10/2.54  Total                : 1.54
% 7.10/2.54  Index Insertion      : 0.00
% 7.10/2.54  Index Deletion       : 0.00
% 7.10/2.54  Index Matching       : 0.00
% 7.10/2.54  BG Taut test         : 0.00
%------------------------------------------------------------------------------