TSTP Solution File: LCL219-3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : LCL219-3 : 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/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 : n007.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 10:47:42 EDT 2023

% Result   : Unsatisfiable 199.96s 183.25s
% Output   : CNFRefutation 200.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   16
% Syntax   : Number of formulae    :  102 (  42 unt;   7 typ;   0 def)
%            Number of atoms       :  163 (   3 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  139 (  71   ~;  68   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   5 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   5   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :  223 (; 223   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ theorem > axiom > or > implies > #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(axiom,type,
    axiom: $i > $o ).

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

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

tff(f_56,axiom,
    ! [X,Y] : ( implies(X,Y) = or(not(X),Y) ),
    file(unknown,unknown) ).

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_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_54,axiom,
    ! [A,B,C] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
    file(unknown,unknown) ).

tff(f_77,axiom,
    ~ theorem(implies(implies(implies(p,q),q),or(p,q))),
    file(unknown,unknown) ).

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_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_129,plain,
    ! [A_40,B_41,C_42] : axiom(implies(or(A_40,or(B_41,C_42)),or(B_41,or(A_40,C_42)))),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_142,plain,
    ! [X_12,B_41,Y_13] : axiom(implies(or(not(X_12),or(B_41,Y_13)),or(B_41,implies(X_12,Y_13)))),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_129]) ).

tff(c_456,plain,
    ! [X_92,B_93,Y_94] : axiom(implies(implies(X_92,or(B_93,Y_94)),or(B_93,implies(X_92,Y_94)))),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_142]) ).

tff(c_39,plain,
    ! [Y_25,X_26] :
      ( ~ theorem(Y_25)
      | ~ theorem(implies(Y_25,X_26))
      | theorem(X_26) ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_43,plain,
    ! [Y_25,X_26] :
      ( ~ theorem(Y_25)
      | theorem(X_26)
      | ~ axiom(implies(Y_25,X_26)) ),
    inference(resolution,[status(thm)],[c_14,c_39]) ).

tff(c_467,plain,
    ! [X_92,B_93,Y_94] :
      ( ~ theorem(implies(X_92,or(B_93,Y_94)))
      | theorem(or(B_93,implies(X_92,Y_94))) ),
    inference(resolution,[status(thm)],[c_456,c_43]) ).

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_52,plain,
    ! [Y_30,X_31] :
      ( ~ theorem(Y_30)
      | theorem(X_31)
      | ~ axiom(implies(Y_30,X_31)) ),
    inference(resolution,[status(thm)],[c_14,c_39]) ).

tff(c_72,plain,
    ! [A_2,B_3] :
      ( ~ theorem(A_2)
      | theorem(or(B_3,A_2)) ),
    inference(resolution,[status(thm)],[c_4,c_52]) ).

tff(c_380,plain,
    ! [A_80,B_81,C_82] :
      ( ~ theorem(or(A_80,or(B_81,C_82)))
      | theorem(or(B_81,or(A_80,C_82))) ),
    inference(resolution,[status(thm)],[c_129,c_43]) ).

tff(c_506,plain,
    ! [B_104,B_105,C_106] :
      ( theorem(or(B_104,or(B_105,C_106)))
      | ~ theorem(or(B_104,C_106)) ),
    inference(resolution,[status(thm)],[c_72,c_380]) ).

tff(c_521,plain,
    ! [X_12,B_105,C_106] :
      ( theorem(implies(X_12,or(B_105,C_106)))
      | ~ theorem(or(not(X_12),C_106)) ),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_506]) ).

tff(c_668,plain,
    ! [X_119,B_120,C_121] :
      ( theorem(implies(X_119,or(B_120,C_121)))
      | ~ theorem(implies(X_119,C_121)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_521]) ).

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_868,plain,
    ! [X_139,B_140,C_141] :
      ( ~ theorem(X_139)
      | theorem(or(B_140,C_141))
      | ~ theorem(implies(X_139,C_141)) ),
    inference(resolution,[status(thm)],[c_668,c_16]) ).

tff(c_900,plain,
    ! [X_144,B_145,C_146] :
      ( ~ theorem(X_144)
      | theorem(or(B_145,C_146))
      | ~ axiom(implies(X_144,C_146)) ),
    inference(resolution,[status(thm)],[c_14,c_868]) ).

tff(c_1256,plain,
    ! [A_190,B_191,B_192] :
      ( ~ theorem(or(A_190,B_191))
      | theorem(or(B_192,or(B_191,A_190))) ),
    inference(resolution,[status(thm)],[c_6,c_900]) ).

tff(c_147,plain,
    ! [A_40,B_41,C_42] :
      ( ~ theorem(or(A_40,or(B_41,C_42)))
      | theorem(or(B_41,or(A_40,C_42))) ),
    inference(resolution,[status(thm)],[c_129,c_43]) ).

tff(c_1446,plain,
    ! [B_210,B_211,A_212] :
      ( theorem(or(B_210,or(B_211,A_212)))
      | ~ theorem(or(A_212,B_210)) ),
    inference(resolution,[status(thm)],[c_1256,c_147]) ).

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

tff(c_71,plain,
    ! [A_1] :
      ( ~ theorem(or(A_1,A_1))
      | theorem(A_1) ),
    inference(resolution,[status(thm)],[c_2,c_52]) ).

tff(c_1551,plain,
    ! [B_220,A_221] :
      ( theorem(or(B_220,A_221))
      | ~ theorem(or(A_221,or(B_220,A_221))) ),
    inference(resolution,[status(thm)],[c_1446,c_71]) ).

tff(c_1626,plain,
    ! [X_12,Y_13] :
      ( theorem(or(not(X_12),Y_13))
      | ~ theorem(or(Y_13,implies(X_12,Y_13))) ),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_1551]) ).

tff(c_1888,plain,
    ! [X_243,Y_244] :
      ( theorem(implies(X_243,Y_244))
      | ~ theorem(or(Y_244,implies(X_243,Y_244))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_1626]) ).

tff(c_2093,plain,
    ! [X_256,Y_257] :
      ( theorem(implies(X_256,Y_257))
      | ~ theorem(implies(X_256,or(Y_257,Y_257))) ),
    inference(resolution,[status(thm)],[c_467,c_1888]) ).

tff(c_2171,plain,
    ! [X_261,Y_262] :
      ( theorem(implies(X_261,Y_262))
      | ~ axiom(implies(X_261,or(Y_262,Y_262))) ),
    inference(resolution,[status(thm)],[c_14,c_2093]) ).

tff(c_2205,plain,
    ! [A_2] : theorem(implies(A_2,A_2)),
    inference(resolution,[status(thm)],[c_4,c_2171]) ).

tff(c_135,plain,
    ! [A_40,X_12,Y_13] : axiom(implies(or(A_40,implies(X_12,Y_13)),or(not(X_12),or(A_40,Y_13)))),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_129]) ).

tff(c_650,plain,
    ! [A_114,X_115,Y_116] : axiom(implies(or(A_114,implies(X_115,Y_116)),implies(X_115,or(A_114,Y_116)))),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_135]) ).

tff(c_1768,plain,
    ! [A_232,X_233,Y_234] :
      ( ~ theorem(or(A_232,implies(X_233,Y_234)))
      | theorem(implies(X_233,or(A_232,Y_234))) ),
    inference(resolution,[status(thm)],[c_650,c_43]) ).

tff(c_1839,plain,
    ! [X_12,X_233,Y_234] :
      ( ~ theorem(implies(X_12,implies(X_233,Y_234)))
      | theorem(implies(X_233,or(not(X_12),Y_234))) ),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_1768]) ).

tff(c_3607,plain,
    ! [X_309,X_310,Y_311] :
      ( ~ theorem(implies(X_309,implies(X_310,Y_311)))
      | theorem(implies(X_310,implies(X_309,Y_311))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_1839]) ).

tff(c_3648,plain,
    ! [X_310,Y_311] : theorem(implies(X_310,implies(implies(X_310,Y_311),Y_311))),
    inference(resolution,[status(thm)],[c_2205,c_3607]) ).

tff(c_102,plain,
    ! [A_36,B_37,C_38] : axiom(implies(implies(A_36,B_37),implies(or(C_38,A_36),or(C_38,B_37)))),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_108,plain,
    ! [Y_13,B_37,X_12] : axiom(implies(implies(Y_13,B_37),implies(implies(X_12,Y_13),or(not(X_12),B_37)))),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_102]) ).

tff(c_305,plain,
    ! [Y_66,B_67,X_68] : axiom(implies(implies(Y_66,B_67),implies(implies(X_68,Y_66),implies(X_68,B_67)))),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_108]) ).

tff(c_1987,plain,
    ! [Y_245,B_246,X_247] :
      ( ~ theorem(implies(Y_245,B_246))
      | theorem(implies(implies(X_247,Y_245),implies(X_247,B_246))) ),
    inference(resolution,[status(thm)],[c_305,c_43]) ).

tff(c_2551,plain,
    ! [X_280,Y_281,B_282] :
      ( ~ theorem(implies(X_280,Y_281))
      | theorem(implies(X_280,B_282))
      | ~ theorem(implies(Y_281,B_282)) ),
    inference(resolution,[status(thm)],[c_1987,c_16]) ).

tff(c_6155,plain,
    ! [X_459,B_460,Y_461] :
      ( theorem(implies(X_459,B_460))
      | ~ theorem(implies(Y_461,B_460))
      | ~ axiom(implies(X_459,Y_461)) ),
    inference(resolution,[status(thm)],[c_14,c_2551]) ).

tff(c_15957,plain,
    ! [X_860,B_861,Y_862] :
      ( theorem(implies(X_860,B_861))
      | ~ axiom(implies(X_860,Y_862))
      | ~ axiom(implies(Y_862,B_861)) ),
    inference(resolution,[status(thm)],[c_14,c_6155]) ).

tff(c_17094,plain,
    ! [A_889,B_890,B_891] :
      ( theorem(implies(A_889,B_890))
      | ~ axiom(implies(or(B_891,A_889),B_890)) ),
    inference(resolution,[status(thm)],[c_4,c_15957]) ).

tff(c_17130,plain,
    ! [B_892,A_893] : theorem(implies(B_892,or(B_892,A_893))),
    inference(resolution,[status(thm)],[c_6,c_17094]) ).

tff(c_1997,plain,
    ! [X_247,Y_245,B_246] :
      ( ~ theorem(implies(X_247,Y_245))
      | theorem(implies(X_247,B_246))
      | ~ theorem(implies(Y_245,B_246)) ),
    inference(resolution,[status(thm)],[c_1987,c_16]) ).

tff(c_48136,plain,
    ! [B_1744,B_1745,A_1746] :
      ( theorem(implies(B_1744,B_1745))
      | ~ theorem(implies(or(B_1744,A_1746),B_1745)) ),
    inference(resolution,[status(thm)],[c_17130,c_1997]) ).

tff(c_149029,plain,
    ! [B_3506,A_3507,Y_3508] : theorem(implies(B_3506,implies(implies(or(B_3506,A_3507),Y_3508),Y_3508))),
    inference(resolution,[status(thm)],[c_3648,c_48136]) ).

tff(c_44,plain,
    ! [A_27,B_28] : axiom(implies(or(A_27,B_28),or(B_28,A_27))),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_47,plain,
    ! [X_12,Y_13] : axiom(implies(implies(X_12,Y_13),or(Y_13,not(X_12)))),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_44]) ).

tff(c_22,plain,
    ! [X_21,Y_22] : ( or(not(X_21),Y_22) = implies(X_21,Y_22) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_32,plain,
    ! [Y_22,X_21] : axiom(implies(Y_22,implies(X_21,Y_22))),
    inference(superposition,[status(thm),theory(equality)],[c_22,c_4]) ).

tff(c_16000,plain,
    ! [Y_863,B_864,X_865] :
      ( theorem(implies(Y_863,B_864))
      | ~ axiom(implies(implies(X_865,Y_863),B_864)) ),
    inference(resolution,[status(thm)],[c_32,c_15957]) ).

tff(c_16215,plain,
    ! [Y_870,B_871,X_872] : theorem(implies(Y_870,or(B_871,implies(X_872,Y_870)))),
    inference(resolution,[status(thm)],[c_4,c_16000]) ).

tff(c_1344,plain,
    ! [X_199,B_200,Y_201] :
      ( ~ theorem(implies(X_199,or(B_200,Y_201)))
      | theorem(or(B_200,implies(X_199,Y_201))) ),
    inference(resolution,[status(thm)],[c_456,c_43]) ).

tff(c_1374,plain,
    ! [X_199,Y_201] :
      ( theorem(implies(X_199,Y_201))
      | ~ theorem(implies(X_199,or(implies(X_199,Y_201),Y_201))) ),
    inference(resolution,[status(thm)],[c_1344,c_71]) ).

tff(c_16331,plain,
    ! [Y_873,X_874] : theorem(implies(Y_873,implies(X_874,Y_873))),
    inference(resolution,[status(thm)],[c_16215,c_1374]) ).

tff(c_1861,plain,
    ! [X_12,X_233,Y_234] :
      ( ~ theorem(implies(X_12,implies(X_233,Y_234)))
      | theorem(implies(X_233,implies(X_12,Y_234))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_1839]) ).

tff(c_16428,plain,
    ! [X_875,Y_876] : theorem(implies(X_875,implies(Y_876,Y_876))),
    inference(resolution,[status(thm)],[c_16331,c_1861]) ).

tff(c_2147,plain,
    ! [A_258,B_259,C_260] :
      ( ~ theorem(implies(A_258,B_259))
      | theorem(implies(or(C_260,A_258),or(C_260,B_259))) ),
    inference(resolution,[status(thm)],[c_102,c_43]) ).

tff(c_2300,plain,
    ! [C_269,A_270,B_271] :
      ( ~ theorem(or(C_269,A_270))
      | theorem(or(C_269,B_271))
      | ~ theorem(implies(A_270,B_271)) ),
    inference(resolution,[status(thm)],[c_2147,c_16]) ).

tff(c_2392,plain,
    ! [B_3,B_271,A_2] :
      ( theorem(or(B_3,B_271))
      | ~ theorem(implies(A_2,B_271))
      | ~ theorem(A_2) ),
    inference(resolution,[status(thm)],[c_72,c_2300]) ).

tff(c_16537,plain,
    ! [B_3,Y_876,X_875] :
      ( theorem(or(B_3,implies(Y_876,Y_876)))
      | ~ theorem(X_875) ),
    inference(resolution,[status(thm)],[c_16428,c_2392]) ).

tff(c_18161,plain,
    ! [X_875] : ~ theorem(X_875),
    inference(splitLeft,[status(thm)],[c_16537]) ).

tff(c_17527,plain,
    ! [A_904,B_905,B_906] : theorem(implies(A_904,or(B_905,or(B_906,A_904)))),
    inference(resolution,[status(thm)],[c_4,c_17094]) ).

tff(c_17796,plain,
    ! [A_909,B_910] : theorem(implies(A_909,or(B_910,A_909))),
    inference(resolution,[status(thm)],[c_17527,c_1374]) ).

tff(c_69,plain,
    ! [A_4,B_5] :
      ( ~ theorem(or(A_4,B_5))
      | theorem(or(B_5,A_4)) ),
    inference(resolution,[status(thm)],[c_6,c_52]) ).

tff(c_4856,plain,
    ! [X_390,Y_391,B_392] :
      ( theorem(or(implies(X_390,Y_391),B_392))
      | ~ theorem(implies(X_390,or(B_392,Y_391))) ),
    inference(resolution,[status(thm)],[c_1344,c_69]) ).

tff(c_661,plain,
    ! [A_114,X_115,Y_116] :
      ( ~ theorem(or(A_114,implies(X_115,Y_116)))
      | theorem(implies(X_115,or(A_114,Y_116))) ),
    inference(resolution,[status(thm)],[c_650,c_43]) ).

tff(c_4905,plain,
    ! [X_115,X_390,Y_391,Y_116] :
      ( theorem(implies(X_115,or(implies(X_390,Y_391),Y_116)))
      | ~ theorem(implies(X_390,or(implies(X_115,Y_116),Y_391))) ),
    inference(resolution,[status(thm)],[c_4856,c_661]) ).

tff(c_17889,plain,
    ! [X_115,A_909,Y_116] : theorem(implies(X_115,or(implies(A_909,A_909),Y_116))),
    inference(resolution,[status(thm)],[c_17796,c_4905]) ).

tff(c_18745,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_18161,c_17889]) ).

tff(c_18747,plain,
    ! [B_921,Y_922] : theorem(or(B_921,implies(Y_922,Y_922))),
    inference(splitRight,[status(thm)],[c_16537]) ).

tff(c_1972,plain,
    ! [X_92,Y_94] :
      ( theorem(implies(X_92,Y_94))
      | ~ theorem(implies(X_92,or(Y_94,Y_94))) ),
    inference(resolution,[status(thm)],[c_467,c_1888]) ).

tff(c_2773,plain,
    ! [B_289,A_290] :
      ( theorem(implies(or(B_289,A_290),B_289))
      | ~ theorem(implies(A_290,B_289)) ),
    inference(resolution,[status(thm)],[c_2147,c_1972]) ).

tff(c_2799,plain,
    ! [B_289,A_290] :
      ( ~ theorem(or(B_289,A_290))
      | theorem(B_289)
      | ~ theorem(implies(A_290,B_289)) ),
    inference(resolution,[status(thm)],[c_2773,c_16]) ).

tff(c_19295,plain,
    ! [B_945,Y_946] :
      ( theorem(B_945)
      | ~ theorem(implies(implies(Y_946,Y_946),B_945)) ),
    inference(resolution,[status(thm)],[c_18747,c_2799]) ).

tff(c_19798,plain,
    ! [B_953,Y_954] :
      ( theorem(B_953)
      | ~ axiom(implies(implies(Y_954,Y_954),B_953)) ),
    inference(resolution,[status(thm)],[c_14,c_19295]) ).

tff(c_19845,plain,
    ! [Y_955] : theorem(or(Y_955,not(Y_955))),
    inference(resolution,[status(thm)],[c_47,c_19798]) ).

tff(c_2168,plain,
    ! [C_260,A_258,B_259] :
      ( ~ theorem(or(C_260,A_258))
      | theorem(or(C_260,B_259))
      | ~ theorem(implies(A_258,B_259)) ),
    inference(resolution,[status(thm)],[c_2147,c_16]) ).

tff(c_19861,plain,
    ! [Y_955,B_259] :
      ( theorem(or(Y_955,B_259))
      | ~ theorem(implies(not(Y_955),B_259)) ),
    inference(resolution,[status(thm)],[c_19845,c_2168]) ).

tff(c_149150,plain,
    ! [Y_955,A_3507,Y_3508] : theorem(or(Y_955,implies(implies(or(not(Y_955),A_3507),Y_3508),Y_3508))),
    inference(resolution,[status(thm)],[c_149029,c_19861]) ).

tff(c_254746,plain,
    ! [Y_4731,A_4732,Y_4733] : theorem(or(Y_4731,implies(implies(implies(Y_4731,A_4732),Y_4733),Y_4733))),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_149150]) ).

tff(c_254819,plain,
    ! [Y_4731,A_4732,Y_4733] : theorem(implies(implies(implies(Y_4731,A_4732),Y_4733),or(Y_4731,Y_4733))),
    inference(resolution,[status(thm)],[c_254746,c_661]) ).

tff(c_18,plain,
    ~ theorem(implies(implies(implies(p,q),q),or(p,q))),
    inference(cnfTransformation,[status(thm)],[f_77]) ).

tff(c_337390,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_254819,c_18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : LCL219-3 : TPTP v8.1.2. Released v2.3.0.
% 0.00/0.15  % 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
% 0.18/0.36  % Computer : n007.cluster.edu
% 0.18/0.36  % Model    : x86_64 x86_64
% 0.18/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.36  % Memory   : 8042.1875MB
% 0.18/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.36  % CPULimit : 300
% 0.18/0.36  % WCLimit  : 300
% 0.18/0.36  % DateTime : Thu Aug  3 13:47:08 EDT 2023
% 0.18/0.37  % CPUTime  : 
% 199.96/183.25  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 199.98/183.26  
% 199.98/183.26  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 200.17/183.31  
% 200.17/183.31  Inference rules
% 200.17/183.31  ----------------------
% 200.17/183.31  #Ref     : 0
% 200.17/183.31  #Sup     : 84281
% 200.17/183.31  #Fact    : 0
% 200.17/183.31  #Define  : 0
% 200.17/183.31  #Split   : 5
% 200.17/183.31  #Chain   : 0
% 200.17/183.31  #Close   : 0
% 200.17/183.31  
% 200.17/183.31  Ordering : KBO
% 200.17/183.31  
% 200.17/183.31  Simplification rules
% 200.17/183.31  ----------------------
% 200.17/183.31  #Subsume      : 15284
% 200.17/183.31  #Demod        : 18201
% 200.17/183.31  #Tautology    : 15484
% 200.17/183.31  #SimpNegUnit  : 606
% 200.17/183.31  #BackRed      : 205
% 200.17/183.31  
% 200.17/183.31  #Partial instantiations: 0
% 200.17/183.31  #Strategies tried      : 1
% 200.17/183.31  
% 200.17/183.31  Timing (in seconds)
% 200.17/183.31  ----------------------
% 200.17/183.32  Preprocessing        : 0.42
% 200.17/183.32  Parsing              : 0.23
% 200.17/183.32  CNF conversion       : 0.02
% 200.17/183.32  Main loop            : 181.79
% 200.17/183.32  Inferencing          : 8.38
% 200.17/183.32  Reduction            : 70.63
% 200.17/183.32  Demodulation         : 54.85
% 200.17/183.32  BG Simplification    : 0.36
% 200.17/183.32  Subsumption          : 90.52
% 200.17/183.32  Abstraction          : 0.57
% 200.17/183.32  MUC search           : 0.00
% 200.17/183.32  Cooper               : 0.00
% 200.17/183.32  Total                : 182.28
% 200.17/183.32  Index Insertion      : 0.00
% 200.17/183.32  Index Deletion       : 0.00
% 200.17/183.32  Index Matching       : 0.00
% 200.17/183.32  BG Taut test         : 0.00
%------------------------------------------------------------------------------