TSTP Solution File: LCL089-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : LCL089-1 : 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 : n022.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 8.25s 3.18s
% Output   : CNFRefutation 8.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   97 (  62 unt;   5 typ;   0 def)
%            Number of atoms       :  128 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   84 (  48   ~;  36   |;   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    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :  266 (; 266   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ is_a_theorem > implies > #nlpp > c > 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(c,type,
    c: $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(a,b),implies(implies(b,c),implies(a,c)))),
    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_345,plain,
    ! [T_69] : ~ is_a_theorem(T_69),
    inference(splitLeft,[status(thm)],[c_258]) ).

tff(c_39,plain,
    ! [R_26,T_28,P_29,S_27,Q_30,T_10] : is_a_theorem(implies(T_10,implies(implies(implies(P_29,Q_30),implies(implies(S_27,P_29),implies(R_26,P_29))),implies(T_28,implies(implies(S_27,P_29),implies(R_26,P_29)))))),
    inference(resolution,[status(thm)],[c_33,c_12]) ).

tff(c_365,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_345,c_39]) ).

tff(c_389,plain,
    ! [R_86,P_87] : is_a_theorem(implies(implies(implies(R_86,P_87),R_86),implies(P_87,R_86))),
    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_413,plain,
    ! [T_88,P_89,R_90] : is_a_theorem(implies(T_88,implies(P_89,implies(R_90,P_89)))),
    inference(resolution,[status(thm)],[c_389,c_40]) ).

tff(c_931,plain,
    ! [T_136,R_137,P_138,P_139] : is_a_theorem(implies(T_136,implies(implies(implies(R_137,P_138),P_139),implies(P_138,P_139)))),
    inference(resolution,[status(thm)],[c_413,c_12]) ).

tff(c_965,plain,
    ! [R_137,P_138,P_139,T_136] :
      ( is_a_theorem(implies(implies(implies(R_137,P_138),P_139),implies(P_138,P_139)))
      | ~ is_a_theorem(T_136) ),
    inference(resolution,[status(thm)],[c_931,c_2]) ).

tff(c_1002,plain,
    ! [T_136] : ~ is_a_theorem(T_136),
    inference(splitLeft,[status(thm)],[c_965]) ).

tff(c_407,plain,
    ! [T_28,P_87,R_26] : is_a_theorem(implies(T_28,implies(P_87,implies(R_26,P_87)))),
    inference(resolution,[status(thm)],[c_389,c_40]) ).

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_738,plain,
    ! [R_114,P_115,R_116] :
      ( is_a_theorem(implies(R_114,implies(P_115,R_116)))
      | ~ is_a_theorem(implies(implies(R_116,P_115),R_116)) ),
    inference(resolution,[status(thm)],[c_389,c_114]) ).

tff(c_820,plain,
    ! [R_120,P_121,P_122,R_123] : is_a_theorem(implies(R_120,implies(P_121,implies(P_122,implies(R_123,P_122))))),
    inference(resolution,[status(thm)],[c_407,c_738]) ).

tff(c_406,plain,
    ! [R_48,P_87,R_86] :
      ( is_a_theorem(implies(R_48,implies(P_87,R_86)))
      | ~ is_a_theorem(implies(implies(R_86,P_87),R_86)) ),
    inference(resolution,[status(thm)],[c_389,c_114]) ).

tff(c_844,plain,
    ! [P_87,P_122,P_121,R_123,R_48] : is_a_theorem(implies(R_48,implies(P_87,implies(P_121,implies(P_122,implies(R_123,P_122)))))),
    inference(resolution,[status(thm)],[c_820,c_406]) ).

tff(c_1032,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1002,c_844]) ).

tff(c_1035,plain,
    ! [R_145,P_146,P_147] : is_a_theorem(implies(implies(implies(R_145,P_146),P_147),implies(P_146,P_147))),
    inference(splitRight,[status(thm)],[c_965]) ).

tff(c_1070,plain,
    ! [P_148,P_149,R_150] :
      ( is_a_theorem(implies(P_148,P_149))
      | ~ is_a_theorem(implies(implies(R_150,P_148),P_149)) ),
    inference(resolution,[status(thm)],[c_1035,c_2]) ).

tff(c_1182,plain,
    ! [R_4,S_5,T_7,P_3] : is_a_theorem(implies(implies(R_4,S_5),implies(T_7,implies(implies(S_5,P_3),implies(R_4,P_3))))),
    inference(resolution,[status(thm)],[c_4,c_1070]) ).

tff(c_434,plain,
    ! [P_89,R_90,T_88] :
      ( is_a_theorem(implies(P_89,implies(R_90,P_89)))
      | ~ is_a_theorem(T_88) ),
    inference(resolution,[status(thm)],[c_413,c_2]) ).

tff(c_435,plain,
    ! [T_88] : ~ is_a_theorem(T_88),
    inference(splitLeft,[status(thm)],[c_434]) ).

tff(c_454,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_435,c_407]) ).

tff(c_478,plain,
    ! [P_91,R_92] : is_a_theorem(implies(P_91,implies(R_92,P_91))),
    inference(splitRight,[status(thm)],[c_434]) ).

tff(c_1385,plain,
    ! [T_168,P_169,Q_170,R_171] : is_a_theorem(implies(T_168,implies(implies(implies(P_169,Q_170),P_169),implies(R_171,P_169)))),
    inference(resolution,[status(thm)],[c_478,c_12]) ).

tff(c_1424,plain,
    ! [P_169,Q_170,R_171,T_168] :
      ( is_a_theorem(implies(implies(implies(P_169,Q_170),P_169),implies(R_171,P_169)))
      | ~ is_a_theorem(T_168) ),
    inference(resolution,[status(thm)],[c_1385,c_2]) ).

tff(c_1461,plain,
    ! [T_168] : ~ is_a_theorem(T_168),
    inference(splitLeft,[status(thm)],[c_1424]) ).

tff(c_496,plain,
    ! [T_10,P_14,Q_13,R_92] : is_a_theorem(implies(T_10,implies(implies(implies(P_14,Q_13),P_14),implies(R_92,P_14)))),
    inference(resolution,[status(thm)],[c_478,c_12]) ).

tff(c_1496,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1461,c_496]) ).

tff(c_1497,plain,
    ! [P_169,Q_170,R_171] : is_a_theorem(implies(implies(implies(P_169,Q_170),P_169),implies(R_171,P_169))),
    inference(splitRight,[status(thm)],[c_1424]) ).

tff(c_1931,plain,
    ! [R_198,S_199,T_200,P_201] : is_a_theorem(implies(implies(R_198,S_199),implies(T_200,implies(implies(S_199,P_201),implies(R_198,P_201))))),
    inference(resolution,[status(thm)],[c_4,c_1070]) ).

tff(c_3728,plain,
    ! [T_300,S_301,P_302,R_303] :
      ( is_a_theorem(implies(T_300,implies(implies(S_301,P_302),implies(R_303,P_302))))
      | ~ is_a_theorem(implies(R_303,S_301)) ),
    inference(resolution,[status(thm)],[c_1931,c_2]) ).

tff(c_3790,plain,
    ! [S_301,P_302,R_303,T_300] :
      ( is_a_theorem(implies(implies(S_301,P_302),implies(R_303,P_302)))
      | ~ is_a_theorem(T_300)
      | ~ is_a_theorem(implies(R_303,S_301)) ),
    inference(resolution,[status(thm)],[c_3728,c_2]) ).

tff(c_4236,plain,
    ! [T_300] : ~ is_a_theorem(T_300),
    inference(splitLeft,[status(thm)],[c_3790]) ).

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_157,plain,
    ! [S_5,R_56,T_7,P_3,R_4,Q_6] :
      ( is_a_theorem(implies(R_56,implies(T_7,implies(implies(S_5,P_3),implies(R_4,P_3)))))
      | ~ is_a_theorem(implies(implies(P_3,Q_6),implies(R_4,S_5))) ),
    inference(resolution,[status(thm)],[c_4,c_129]) ).

tff(c_493,plain,
    ! [R_56,R_92,T_7,P_3,Q_6] : is_a_theorem(implies(R_56,implies(T_7,implies(implies(implies(P_3,Q_6),P_3),implies(R_92,P_3))))),
    inference(resolution,[status(thm)],[c_478,c_157]) ).

tff(c_4304,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_4236,c_493]) ).

tff(c_4306,plain,
    ! [S_333,P_334,R_335] :
      ( is_a_theorem(implies(implies(S_333,P_334),implies(R_335,P_334)))
      | ~ is_a_theorem(implies(R_335,S_333)) ),
    inference(splitRight,[status(thm)],[c_3790]) ).

tff(c_1498,plain,
    ! [P_177,Q_178,R_179] : is_a_theorem(implies(implies(implies(P_177,Q_178),P_177),implies(R_179,P_177))),
    inference(splitRight,[status(thm)],[c_1424]) ).

tff(c_1534,plain,
    ! [R_179,P_177,Q_178] :
      ( is_a_theorem(implies(R_179,P_177))
      | ~ is_a_theorem(implies(implies(P_177,Q_178),P_177)) ),
    inference(resolution,[status(thm)],[c_1498,c_2]) ).

tff(c_4374,plain,
    ! [R_336,R_337,P_338] :
      ( is_a_theorem(implies(R_336,implies(R_337,P_338)))
      | ~ is_a_theorem(implies(R_337,implies(R_337,P_338))) ),
    inference(resolution,[status(thm)],[c_4306,c_1534]) ).

tff(c_4598,plain,
    ! [R_339,P_340,Q_341] : is_a_theorem(implies(R_339,implies(implies(implies(P_340,Q_341),P_340),P_340))),
    inference(resolution,[status(thm)],[c_1497,c_4374]) ).

tff(c_4672,plain,
    ! [P_340,Q_341,R_339] :
      ( is_a_theorem(implies(implies(implies(P_340,Q_341),P_340),P_340))
      | ~ is_a_theorem(R_339) ),
    inference(resolution,[status(thm)],[c_4598,c_2]) ).

tff(c_4966,plain,
    ! [R_339] : ~ is_a_theorem(R_339),
    inference(splitLeft,[status(thm)],[c_4672]) ).

tff(c_1535,plain,
    ! [R_180,P_181,Q_182] :
      ( is_a_theorem(implies(R_180,P_181))
      | ~ is_a_theorem(implies(implies(P_181,Q_182),P_181)) ),
    inference(resolution,[status(thm)],[c_1498,c_2]) ).

tff(c_1636,plain,
    ! [R_183,R_184] : is_a_theorem(implies(R_183,implies(R_184,R_184))),
    inference(resolution,[status(thm)],[c_1497,c_1535]) ).

tff(c_1794,plain,
    ! [R_186,P_187,R_188] : is_a_theorem(implies(R_186,implies(P_187,implies(R_188,R_188)))),
    inference(resolution,[status(thm)],[c_1636,c_406]) ).

tff(c_2753,plain,
    ! [T_252,R_253,P_254,P_255] : is_a_theorem(implies(T_252,implies(implies(implies(R_253,R_253),P_254),implies(P_255,P_254)))),
    inference(resolution,[status(thm)],[c_1794,c_12]) ).

tff(c_2806,plain,
    ! [R_253,P_254,P_255,T_252] :
      ( is_a_theorem(implies(implies(implies(R_253,R_253),P_254),implies(P_255,P_254)))
      | ~ is_a_theorem(T_252) ),
    inference(resolution,[status(thm)],[c_2753,c_2]) ).

tff(c_2807,plain,
    ! [T_252] : ~ is_a_theorem(T_252),
    inference(splitLeft,[status(thm)],[c_2806]) ).

tff(c_1837,plain,
    ! [T_10,R_188,P_14,P_187] : is_a_theorem(implies(T_10,implies(implies(implies(R_188,R_188),P_14),implies(P_187,P_14)))),
    inference(resolution,[status(thm)],[c_1794,c_12]) ).

tff(c_2860,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2807,c_1837]) ).

tff(c_2861,plain,
    ! [R_253,P_254,P_255] : is_a_theorem(implies(implies(implies(R_253,R_253),P_254),implies(P_255,P_254))),
    inference(splitRight,[status(thm)],[c_2806]) ).

tff(c_4538,plain,
    ! [R_336,R_253,P_254] : is_a_theorem(implies(R_336,implies(implies(implies(R_253,R_253),P_254),P_254))),
    inference(resolution,[status(thm)],[c_2861,c_4374]) ).

tff(c_5040,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_4966,c_4538]) ).

tff(c_5041,plain,
    ! [P_340,Q_341] : is_a_theorem(implies(implies(implies(P_340,Q_341),P_340),P_340)),
    inference(splitRight,[status(thm)],[c_4672]) ).

tff(c_6750,plain,
    ! [R_373,P_374,S_375] :
      ( is_a_theorem(implies(R_373,P_374))
      | ~ is_a_theorem(implies(S_375,P_374))
      | ~ is_a_theorem(implies(R_373,S_375)) ),
    inference(resolution,[status(thm)],[c_4306,c_2]) ).

tff(c_9037,plain,
    ! [R_433,P_434,Q_435] :
      ( is_a_theorem(implies(R_433,P_434))
      | ~ is_a_theorem(implies(R_433,implies(implies(P_434,Q_435),P_434))) ),
    inference(resolution,[status(thm)],[c_5041,c_6750]) ).

tff(c_9330,plain,
    ! [R_4,S_5,P_3] : is_a_theorem(implies(implies(R_4,S_5),implies(implies(S_5,P_3),implies(R_4,P_3)))),
    inference(resolution,[status(thm)],[c_1182,c_9037]) ).

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

tff(c_12756,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_9330,c_6]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : LCL089-1 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13  % 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
% 0.12/0.34  % Computer : n022.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu Aug  3 14:15:19 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 8.25/3.18  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.25/3.19  
% 8.25/3.19  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.47/3.25  
% 8.47/3.25  Inference rules
% 8.47/3.25  ----------------------
% 8.47/3.25  #Ref     : 0
% 8.47/3.25  #Sup     : 2656
% 8.47/3.25  #Fact    : 0
% 8.47/3.25  #Define  : 0
% 8.47/3.25  #Split   : 18
% 8.47/3.25  #Chain   : 0
% 8.47/3.25  #Close   : 0
% 8.47/3.25  
% 8.47/3.25  Ordering : KBO
% 8.47/3.25  
% 8.47/3.25  Simplification rules
% 8.47/3.25  ----------------------
% 8.47/3.25  #Subsume      : 934
% 8.47/3.25  #Demod        : 1053
% 8.47/3.25  #Tautology    : 1096
% 8.47/3.25  #SimpNegUnit  : 727
% 8.47/3.25  #BackRed      : 423
% 8.47/3.25  
% 8.47/3.25  #Partial instantiations: 0
% 8.47/3.25  #Strategies tried      : 1
% 8.47/3.25  
% 8.47/3.25  Timing (in seconds)
% 8.47/3.25  ----------------------
% 8.47/3.25  Preprocessing        : 0.43
% 8.72/3.25  Parsing              : 0.23
% 8.72/3.25  CNF conversion       : 0.02
% 8.72/3.25  Main loop            : 1.67
% 8.72/3.25  Inferencing          : 0.51
% 8.72/3.25  Reduction            : 0.52
% 8.72/3.25  Demodulation         : 0.41
% 8.72/3.25  BG Simplification    : 0.04
% 8.72/3.25  Subsumption          : 0.47
% 8.72/3.25  Abstraction          : 0.05
% 8.72/3.25  MUC search           : 0.00
% 8.72/3.25  Cooper               : 0.00
% 8.72/3.25  Total                : 2.18
% 8.72/3.25  Index Insertion      : 0.00
% 8.72/3.25  Index Deletion       : 0.00
% 8.72/3.25  Index Matching       : 0.00
% 8.72/3.25  BG Taut test         : 0.00
%------------------------------------------------------------------------------