TSTP Solution File: ALG082+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ALG082+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 : n028.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 10:31:07 EDT 2023

% Result   : Theorem 8.24s 2.99s
% Output   : CNFRefutation 8.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   18
% Syntax   : Number of formulae    :  169 ( 139 unt;  14 typ;   0 def)
%            Number of atoms       :  357 ( 338 equ)
%            Maximal formula atoms :  110 (   2 avg)
%            Number of connectives :  228 (  26   ~;  76   |; 125   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   63 (   2 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    6 (   4   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;  10 con; 0-2 aty)
%            Number of variables   :    0 (;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ op2 > op1 > #nlpp > j > h > e24 > e23 > e22 > e21 > e20 > e14 > e13 > e12 > e11 > e10

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(e21,type,
    e21: $i ).

tff(e24,type,
    e24: $i ).

tff(e20,type,
    e20: $i ).

tff(e13,type,
    e13: $i ).

tff(e22,type,
    e22: $i ).

tff(op2,type,
    op2: ( $i * $i ) > $i ).

tff(op1,type,
    op1: ( $i * $i ) > $i ).

tff(e10,type,
    e10: $i ).

tff(h,type,
    h: $i > $i ).

tff(e23,type,
    e23: $i ).

tff(e14,type,
    e14: $i ).

tff(e12,type,
    e12: $i ).

tff(j,type,
    j: $i > $i ).

tff(e11,type,
    e11: $i ).

tff(f_54,axiom,
    ( ( e10 != e11 )
    & ( e10 != e12 )
    & ( e10 != e13 )
    & ( e10 != e14 )
    & ( e11 != e12 )
    & ( e11 != e13 )
    & ( e11 != e14 )
    & ( e12 != e13 )
    & ( e12 != e14 )
    & ( e13 != e14 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).

tff(f_206,axiom,
    ( ( op1(e10,e10) = e10 )
    & ( op1(e10,e11) = e11 )
    & ( op1(e10,e12) = e12 )
    & ( op1(e10,e13) = e13 )
    & ( op1(e10,e14) = e14 )
    & ( op1(e11,e10) = e11 )
    & ( op1(e11,e11) = e14 )
    & ( op1(e11,e12) = e10 )
    & ( op1(e11,e13) = e12 )
    & ( op1(e11,e14) = e13 )
    & ( op1(e12,e10) = e12 )
    & ( op1(e12,e11) = e10 )
    & ( op1(e12,e12) = e13 )
    & ( op1(e12,e13) = e14 )
    & ( op1(e12,e14) = e11 )
    & ( op1(e13,e10) = e13 )
    & ( op1(e13,e11) = e12 )
    & ( op1(e13,e12) = e14 )
    & ( op1(e13,e13) = e11 )
    & ( op1(e13,e14) = e10 )
    & ( op1(e14,e10) = e14 )
    & ( op1(e14,e11) = e13 )
    & ( op1(e14,e12) = e11 )
    & ( op1(e14,e13) = e10 )
    & ( op1(e14,e14) = e12 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).

tff(f_476,negated_conjecture,
    ~ ( ( ( ( h(e10) = e20 )
          | ( h(e10) = e21 )
          | ( h(e10) = e22 )
          | ( h(e10) = e23 )
          | ( h(e10) = e24 ) )
        & ( ( h(e11) = e20 )
          | ( h(e11) = e21 )
          | ( h(e11) = e22 )
          | ( h(e11) = e23 )
          | ( h(e11) = e24 ) )
        & ( ( h(e12) = e20 )
          | ( h(e12) = e21 )
          | ( h(e12) = e22 )
          | ( h(e12) = e23 )
          | ( h(e12) = e24 ) )
        & ( ( h(e13) = e20 )
          | ( h(e13) = e21 )
          | ( h(e13) = e22 )
          | ( h(e13) = e23 )
          | ( h(e13) = e24 ) )
        & ( ( h(e14) = e20 )
          | ( h(e14) = e21 )
          | ( h(e14) = e22 )
          | ( h(e14) = e23 )
          | ( h(e14) = e24 ) )
        & ( ( j(e20) = e10 )
          | ( j(e20) = e11 )
          | ( j(e20) = e12 )
          | ( j(e20) = e13 )
          | ( j(e20) = e14 ) )
        & ( ( j(e21) = e10 )
          | ( j(e21) = e11 )
          | ( j(e21) = e12 )
          | ( j(e21) = e13 )
          | ( j(e21) = e14 ) )
        & ( ( j(e22) = e10 )
          | ( j(e22) = e11 )
          | ( j(e22) = e12 )
          | ( j(e22) = e13 )
          | ( j(e22) = e14 ) )
        & ( ( j(e23) = e10 )
          | ( j(e23) = e11 )
          | ( j(e23) = e12 )
          | ( j(e23) = e13 )
          | ( j(e23) = e14 ) )
        & ( ( j(e24) = e10 )
          | ( j(e24) = e11 )
          | ( j(e24) = e12 )
          | ( j(e24) = e13 )
          | ( j(e24) = e14 ) ) )
     => ~ ( ( h(op1(e10,e10)) = op2(h(e10),h(e10)) )
          & ( h(op1(e10,e11)) = op2(h(e10),h(e11)) )
          & ( h(op1(e10,e12)) = op2(h(e10),h(e12)) )
          & ( h(op1(e10,e13)) = op2(h(e10),h(e13)) )
          & ( h(op1(e10,e14)) = op2(h(e10),h(e14)) )
          & ( h(op1(e11,e10)) = op2(h(e11),h(e10)) )
          & ( h(op1(e11,e11)) = op2(h(e11),h(e11)) )
          & ( h(op1(e11,e12)) = op2(h(e11),h(e12)) )
          & ( h(op1(e11,e13)) = op2(h(e11),h(e13)) )
          & ( h(op1(e11,e14)) = op2(h(e11),h(e14)) )
          & ( h(op1(e12,e10)) = op2(h(e12),h(e10)) )
          & ( h(op1(e12,e11)) = op2(h(e12),h(e11)) )
          & ( h(op1(e12,e12)) = op2(h(e12),h(e12)) )
          & ( h(op1(e12,e13)) = op2(h(e12),h(e13)) )
          & ( h(op1(e12,e14)) = op2(h(e12),h(e14)) )
          & ( h(op1(e13,e10)) = op2(h(e13),h(e10)) )
          & ( h(op1(e13,e11)) = op2(h(e13),h(e11)) )
          & ( h(op1(e13,e12)) = op2(h(e13),h(e12)) )
          & ( h(op1(e13,e13)) = op2(h(e13),h(e13)) )
          & ( h(op1(e13,e14)) = op2(h(e13),h(e14)) )
          & ( h(op1(e14,e10)) = op2(h(e14),h(e10)) )
          & ( h(op1(e14,e11)) = op2(h(e14),h(e11)) )
          & ( h(op1(e14,e12)) = op2(h(e14),h(e12)) )
          & ( h(op1(e14,e13)) = op2(h(e14),h(e13)) )
          & ( h(op1(e14,e14)) = op2(h(e14),h(e14)) )
          & ( j(op2(e20,e20)) = op1(j(e20),j(e20)) )
          & ( j(op2(e20,e21)) = op1(j(e20),j(e21)) )
          & ( j(op2(e20,e22)) = op1(j(e20),j(e22)) )
          & ( j(op2(e20,e23)) = op1(j(e20),j(e23)) )
          & ( j(op2(e20,e24)) = op1(j(e20),j(e24)) )
          & ( j(op2(e21,e20)) = op1(j(e21),j(e20)) )
          & ( j(op2(e21,e21)) = op1(j(e21),j(e21)) )
          & ( j(op2(e21,e22)) = op1(j(e21),j(e22)) )
          & ( j(op2(e21,e23)) = op1(j(e21),j(e23)) )
          & ( j(op2(e21,e24)) = op1(j(e21),j(e24)) )
          & ( j(op2(e22,e20)) = op1(j(e22),j(e20)) )
          & ( j(op2(e22,e21)) = op1(j(e22),j(e21)) )
          & ( j(op2(e22,e22)) = op1(j(e22),j(e22)) )
          & ( j(op2(e22,e23)) = op1(j(e22),j(e23)) )
          & ( j(op2(e22,e24)) = op1(j(e22),j(e24)) )
          & ( j(op2(e23,e20)) = op1(j(e23),j(e20)) )
          & ( j(op2(e23,e21)) = op1(j(e23),j(e21)) )
          & ( j(op2(e23,e22)) = op1(j(e23),j(e22)) )
          & ( j(op2(e23,e23)) = op1(j(e23),j(e23)) )
          & ( j(op2(e23,e24)) = op1(j(e23),j(e24)) )
          & ( j(op2(e24,e20)) = op1(j(e24),j(e20)) )
          & ( j(op2(e24,e21)) = op1(j(e24),j(e21)) )
          & ( j(op2(e24,e22)) = op1(j(e24),j(e22)) )
          & ( j(op2(e24,e23)) = op1(j(e24),j(e23)) )
          & ( j(op2(e24,e24)) = op1(j(e24),j(e24)) )
          & ( h(j(e20)) = e20 )
          & ( h(j(e21)) = e21 )
          & ( h(j(e22)) = e22 )
          & ( h(j(e23)) = e23 )
          & ( h(j(e24)) = e24 )
          & ( j(h(e10)) = e10 )
          & ( j(h(e11)) = e11 )
          & ( j(h(e12)) = e12 )
          & ( j(h(e13)) = e13 )
          & ( j(h(e14)) = e14 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

tff(f_255,axiom,
    ( ( op2(e20,e20) = e20 )
    & ( op2(e20,e21) = e21 )
    & ( op2(e20,e22) = e22 )
    & ( op2(e20,e23) = e23 )
    & ( op2(e20,e24) = e24 )
    & ( op2(e21,e20) = e21 )
    & ( op2(e21,e21) = e24 )
    & ( op2(e21,e22) = e23 )
    & ( op2(e21,e23) = e20 )
    & ( op2(e21,e24) = e22 )
    & ( op2(e22,e20) = e22 )
    & ( op2(e22,e21) = e20 )
    & ( op2(e22,e22) = e24 )
    & ( op2(e22,e23) = e21 )
    & ( op2(e22,e24) = e23 )
    & ( op2(e23,e20) = e23 )
    & ( op2(e23,e21) = e22 )
    & ( op2(e23,e22) = e20 )
    & ( op2(e23,e23) = e24 )
    & ( op2(e23,e24) = e21 )
    & ( op2(e24,e20) = e24 )
    & ( op2(e24,e21) = e23 )
    & ( op2(e24,e22) = e21 )
    & ( op2(e24,e23) = e22 )
    & ( op2(e24,e24) = e20 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).

tff(c_10,plain,
    e13 != e11,
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_104,plain,
    op1(e13,e13) = e11,
    inference(cnfTransformation,[status(thm)],[f_206]) ).

tff(c_324,plain,
    ( ( h(e13) = e24 )
    | ( h(e13) = e23 )
    | ( h(e13) = e22 )
    | ( h(e13) = e21 )
    | ( h(e13) = e20 ) ),
    inference(cnfTransformation,[status(thm)],[f_476]) ).

tff(c_1913,plain,
    h(e13) = e20,
    inference(splitLeft,[status(thm)],[c_324]) ).

tff(c_194,plain,
    j(h(e13)) = e13,
    inference(cnfTransformation,[status(thm)],[f_476]) ).

tff(c_1919,plain,
    j(e20) = e13,
    inference(demodulation,[status(thm),theory(equality)],[c_1913,c_194]) ).

tff(c_190,plain,
    op2(e20,e20) = e20,
    inference(cnfTransformation,[status(thm)],[f_255]) ).

tff(c_260,plain,
    op1(j(e20),j(e20)) = j(op2(e20,e20)),
    inference(cnfTransformation,[status(thm)],[f_476]) ).

tff(c_331,plain,
    op1(j(e20),j(e20)) = j(e20),
    inference(demodulation,[status(thm),theory(equality)],[c_190,c_260]) ).

tff(c_2074,plain,
    e13 = e11,
    inference(demodulation,[status(thm),theory(equality)],[c_104,c_1919,c_1919,c_1919,c_331]) ).

tff(c_2075,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_10,c_2074]) ).

tff(c_2077,plain,
    h(e13) != e20,
    inference(splitRight,[status(thm)],[c_324]) ).

tff(c_326,plain,
    ( ( h(e12) = e24 )
    | ( h(e12) = e23 )
    | ( h(e12) = e22 )
    | ( h(e12) = e21 )
    | ( h(e12) = e20 ) ),
    inference(cnfTransformation,[status(thm)],[f_476]) ).

tff(c_2127,plain,
    h(e12) = e20,
    inference(splitLeft,[status(thm)],[c_326]) ).

tff(c_116,plain,
    op1(e12,e12) = e13,
    inference(cnfTransformation,[status(thm)],[f_206]) ).

tff(c_286,plain,
    op2(h(e12),h(e12)) = h(op1(e12,e12)),
    inference(cnfTransformation,[status(thm)],[f_476]) ).

tff(c_368,plain,
    op2(h(e12),h(e12)) = h(e13),
    inference(demodulation,[status(thm),theory(equality)],[c_116,c_286]) ).

tff(c_2134,plain,
    op2(e20,e20) = h(e13),
    inference(demodulation,[status(thm),theory(equality)],[c_2127,c_2127,c_368]) ).

tff(c_2137,plain,
    h(e13) = e20,
    inference(demodulation,[status(thm),theory(equality)],[c_190,c_2134]) ).

tff(c_2139,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2077,c_2137]) ).

tff(c_2141,plain,
    h(e12) != e20,
    inference(splitRight,[status(thm)],[c_326]) ).

tff(c_92,plain,
    op1(e14,e14) = e12,
    inference(cnfTransformation,[status(thm)],[f_206]) ).

tff(c_328,plain,
    ( ( h(e11) = e24 )
    | ( h(e11) = e23 )
    | ( h(e11) = e22 )
    | ( h(e11) = e21 )
    | ( h(e11) = e20 ) ),
    inference(cnfTransformation,[status(thm)],[f_476]) ).

tff(c_597,plain,
    h(e11) = e20,
    inference(splitLeft,[status(thm)],[c_328]) ).

tff(c_198,plain,
    j(h(e11)) = e11,
    inference(cnfTransformation,[status(thm)],[f_476]) ).

tff(c_598,plain,
    j(e20) = e11,
    inference(demodulation,[status(thm),theory(equality)],[c_597,c_198]) ).

tff(c_818,plain,
    h(e13) = e20,
    inference(splitLeft,[status(thm)],[c_324]) ).

tff(c_825,plain,
    j(e20) = e13,
    inference(demodulation,[status(thm),theory(equality)],[c_818,c_194]) ).

tff(c_830,plain,
    e13 = e11,
    inference(demodulation,[status(thm),theory(equality)],[c_598,c_825]) ).

tff(c_832,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_10,c_830]) ).

tff(c_834,plain,
    h(e13) != e20,
    inference(splitRight,[status(thm)],[c_324]) ).

tff(c_322,plain,
    ( ( h(e14) = e24 )
    | ( h(e14) = e23 )
    | ( h(e14) = e22 )
    | ( h(e14) = e21 )
    | ( h(e14) = e20 ) ),
    inference(cnfTransformation,[status(thm)],[f_476]) ).

tff(c_867,plain,
    h(e14) = e20,
    inference(splitLeft,[status(thm)],[c_322]) ).

tff(c_122,plain,
    op1(e11,e14) = e13,
    inference(cnfTransformation,[status(thm)],[f_206]) ).

tff(c_292,plain,
    op2(h(e11),h(e14)) = h(op1(e11,e14)),
    inference(cnfTransformation,[status(thm)],[f_476]) ).

tff(c_365,plain,
    op2(h(e11),h(e14)) = h(e13),
    inference(demodulation,[status(thm),theory(equality)],[c_122,c_292]) ).

tff(c_839,plain,
    op2(e20,h(e14)) = h(e13),
    inference(demodulation,[status(thm),theory(equality)],[c_597,c_365]) ).

tff(c_869,plain,
    op2(e20,e20) = h(e13),
    inference(demodulation,[status(thm),theory(equality)],[c_867,c_839]) ).

tff(c_879,plain,
    h(e13) = e20,
    inference(demodulation,[status(thm),theory(equality)],[c_190,c_869]) ).

tff(c_881,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_834,c_879]) ).

tff(c_883,plain,
    h(e14) != e20,
    inference(splitRight,[status(thm)],[c_322]) ).

tff(c_128,plain,
    op1(e11,e11) = e14,
    inference(cnfTransformation,[status(thm)],[f_206]) ).

tff(c_298,plain,
    op2(h(e11),h(e11)) = h(op1(e11,e11)),
    inference(cnfTransformation,[status(thm)],[f_476]) ).

tff(c_362,plain,
    op2(h(e11),h(e11)) = h(e14),
    inference(demodulation,[status(thm),theory(equality)],[c_128,c_298]) ).

tff(c_888,plain,
    h(e14) = e20,
    inference(demodulation,[status(thm),theory(equality)],[c_190,c_597,c_597,c_362]) ).

tff(c_889,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_883,c_888]) ).

tff(c_891,plain,
    h(e11) != e20,
    inference(splitRight,[status(thm)],[c_328]) ).

tff(c_1030,plain,
    h(e13) = e20,
    inference(splitLeft,[status(thm)],[c_324]) ).

tff(c_274,plain,
    op2(h(e13),h(e13)) = h(op1(e13,e13)),
    inference(cnfTransformation,[status(thm)],[f_476]) ).

tff(c_374,plain,
    op2(h(e13),h(e13)) = h(e11),
    inference(demodulation,[status(thm),theory(equality)],[c_104,c_274]) ).

tff(c_1032,plain,
    op2(e20,e20) = h(e11),
    inference(demodulation,[status(thm),theory(equality)],[c_1030,c_1030,c_374]) ).

tff(c_1035,plain,
    h(e11) = e20,
    inference(demodulation,[status(thm),theory(equality)],[c_190,c_1032]) ).

tff(c_1037,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_891,c_1035]) ).

tff(c_1039,plain,
    h(e13) != e20,
    inference(splitRight,[status(thm)],[c_324]) ).

tff(c_1427,plain,
    h(e12) = e20,
    inference(splitLeft,[status(thm)],[c_326]) ).

tff(c_1457,plain,
    op2(e20,e20) = h(e13),
    inference(demodulation,[status(thm),theory(equality)],[c_1427,c_1427,c_368]) ).

tff(c_1463,plain,
    h(e13) = e20,
    inference(demodulation,[status(thm),theory(equality)],[c_190,c_1457]) ).

tff(c_1465,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1039,c_1463]) ).

tff(c_1467,plain,
    h(e12) != e20,
    inference(splitRight,[status(thm)],[c_326]) ).

tff(c_142,plain,
    op2(e24,e24) = e20,
    inference(cnfTransformation,[status(thm)],[f_255]) ).

tff(c_166,plain,
    op2(e22,e22) = e24,
    inference(cnfTransformation,[status(thm)],[f_255]) ).

tff(c_154,plain,
    op2(e23,e23) = e24,
    inference(cnfTransformation,[status(thm)],[f_255]) ).

tff(c_178,plain,
    op2(e21,e21) = e24,
    inference(cnfTransformation,[status(thm)],[f_255]) ).

tff(c_14,plain,
    e14 != e10,
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_320,plain,
    ( ( j(e20) = e14 )
    | ( j(e20) = e13 )
    | ( j(e20) = e12 )
    | ( j(e20) = e11 )
    | ( j(e20) = e10 ) ),
    inference(cnfTransformation,[status(thm)],[f_476]) ).

tff(c_908,plain,
    j(e20) = e10,
    inference(splitLeft,[status(thm)],[c_320]) ).

tff(c_987,plain,
    h(e14) = e20,
    inference(splitLeft,[status(thm)],[c_322]) ).

tff(c_192,plain,
    j(h(e14)) = e14,
    inference(cnfTransformation,[status(thm)],[f_476]) ).

tff(c_991,plain,
    j(e20) = e14,
    inference(demodulation,[status(thm),theory(equality)],[c_987,c_192]) ).

tff(c_993,plain,
    e14 = e10,
    inference(demodulation,[status(thm),theory(equality)],[c_908,c_991]) ).

tff(c_995,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_14,c_993]) ).

tff(c_997,plain,
    h(e14) != e20,
    inference(splitRight,[status(thm)],[c_322]) ).

tff(c_890,plain,
    ( ( h(e11) = e21 )
    | ( h(e11) = e22 )
    | ( h(e11) = e23 )
    | ( h(e11) = e24 ) ),
    inference(splitRight,[status(thm)],[c_328]) ).

tff(c_1245,plain,
    h(e11) = e24,
    inference(splitLeft,[status(thm)],[c_890]) ).

tff(c_1248,plain,
    op2(e24,e24) = h(e14),
    inference(demodulation,[status(thm),theory(equality)],[c_1245,c_1245,c_362]) ).

tff(c_1260,plain,
    h(e14) = e20,
    inference(demodulation,[status(thm),theory(equality)],[c_142,c_1248]) ).

tff(c_1262,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_997,c_1260]) ).

tff(c_1263,plain,
    ( ( h(e11) = e23 )
    | ( h(e11) = e22 )
    | ( h(e11) = e21 ) ),
    inference(splitRight,[status(thm)],[c_890]) ).

tff(c_1265,plain,
    h(e11) = e21,
    inference(splitLeft,[status(thm)],[c_1263]) ).

tff(c_1269,plain,
    op2(e21,e21) = h(e14),
    inference(demodulation,[status(thm),theory(equality)],[c_1265,c_1265,c_362]) ).

tff(c_1281,plain,
    h(e14) = e24,
    inference(demodulation,[status(thm),theory(equality)],[c_178,c_1269]) ).

tff(c_262,plain,
    op2(h(e14),h(e14)) = h(op1(e14,e14)),
    inference(cnfTransformation,[status(thm)],[f_476]) ).

tff(c_380,plain,
    op2(h(e14),h(e14)) = h(e12),
    inference(demodulation,[status(thm),theory(equality)],[c_92,c_262]) ).

tff(c_1291,plain,
    op2(e24,e24) = h(e12),
    inference(demodulation,[status(thm),theory(equality)],[c_1281,c_1281,c_380]) ).

tff(c_1297,plain,
    h(e12) = e20,
    inference(demodulation,[status(thm),theory(equality)],[c_142,c_1291]) ).

tff(c_1345,plain,
    op2(e20,e20) = h(e13),
    inference(demodulation,[status(thm),theory(equality)],[c_1297,c_1297,c_368]) ).

tff(c_1349,plain,
    h(e13) = e20,
    inference(demodulation,[status(thm),theory(equality)],[c_190,c_1345]) ).

tff(c_1351,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1039,c_1349]) ).

tff(c_1352,plain,
    ( ( h(e11) = e22 )
    | ( h(e11) = e23 ) ),
    inference(splitRight,[status(thm)],[c_1263]) ).

tff(c_1354,plain,
    h(e11) = e23,
    inference(splitLeft,[status(thm)],[c_1352]) ).

tff(c_1359,plain,
    op2(e23,e23) = h(e14),
    inference(demodulation,[status(thm),theory(equality)],[c_1354,c_1354,c_362]) ).

tff(c_1371,plain,
    h(e14) = e24,
    inference(demodulation,[status(thm),theory(equality)],[c_154,c_1359]) ).

tff(c_1381,plain,
    op2(e24,e24) = h(e12),
    inference(demodulation,[status(thm),theory(equality)],[c_1371,c_1371,c_380]) ).

tff(c_1387,plain,
    h(e12) = e20,
    inference(demodulation,[status(thm),theory(equality)],[c_142,c_1381]) ).

tff(c_1418,plain,
    op2(e20,e20) = h(e13),
    inference(demodulation,[status(thm),theory(equality)],[c_1387,c_1387,c_368]) ).

tff(c_1422,plain,
    h(e13) = e20,
    inference(demodulation,[status(thm),theory(equality)],[c_190,c_1418]) ).

tff(c_1424,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1039,c_1422]) ).

tff(c_1425,plain,
    h(e11) = e22,
    inference(splitRight,[status(thm)],[c_1352]) ).

tff(c_1473,plain,
    op2(e22,e22) = h(e14),
    inference(demodulation,[status(thm),theory(equality)],[c_1425,c_1425,c_362]) ).

tff(c_1485,plain,
    h(e14) = e24,
    inference(demodulation,[status(thm),theory(equality)],[c_166,c_1473]) ).

tff(c_1495,plain,
    op2(e24,e24) = h(e12),
    inference(demodulation,[status(thm),theory(equality)],[c_1485,c_1485,c_380]) ).

tff(c_1501,plain,
    h(e12) = e20,
    inference(demodulation,[status(thm),theory(equality)],[c_142,c_1495]) ).

tff(c_1503,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1467,c_1501]) ).

tff(c_1505,plain,
    j(e20) != e10,
    inference(splitRight,[status(thm)],[c_320]) ).

tff(c_140,plain,
    op1(e10,e10) = e10,
    inference(cnfTransformation,[status(thm)],[f_206]) ).

tff(c_312,plain,
    ( ( j(e24) = e14 )
    | ( j(e24) = e13 )
    | ( j(e24) = e12 )
    | ( j(e24) = e11 )
    | ( j(e24) = e10 ) ),
    inference(cnfTransformation,[status(thm)],[f_476]) ).

tff(c_1798,plain,
    j(e24) = e10,
    inference(splitLeft,[status(thm)],[c_312]) ).

tff(c_212,plain,
    op1(j(e24),j(e24)) = j(op2(e24,e24)),
    inference(cnfTransformation,[status(thm)],[f_476]) ).

tff(c_355,plain,
    op1(j(e24),j(e24)) = j(e20),
    inference(demodulation,[status(thm),theory(equality)],[c_142,c_212]) ).

tff(c_1856,plain,
    j(e20) = e10,
    inference(demodulation,[status(thm),theory(equality)],[c_140,c_1798,c_1798,c_355]) ).

tff(c_1857,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1505,c_1856]) ).

tff(c_1858,plain,
    ( ( j(e24) = e11 )
    | ( j(e24) = e12 )
    | ( j(e24) = e13 )
    | ( j(e24) = e14 ) ),
    inference(splitRight,[status(thm)],[c_312]) ).

tff(c_2258,plain,
    j(e24) = e14,
    inference(splitLeft,[status(thm)],[c_1858]) ).

tff(c_2269,plain,
    op1(e14,e14) = j(e20),
    inference(demodulation,[status(thm),theory(equality)],[c_2258,c_2258,c_355]) ).

tff(c_2273,plain,
    j(e20) = e12,
    inference(demodulation,[status(thm),theory(equality)],[c_92,c_2269]) ).

tff(c_210,plain,
    h(j(e20)) = e20,
    inference(cnfTransformation,[status(thm)],[f_476]) ).

tff(c_2289,plain,
    h(e12) = e20,
    inference(demodulation,[status(thm),theory(equality)],[c_2273,c_210]) ).

tff(c_2291,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2141,c_2289]) ).

tff(c_2293,plain,
    j(e24) != e14,
    inference(splitRight,[status(thm)],[c_1858]) ).

tff(c_4,plain,
    e14 != e12,
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_1591,plain,
    h(e14) = e20,
    inference(splitLeft,[status(thm)],[c_322]) ).

tff(c_1594,plain,
    j(e20) = e14,
    inference(demodulation,[status(thm),theory(equality)],[c_1591,c_192]) ).

tff(c_1626,plain,
    e14 = e12,
    inference(demodulation,[status(thm),theory(equality)],[c_1594,c_92,c_1594,c_1594,c_331]) ).

tff(c_1627,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_4,c_1626]) ).

tff(c_1629,plain,
    h(e14) != e20,
    inference(splitRight,[status(thm)],[c_322]) ).

tff(c_2238,plain,
    h(e11) = e24,
    inference(splitLeft,[status(thm)],[c_890]) ).

tff(c_2240,plain,
    op2(e24,e24) = h(e14),
    inference(demodulation,[status(thm),theory(equality)],[c_2238,c_2238,c_362]) ).

tff(c_2253,plain,
    h(e14) = e20,
    inference(demodulation,[status(thm),theory(equality)],[c_142,c_2240]) ).

tff(c_2255,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1629,c_2253]) ).

tff(c_2256,plain,
    ( ( h(e11) = e23 )
    | ( h(e11) = e22 )
    | ( h(e11) = e21 ) ),
    inference(splitRight,[status(thm)],[c_890]) ).

tff(c_2294,plain,
    h(e11) = e21,
    inference(splitLeft,[status(thm)],[c_2256]) ).

tff(c_2297,plain,
    op2(e21,e21) = h(e14),
    inference(demodulation,[status(thm),theory(equality)],[c_2294,c_2294,c_362]) ).

tff(c_2310,plain,
    h(e14) = e24,
    inference(demodulation,[status(thm),theory(equality)],[c_178,c_2297]) ).

tff(c_2318,plain,
    op2(e24,e24) = h(e12),
    inference(demodulation,[status(thm),theory(equality)],[c_2310,c_2310,c_380]) ).

tff(c_2324,plain,
    h(e12) = e20,
    inference(demodulation,[status(thm),theory(equality)],[c_142,c_2318]) ).

tff(c_2326,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2141,c_2324]) ).

tff(c_2327,plain,
    ( ( h(e11) = e22 )
    | ( h(e11) = e23 ) ),
    inference(splitRight,[status(thm)],[c_2256]) ).

tff(c_2329,plain,
    h(e11) = e23,
    inference(splitLeft,[status(thm)],[c_2327]) ).

tff(c_2345,plain,
    j(e23) = e11,
    inference(demodulation,[status(thm),theory(equality)],[c_2329,c_198]) ).

tff(c_224,plain,
    op1(j(e23),j(e23)) = j(op2(e23,e23)),
    inference(cnfTransformation,[status(thm)],[f_476]) ).

tff(c_349,plain,
    op1(j(e23),j(e23)) = j(e24),
    inference(demodulation,[status(thm),theory(equality)],[c_154,c_224]) ).

tff(c_2351,plain,
    op1(e11,e11) = j(e24),
    inference(demodulation,[status(thm),theory(equality)],[c_2345,c_2345,c_349]) ).

tff(c_2365,plain,
    j(e24) = e14,
    inference(demodulation,[status(thm),theory(equality)],[c_128,c_2351]) ).

tff(c_2367,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2293,c_2365]) ).

tff(c_2368,plain,
    h(e11) = e22,
    inference(splitRight,[status(thm)],[c_2327]) ).

tff(c_2385,plain,
    j(e22) = e11,
    inference(demodulation,[status(thm),theory(equality)],[c_2368,c_198]) ).

tff(c_236,plain,
    op1(j(e22),j(e22)) = j(op2(e22,e22)),
    inference(cnfTransformation,[status(thm)],[f_476]) ).

tff(c_343,plain,
    op1(j(e22),j(e22)) = j(e24),
    inference(demodulation,[status(thm),theory(equality)],[c_166,c_236]) ).

tff(c_2404,plain,
    op1(e11,e11) = j(e24),
    inference(demodulation,[status(thm),theory(equality)],[c_2385,c_2385,c_343]) ).

tff(c_2406,plain,
    j(e24) = e14,
    inference(demodulation,[status(thm),theory(equality)],[c_128,c_2404]) ).

tff(c_2408,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2293,c_2406]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : ALG082+1 : TPTP v8.1.2. Released v2.7.0.
% 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
% 0.15/0.35  % Computer : n028.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu Aug  3 20:42:24 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 8.24/2.99  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.65/3.01  
% 8.65/3.01  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.65/3.06  
% 8.65/3.06  Inference rules
% 8.65/3.06  ----------------------
% 8.65/3.06  #Ref     : 0
% 8.65/3.06  #Sup     : 614
% 8.65/3.06  #Fact    : 0
% 8.65/3.06  #Define  : 0
% 8.65/3.06  #Split   : 35
% 8.65/3.06  #Chain   : 0
% 8.65/3.06  #Close   : 0
% 8.65/3.06  
% 8.65/3.06  Ordering : KBO
% 8.65/3.06  
% 8.65/3.06  Simplification rules
% 8.65/3.06  ----------------------
% 8.65/3.06  #Subsume      : 32
% 8.65/3.06  #Demod        : 819
% 8.65/3.06  #Tautology    : 669
% 8.65/3.06  #SimpNegUnit  : 39
% 8.65/3.06  #BackRed      : 450
% 8.65/3.06  
% 8.65/3.06  #Partial instantiations: 0
% 8.65/3.06  #Strategies tried      : 1
% 8.65/3.06  
% 8.65/3.06  Timing (in seconds)
% 8.65/3.06  ----------------------
% 8.65/3.07  Preprocessing        : 0.65
% 8.65/3.07  Parsing              : 0.34
% 8.65/3.07  CNF conversion       : 0.03
% 8.65/3.07  Main loop            : 1.25
% 8.65/3.07  Inferencing          : 0.32
% 8.65/3.07  Reduction            : 0.51
% 8.65/3.07  Demodulation         : 0.36
% 8.65/3.07  BG Simplification    : 0.04
% 8.65/3.07  Subsumption          : 0.25
% 8.65/3.07  Abstraction          : 0.03
% 8.65/3.07  MUC search           : 0.00
% 8.65/3.07  Cooper               : 0.00
% 8.65/3.07  Total                : 1.99
% 8.65/3.07  Index Insertion      : 0.00
% 8.65/3.07  Index Deletion       : 0.00
% 8.65/3.07  Index Matching       : 0.00
% 8.65/3.07  BG Taut test         : 0.00
%------------------------------------------------------------------------------