TSTP Solution File: LCL088-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : LCL088-1 : 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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n018.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 10:47:20 EDT 2023

% Result   : Unsatisfiable 5.76s 2.47s
% Output   : CNFRefutation 6.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   99 (  64 unt;   4 typ;   0 def)
%            Number of atoms       :  132 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   86 (  49   ~;  37   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   2   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-1 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :  270 (; 270   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ is_a_theorem > implies > #nlpp > b > a

%Foreground sorts:

%Background operators:

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

tff(is_a_theorem,type,
    is_a_theorem: $i > $o ).

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

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

tff(f_35,axiom,
    ! [P,R,S,Q,T] : is_a_theorem(implies(implies(implies(P,Q),implies(R,S)),implies(T,implies(implies(S,P),implies(R,P))))),
    file(unknown,unknown) ).

tff(f_33,axiom,
    ! [X,Y] :
      ( ~ is_a_theorem(implies(X,Y))
      | ~ is_a_theorem(X)
      | is_a_theorem(Y) ),
    file(unknown,unknown) ).

tff(f_37,axiom,
    ~ is_a_theorem(implies(implies(implies(a,b),a),a)),
    file(unknown,unknown) ).

tff(c_4,plain,
    ! [S_5,T_7,P_3,R_4,Q_6] : is_a_theorem(implies(implies(implies(P_3,Q_6),implies(R_4,S_5)),implies(T_7,implies(implies(S_5,P_3),implies(R_4,P_3))))),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_8,plain,
    ! [P_14,Q_13,S_11,T_10,R_12] : is_a_theorem(implies(implies(implies(P_14,Q_13),implies(R_12,S_11)),implies(T_10,implies(implies(S_11,P_14),implies(R_12,P_14))))),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_2,plain,
    ! [Y_2,X_1] :
      ( is_a_theorem(Y_2)
      | ~ is_a_theorem(X_1)
      | ~ is_a_theorem(implies(X_1,Y_2)) ),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_13,plain,
    ! [R_18,T_16,P_19,Q_15,S_17] :
      ( is_a_theorem(implies(T_16,implies(implies(S_17,P_19),implies(R_18,P_19))))
      | ~ is_a_theorem(implies(implies(P_19,Q_15),implies(R_18,S_17))) ),
    inference(resolution,[status(thm)],[c_8,c_2]) ).

tff(c_17,plain,
    ! [T_20,P_25,Q_24,S_21,T_22,R_23] : is_a_theorem(implies(T_22,implies(implies(implies(implies(S_21,P_25),implies(R_23,P_25)),implies(P_25,Q_24)),implies(T_20,implies(P_25,Q_24))))),
    inference(resolution,[status(thm)],[c_4,c_13]) ).

tff(c_25,plain,
    ! [T_20,P_25,Q_24,S_21,T_22,R_23] :
      ( is_a_theorem(implies(implies(implies(implies(S_21,P_25),implies(R_23,P_25)),implies(P_25,Q_24)),implies(T_20,implies(P_25,Q_24))))
      | ~ is_a_theorem(T_22) ),
    inference(resolution,[status(thm)],[c_17,c_2]) ).

tff(c_26,plain,
    ! [T_22] : ~ is_a_theorem(T_22),
    inference(splitLeft,[status(thm)],[c_25]) ).

tff(c_16,plain,
    ! [S_5,T_7,T_16,P_3,R_4,Q_6] : is_a_theorem(implies(T_16,implies(implies(implies(implies(S_5,P_3),implies(R_4,P_3)),implies(P_3,Q_6)),implies(T_7,implies(P_3,Q_6))))),
    inference(resolution,[status(thm)],[c_4,c_13]) ).

tff(c_31,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_26,c_16]) ).

tff(c_32,plain,
    ! [T_20,P_25,Q_24,S_21,R_23] : is_a_theorem(implies(implies(implies(implies(S_21,P_25),implies(R_23,P_25)),implies(P_25,Q_24)),implies(T_20,implies(P_25,Q_24)))),
    inference(splitRight,[status(thm)],[c_25]) ).

tff(c_33,plain,
    ! [R_26,T_28,P_29,S_27,Q_30] : is_a_theorem(implies(implies(implies(implies(S_27,P_29),implies(R_26,P_29)),implies(P_29,Q_30)),implies(T_28,implies(P_29,Q_30)))),
    inference(splitRight,[status(thm)],[c_25]) ).

tff(c_41,plain,
    ! [P_34,T_31,S_33,R_32,Q_35] :
      ( is_a_theorem(implies(T_31,implies(P_34,Q_35)))
      | ~ is_a_theorem(implies(implies(implies(S_33,P_34),implies(R_32,P_34)),implies(P_34,Q_35))) ),
    inference(resolution,[status(thm)],[c_33,c_2]) ).

tff(c_69,plain,
    ! [T_40,R_41,P_42] : is_a_theorem(implies(T_40,implies(implies(R_41,P_42),implies(P_42,implies(R_41,P_42))))),
    inference(resolution,[status(thm)],[c_32,c_41]) ).

tff(c_82,plain,
    ! [R_41,P_42,T_40] :
      ( is_a_theorem(implies(implies(R_41,P_42),implies(P_42,implies(R_41,P_42))))
      | ~ is_a_theorem(T_40) ),
    inference(resolution,[status(thm)],[c_69,c_2]) ).

tff(c_158,plain,
    ! [T_40] : ~ is_a_theorem(T_40),
    inference(splitLeft,[status(thm)],[c_82]) ).

tff(c_12,plain,
    ! [P_14,Q_13,S_11,T_10,R_12] :
      ( is_a_theorem(implies(T_10,implies(implies(S_11,P_14),implies(R_12,P_14))))
      | ~ is_a_theorem(implies(implies(P_14,Q_13),implies(R_12,S_11))) ),
    inference(resolution,[status(thm)],[c_8,c_2]) ).

tff(c_24,plain,
    ! [T_20,P_14,P_25,Q_24,S_21,T_10,R_23] : is_a_theorem(implies(T_10,implies(implies(implies(T_20,implies(P_25,Q_24)),P_14),implies(implies(implies(implies(S_21,P_25),implies(R_23,P_25)),implies(P_25,Q_24)),P_14)))),
    inference(resolution,[status(thm)],[c_17,c_12]) ).

tff(c_171,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_158,c_24]) ).

tff(c_203,plain,
    ! [R_65,P_66] : is_a_theorem(implies(implies(R_65,P_66),implies(P_66,implies(R_65,P_66)))),
    inference(splitRight,[status(thm)],[c_82]) ).

tff(c_237,plain,
    ! [T_69,R_70,P_71] : is_a_theorem(implies(T_69,implies(implies(implies(R_70,P_71),R_70),implies(P_71,R_70)))),
    inference(resolution,[status(thm)],[c_203,c_12]) ).

tff(c_258,plain,
    ! [R_70,P_71,T_69] :
      ( is_a_theorem(implies(implies(implies(R_70,P_71),R_70),implies(P_71,R_70)))
      | ~ is_a_theorem(T_69) ),
    inference(resolution,[status(thm)],[c_237,c_2]) ).

tff(c_337,plain,
    ! [T_69] : ~ is_a_theorem(T_69),
    inference(splitLeft,[status(thm)],[c_258]) ).

tff(c_215,plain,
    ! [T_10,R_65,P_66] : is_a_theorem(implies(T_10,implies(implies(implies(R_65,P_66),R_65),implies(P_66,R_65)))),
    inference(resolution,[status(thm)],[c_203,c_12]) ).

tff(c_356,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_337,c_215]) ).

tff(c_379,plain,
    ! [R_80,P_81] : is_a_theorem(implies(implies(implies(R_80,P_81),R_80),implies(P_81,R_80))),
    inference(splitRight,[status(thm)],[c_258]) ).

tff(c_40,plain,
    ! [R_26,T_28,P_29,S_27,Q_30] :
      ( is_a_theorem(implies(T_28,implies(P_29,Q_30)))
      | ~ is_a_theorem(implies(implies(implies(S_27,P_29),implies(R_26,P_29)),implies(P_29,Q_30))) ),
    inference(resolution,[status(thm)],[c_33,c_2]) ).

tff(c_403,plain,
    ! [T_82,P_83,R_84] : is_a_theorem(implies(T_82,implies(P_83,implies(R_84,P_83)))),
    inference(resolution,[status(thm)],[c_379,c_40]) ).

tff(c_424,plain,
    ! [P_83,R_84,T_82] :
      ( is_a_theorem(implies(P_83,implies(R_84,P_83)))
      | ~ is_a_theorem(T_82) ),
    inference(resolution,[status(thm)],[c_403,c_2]) ).

tff(c_425,plain,
    ! [T_82] : ~ is_a_theorem(T_82),
    inference(splitLeft,[status(thm)],[c_424]) ).

tff(c_397,plain,
    ! [T_28,P_81,R_26] : is_a_theorem(implies(T_28,implies(P_81,implies(R_26,P_81)))),
    inference(resolution,[status(thm)],[c_379,c_40]) ).

tff(c_443,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_425,c_397]) ).

tff(c_460,plain,
    ! [P_91,R_92] : is_a_theorem(implies(P_91,implies(R_92,P_91))),
    inference(splitRight,[status(thm)],[c_424]) ).

tff(c_894,plain,
    ! [T_132,P_133,Q_134,R_135] : is_a_theorem(implies(T_132,implies(implies(implies(P_133,Q_134),P_133),implies(R_135,P_133)))),
    inference(resolution,[status(thm)],[c_460,c_12]) ).

tff(c_928,plain,
    ! [P_133,Q_134,R_135,T_132] :
      ( is_a_theorem(implies(implies(implies(P_133,Q_134),P_133),implies(R_135,P_133)))
      | ~ is_a_theorem(T_132) ),
    inference(resolution,[status(thm)],[c_894,c_2]) ).

tff(c_1450,plain,
    ! [T_132] : ~ is_a_theorem(T_132),
    inference(splitLeft,[status(thm)],[c_928]) ).

tff(c_444,plain,
    ! [P_83,R_84] : is_a_theorem(implies(P_83,implies(R_84,P_83))),
    inference(splitRight,[status(thm)],[c_424]) ).

tff(c_859,plain,
    ! [T_128,R_129,P_130,P_131] : is_a_theorem(implies(T_128,implies(implies(implies(R_129,P_130),P_131),implies(P_130,P_131)))),
    inference(resolution,[status(thm)],[c_403,c_12]) ).

tff(c_893,plain,
    ! [R_129,P_130,P_131,T_128] :
      ( is_a_theorem(implies(implies(implies(R_129,P_130),P_131),implies(P_130,P_131)))
      | ~ is_a_theorem(T_128) ),
    inference(resolution,[status(thm)],[c_859,c_2]) ).

tff(c_1036,plain,
    ! [T_128] : ~ is_a_theorem(T_128),
    inference(splitLeft,[status(thm)],[c_893]) ).

tff(c_55,plain,
    ! [T_36,T_37,P_38,R_39] : is_a_theorem(implies(T_36,implies(T_37,implies(implies(T_37,P_38),implies(R_39,P_38))))),
    inference(resolution,[status(thm)],[c_4,c_41]) ).

tff(c_68,plain,
    ! [T_37,P_38,R_39,T_36] :
      ( is_a_theorem(implies(T_37,implies(implies(T_37,P_38),implies(R_39,P_38))))
      | ~ is_a_theorem(T_36) ),
    inference(resolution,[status(thm)],[c_55,c_2]) ).

tff(c_83,plain,
    ! [T_36] : ~ is_a_theorem(T_36),
    inference(splitLeft,[status(thm)],[c_68]) ).

tff(c_51,plain,
    ! [T_31,R_23,P_25] : is_a_theorem(implies(T_31,implies(implies(R_23,P_25),implies(P_25,implies(R_23,P_25))))),
    inference(resolution,[status(thm)],[c_32,c_41]) ).

tff(c_92,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_83,c_51]) ).

tff(c_94,plain,
    ! [T_43,P_44,R_45] : is_a_theorem(implies(T_43,implies(implies(T_43,P_44),implies(R_45,P_44)))),
    inference(splitRight,[status(thm)],[c_68]) ).

tff(c_103,plain,
    ! [T_46,P_47,R_48] :
      ( is_a_theorem(implies(implies(T_46,P_47),implies(R_48,P_47)))
      | ~ is_a_theorem(T_46) ),
    inference(resolution,[status(thm)],[c_94,c_2]) ).

tff(c_114,plain,
    ! [R_48,P_47,T_46] :
      ( is_a_theorem(implies(R_48,P_47))
      | ~ is_a_theorem(implies(T_46,P_47))
      | ~ is_a_theorem(T_46) ),
    inference(resolution,[status(thm)],[c_103,c_2]) ).

tff(c_654,plain,
    ! [R_110,P_111,R_112] :
      ( is_a_theorem(implies(R_110,implies(P_111,R_112)))
      | ~ is_a_theorem(implies(implies(R_112,P_111),R_112)) ),
    inference(resolution,[status(thm)],[c_379,c_114]) ).

tff(c_719,plain,
    ! [R_113,P_114,P_115,R_116] : is_a_theorem(implies(R_113,implies(P_114,implies(P_115,implies(R_116,P_115))))),
    inference(resolution,[status(thm)],[c_397,c_654]) ).

tff(c_396,plain,
    ! [R_48,P_81,R_80] :
      ( is_a_theorem(implies(R_48,implies(P_81,R_80)))
      | ~ is_a_theorem(implies(implies(R_80,P_81),R_80)) ),
    inference(resolution,[status(thm)],[c_379,c_114]) ).

tff(c_741,plain,
    ! [P_114,R_116,P_115,R_48,P_81] : is_a_theorem(implies(R_48,implies(P_81,implies(P_114,implies(P_115,implies(R_116,P_115)))))),
    inference(resolution,[status(thm)],[c_719,c_396]) ).

tff(c_1067,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1036,c_741]) ).

tff(c_1103,plain,
    ! [R_153,P_154,P_155] : is_a_theorem(implies(implies(implies(R_153,P_154),P_155),implies(P_154,P_155))),
    inference(splitRight,[status(thm)],[c_893]) ).

tff(c_1157,plain,
    ! [P_159,P_160,R_161] :
      ( is_a_theorem(implies(P_159,P_160))
      | ~ is_a_theorem(implies(implies(R_161,P_159),P_160)) ),
    inference(resolution,[status(thm)],[c_1103,c_2]) ).

tff(c_1284,plain,
    ! [P_162,R_163,R_164] : is_a_theorem(implies(P_162,implies(R_163,implies(R_164,P_162)))),
    inference(resolution,[status(thm)],[c_444,c_1157]) ).

tff(c_1137,plain,
    ! [P_154,P_155,R_153] :
      ( is_a_theorem(implies(P_154,P_155))
      | ~ is_a_theorem(implies(implies(R_153,P_154),P_155)) ),
    inference(resolution,[status(thm)],[c_1103,c_2]) ).

tff(c_1305,plain,
    ! [P_154,R_163,R_164,R_153] : is_a_theorem(implies(P_154,implies(R_163,implies(R_164,implies(R_153,P_154))))),
    inference(resolution,[status(thm)],[c_1284,c_1137]) ).

tff(c_1485,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1450,c_1305]) ).

tff(c_1486,plain,
    ! [P_133,Q_134,R_135] : is_a_theorem(implies(implies(implies(P_133,Q_134),P_133),implies(R_135,P_133))),
    inference(splitRight,[status(thm)],[c_928]) ).

tff(c_2086,plain,
    ! [R_204,S_205,T_206,P_207] : is_a_theorem(implies(implies(R_204,S_205),implies(T_206,implies(implies(S_205,P_207),implies(R_204,P_207))))),
    inference(resolution,[status(thm)],[c_4,c_1157]) ).

tff(c_3919,plain,
    ! [T_306,S_307,P_308,R_309] :
      ( is_a_theorem(implies(T_306,implies(implies(S_307,P_308),implies(R_309,P_308))))
      | ~ is_a_theorem(implies(R_309,S_307)) ),
    inference(resolution,[status(thm)],[c_2086,c_2]) ).

tff(c_3981,plain,
    ! [S_307,P_308,R_309,T_306] :
      ( is_a_theorem(implies(implies(S_307,P_308),implies(R_309,P_308)))
      | ~ is_a_theorem(T_306)
      | ~ is_a_theorem(implies(R_309,S_307)) ),
    inference(resolution,[status(thm)],[c_3919,c_2]) ).

tff(c_4261,plain,
    ! [T_306] : ~ is_a_theorem(T_306),
    inference(splitLeft,[status(thm)],[c_3981]) ).

tff(c_706,plain,
    ! [R_110,P_111,P_81,R_26] : is_a_theorem(implies(R_110,implies(P_111,implies(P_81,implies(R_26,P_81))))),
    inference(resolution,[status(thm)],[c_397,c_654]) ).

tff(c_357,plain,
    ! [R_70,P_71] : is_a_theorem(implies(implies(implies(R_70,P_71),R_70),implies(P_71,R_70))),
    inference(splitRight,[status(thm)],[c_258]) ).

tff(c_102,plain,
    ! [T_43,P_44,R_45] :
      ( is_a_theorem(implies(implies(T_43,P_44),implies(R_45,P_44)))
      | ~ is_a_theorem(T_43) ),
    inference(resolution,[status(thm)],[c_94,c_2]) ).

tff(c_129,plain,
    ! [R_56,P_57,T_58] :
      ( is_a_theorem(implies(R_56,P_57))
      | ~ is_a_theorem(implies(T_58,P_57))
      | ~ is_a_theorem(T_58) ),
    inference(resolution,[status(thm)],[c_103,c_2]) ).

tff(c_799,plain,
    ! [R_124,R_125,P_126,T_127] :
      ( is_a_theorem(implies(R_124,implies(R_125,P_126)))
      | ~ is_a_theorem(implies(T_127,P_126))
      | ~ is_a_theorem(T_127) ),
    inference(resolution,[status(thm)],[c_102,c_129]) ).

tff(c_3435,plain,
    ! [R_281,R_282,P_283,R_284] :
      ( is_a_theorem(implies(R_281,implies(R_282,implies(P_283,R_284))))
      | ~ is_a_theorem(implies(implies(R_284,P_283),R_284)) ),
    inference(resolution,[status(thm)],[c_357,c_799]) ).

tff(c_3566,plain,
    ! [R_26,R_281,R_282,P_283,P_111,P_81] : is_a_theorem(implies(R_281,implies(R_282,implies(P_283,implies(P_111,implies(P_81,implies(R_26,P_81))))))),
    inference(resolution,[status(thm)],[c_706,c_3435]) ).

tff(c_4328,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_4261,c_3566]) ).

tff(c_4330,plain,
    ! [S_335,P_336,R_337] :
      ( is_a_theorem(implies(implies(S_335,P_336),implies(R_337,P_336)))
      | ~ is_a_theorem(implies(R_337,S_335)) ),
    inference(splitRight,[status(thm)],[c_3981]) ).

tff(c_1487,plain,
    ! [P_175,Q_176,R_177] : is_a_theorem(implies(implies(implies(P_175,Q_176),P_175),implies(R_177,P_175))),
    inference(splitRight,[status(thm)],[c_928]) ).

tff(c_1523,plain,
    ! [R_177,P_175,Q_176] :
      ( is_a_theorem(implies(R_177,P_175))
      | ~ is_a_theorem(implies(implies(P_175,Q_176),P_175)) ),
    inference(resolution,[status(thm)],[c_1487,c_2]) ).

tff(c_4394,plain,
    ! [R_338,R_339,P_340] :
      ( is_a_theorem(implies(R_338,implies(R_339,P_340)))
      | ~ is_a_theorem(implies(R_339,implies(R_339,P_340))) ),
    inference(resolution,[status(thm)],[c_4330,c_1523]) ).

tff(c_4613,plain,
    ! [R_341,P_342,Q_343] : is_a_theorem(implies(R_341,implies(implies(implies(P_342,Q_343),P_342),P_342))),
    inference(resolution,[status(thm)],[c_1486,c_4394]) ).

tff(c_4687,plain,
    ! [P_342,Q_343,R_341] :
      ( is_a_theorem(implies(implies(implies(P_342,Q_343),P_342),P_342))
      | ~ is_a_theorem(R_341) ),
    inference(resolution,[status(thm)],[c_4613,c_2]) ).

tff(c_4905,plain,
    ! [R_341] : ~ is_a_theorem(R_341),
    inference(splitLeft,[status(thm)],[c_4687]) ).

tff(c_1524,plain,
    ! [R_178,P_179,Q_180] :
      ( is_a_theorem(implies(R_178,P_179))
      | ~ is_a_theorem(implies(implies(P_179,Q_180),P_179)) ),
    inference(resolution,[status(thm)],[c_1487,c_2]) ).

tff(c_1621,plain,
    ! [R_181,R_182] : is_a_theorem(implies(R_181,implies(R_182,R_182))),
    inference(resolution,[status(thm)],[c_1486,c_1524]) ).

tff(c_1777,plain,
    ! [R_184,P_185,R_186] : is_a_theorem(implies(R_184,implies(P_185,implies(R_186,R_186)))),
    inference(resolution,[status(thm)],[c_1621,c_396]) ).

tff(c_2790,plain,
    ! [T_262,R_263,P_264,P_265] : is_a_theorem(implies(T_262,implies(implies(implies(R_263,R_263),P_264),implies(P_265,P_264)))),
    inference(resolution,[status(thm)],[c_1777,c_12]) ).

tff(c_2843,plain,
    ! [R_263,P_264,P_265,T_262] :
      ( is_a_theorem(implies(implies(implies(R_263,R_263),P_264),implies(P_265,P_264)))
      | ~ is_a_theorem(T_262) ),
    inference(resolution,[status(thm)],[c_2790,c_2]) ).

tff(c_2845,plain,
    ! [T_262] : ~ is_a_theorem(T_262),
    inference(splitLeft,[status(thm)],[c_2843]) ).

tff(c_1820,plain,
    ! [T_10,R_186,P_14,P_185] : is_a_theorem(implies(T_10,implies(implies(implies(R_186,R_186),P_14),implies(P_185,P_14)))),
    inference(resolution,[status(thm)],[c_1777,c_12]) ).

tff(c_2899,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2845,c_1820]) ).

tff(c_2900,plain,
    ! [R_263,P_264,P_265] : is_a_theorem(implies(implies(implies(R_263,R_263),P_264),implies(P_265,P_264))),
    inference(splitRight,[status(thm)],[c_2843]) ).

tff(c_4550,plain,
    ! [R_338,R_263,P_264] : is_a_theorem(implies(R_338,implies(implies(implies(R_263,R_263),P_264),P_264))),
    inference(resolution,[status(thm)],[c_2900,c_4394]) ).

tff(c_4977,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_4905,c_4550]) ).

tff(c_4978,plain,
    ! [P_342,Q_343] : is_a_theorem(implies(implies(implies(P_342,Q_343),P_342),P_342)),
    inference(splitRight,[status(thm)],[c_4687]) ).

tff(c_6,plain,
    ~ is_a_theorem(implies(implies(implies(a,b),a),a)),
    inference(cnfTransformation,[status(thm)],[f_37]) ).

tff(c_5053,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_4978,c_6]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : LCL088-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.15  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.36  % Computer : n018.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 14:18:35 EDT 2023
% 0.14/0.37  % CPUTime  : 
% 5.76/2.47  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.76/2.48  
% 5.76/2.48  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.09/2.54  
% 6.09/2.54  Inference rules
% 6.09/2.54  ----------------------
% 6.09/2.54  #Ref     : 0
% 6.09/2.54  #Sup     : 1028
% 6.09/2.54  #Fact    : 0
% 6.09/2.54  #Define  : 0
% 6.09/2.54  #Split   : 17
% 6.09/2.54  #Chain   : 0
% 6.09/2.54  #Close   : 0
% 6.09/2.54  
% 6.09/2.54  Ordering : KBO
% 6.09/2.54  
% 6.09/2.54  Simplification rules
% 6.09/2.54  ----------------------
% 6.09/2.54  #Subsume      : 413
% 6.09/2.54  #Demod        : 406
% 6.09/2.54  #Tautology    : 407
% 6.09/2.54  #SimpNegUnit  : 577
% 6.09/2.54  #BackRed      : 343
% 6.09/2.54  
% 6.09/2.54  #Partial instantiations: 0
% 6.09/2.54  #Strategies tried      : 1
% 6.09/2.54  
% 6.09/2.54  Timing (in seconds)
% 6.09/2.54  ----------------------
% 6.09/2.54  Preprocessing        : 0.40
% 6.09/2.54  Parsing              : 0.22
% 6.09/2.54  CNF conversion       : 0.02
% 6.09/2.54  Main loop            : 0.97
% 6.09/2.54  Inferencing          : 0.34
% 6.09/2.54  Reduction            : 0.29
% 6.09/2.54  Demodulation         : 0.21
% 6.09/2.54  BG Simplification    : 0.03
% 6.09/2.54  Subsumption          : 0.23
% 6.09/2.54  Abstraction          : 0.03
% 6.09/2.54  MUC search           : 0.00
% 6.09/2.54  Cooper               : 0.00
% 6.09/2.54  Total                : 1.45
% 6.09/2.54  Index Insertion      : 0.00
% 6.09/2.54  Index Deletion       : 0.00
% 6.09/2.54  Index Matching       : 0.00
% 6.09/2.54  BG Taut test         : 0.00
%------------------------------------------------------------------------------