TSTP Solution File: LCL454+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : LCL454+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n023.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 10:48:09 EDT 2023

% Result   : Theorem 13.20s 4.75s
% Output   : CNFRefutation 13.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :  112
% Syntax   : Number of formulae    :  171 (  46 unt;  92 typ;   0 def)
%            Number of atoms       :  120 (  16 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   75 (  34   ~;  28   |;   1   &)
%                                         (   7 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (   6   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :   34 (  32 usr;  32 prp; 0-2 aty)
%            Number of functors    :   60 (  60 usr;  55 con; 0-2 aty)
%            Number of variables   :   83 (;  83   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ is_a_theorem > or > implies > equiv > and > #nlpp > not > substitution_of_equivalents > r5 > r4 > r3 > r2 > r1 > or_3 > or_2 > or_1 > op_or > op_implies_or > op_implies_and > op_equiv > op_and > modus_tollens > modus_ponens > kn3 > kn2 > kn1 > implies_3 > implies_2 > implies_1 > equivalence_3 > equivalence_2 > equivalence_1 > cn3 > cn2 > cn1 > and_3 > and_2 > and_1 > #skF_33 > #skF_41 > #skF_52 > #skF_49 > #skF_20 > #skF_18 > #skF_17 > #skF_11 > #skF_31 > #skF_15 > #skF_25 > #skF_55 > #skF_38 > #skF_36 > #skF_54 > #skF_43 > #skF_19 > #skF_40 > #skF_48 > #skF_7 > #skF_37 > #skF_10 > #skF_16 > #skF_47 > #skF_26 > #skF_53 > #skF_14 > #skF_51 > #skF_5 > #skF_45 > #skF_46 > #skF_39 > #skF_6 > #skF_13 > #skF_2 > #skF_3 > #skF_1 > #skF_21 > #skF_9 > #skF_32 > #skF_50 > #skF_8 > #skF_30 > #skF_42 > #skF_4 > #skF_22 > #skF_29 > #skF_28 > #skF_35 > #skF_24 > #skF_27 > #skF_23 > #skF_44 > #skF_12 > #skF_34

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(implies_2,type,
    implies_2: $o ).

tff(r1,type,
    r1: $o ).

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

tff('#skF_33',type,
    '#skF_33': $i ).

tff('#skF_41',type,
    '#skF_41': $i ).

tff(r3,type,
    r3: $o ).

tff('#skF_52',type,
    '#skF_52': $i ).

tff(equivalence_2,type,
    equivalence_2: $o ).

tff('#skF_49',type,
    '#skF_49': $i ).

tff(and_2,type,
    and_2: $o ).

tff('#skF_20',type,
    '#skF_20': $i ).

tff(op_implies_or,type,
    op_implies_or: $o ).

tff('#skF_18',type,
    '#skF_18': $i ).

tff('#skF_17',type,
    '#skF_17': $i ).

tff(r5,type,
    r5: $o ).

tff('#skF_11',type,
    '#skF_11': $i ).

tff(kn3,type,
    kn3: $o ).

tff('#skF_31',type,
    '#skF_31': $i ).

tff('#skF_15',type,
    '#skF_15': $i ).

tff('#skF_25',type,
    '#skF_25': $i ).

tff(cn2,type,
    cn2: $o ).

tff('#skF_55',type,
    '#skF_55': $i ).

tff(r4,type,
    r4: $o ).

tff('#skF_38',type,
    '#skF_38': $i ).

tff('#skF_36',type,
    '#skF_36': $i ).

tff('#skF_54',type,
    '#skF_54': $i ).

tff('#skF_43',type,
    '#skF_43': $i ).

tff(op_and,type,
    op_and: $o ).

tff('#skF_19',type,
    '#skF_19': $i ).

tff('#skF_40',type,
    '#skF_40': $i ).

tff('#skF_48',type,
    '#skF_48': $i ).

tff('#skF_7',type,
    '#skF_7': $i ).

tff('#skF_37',type,
    '#skF_37': $i ).

tff(and_3,type,
    and_3: $o ).

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

tff(op_implies_and,type,
    op_implies_and: $o ).

tff(equivalence_1,type,
    equivalence_1: $o ).

tff('#skF_10',type,
    '#skF_10': $i ).

tff(kn2,type,
    kn2: $o ).

tff('#skF_16',type,
    '#skF_16': $i ).

tff(equivalence_3,type,
    equivalence_3: $o ).

tff(and_1,type,
    and_1: $o ).

tff('#skF_47',type,
    '#skF_47': $i ).

tff(cn1,type,
    cn1: $o ).

tff('#skF_26',type,
    '#skF_26': $i ).

tff('#skF_53',type,
    '#skF_53': $i ).

tff('#skF_14',type,
    '#skF_14': $i ).

tff('#skF_51',type,
    '#skF_51': $i ).

tff(or_1,type,
    or_1: $o ).

tff(implies_3,type,
    implies_3: $o ).

tff('#skF_5',type,
    '#skF_5': $i ).

tff('#skF_45',type,
    '#skF_45': $i ).

tff('#skF_46',type,
    '#skF_46': $i ).

tff('#skF_39',type,
    '#skF_39': $i ).

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

tff(modus_tollens,type,
    modus_tollens: $o ).

tff(r2,type,
    r2: $o ).

tff('#skF_6',type,
    '#skF_6': $i ).

tff('#skF_13',type,
    '#skF_13': $i ).

tff(not,type,
    not: $i > $i ).

tff('#skF_2',type,
    '#skF_2': $i ).

tff(modus_ponens,type,
    modus_ponens: $o ).

tff(op_or,type,
    op_or: $o ).

tff('#skF_3',type,
    '#skF_3': $i ).

tff(substitution_of_equivalents,type,
    substitution_of_equivalents: $o ).

tff('#skF_1',type,
    '#skF_1': $i ).

tff('#skF_21',type,
    '#skF_21': $i ).

tff('#skF_9',type,
    '#skF_9': $i ).

tff('#skF_32',type,
    '#skF_32': $i ).

tff(op_equiv,type,
    op_equiv: $o ).

tff('#skF_50',type,
    '#skF_50': $i ).

tff('#skF_8',type,
    '#skF_8': $i ).

tff('#skF_30',type,
    '#skF_30': $i ).

tff('#skF_42',type,
    '#skF_42': $i ).

tff(or_3,type,
    or_3: $o ).

tff('#skF_4',type,
    '#skF_4': $i ).

tff('#skF_22',type,
    '#skF_22': $i ).

tff(kn1,type,
    kn1: $o ).

tff('#skF_29',type,
    '#skF_29': $i ).

tff('#skF_28',type,
    '#skF_28': $i ).

tff('#skF_35',type,
    '#skF_35': $i ).

tff('#skF_24',type,
    '#skF_24': $i ).

tff('#skF_27',type,
    '#skF_27': $i ).

tff('#skF_23',type,
    '#skF_23': $i ).

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

tff(implies_1,type,
    implies_1: $o ).

tff('#skF_44',type,
    '#skF_44': $i ).

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

tff(cn3,type,
    cn3: $o ).

tff(or_2,type,
    or_2: $o ).

tff('#skF_12',type,
    '#skF_12': $i ).

tff('#skF_34',type,
    '#skF_34': $i ).

tff(f_244,axiom,
    op_or,
    file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_op_or) ).

tff(f_245,axiom,
    op_implies_and,
    file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_op_implies_and) ).

tff(f_206,axiom,
    ( op_implies_and
   => ! [X,Y] : ( implies(X,Y) = not(and(X,not(Y))) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).

tff(f_198,axiom,
    ( op_or
   => ! [X,Y] : ( or(X,Y) = not(and(not(X),not(Y))) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_or) ).

tff(f_256,axiom,
    and_3,
    file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_3) ).

tff(f_96,axiom,
    ( and_3
  <=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_3) ).

tff(f_252,axiom,
    implies_2,
    file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).

tff(f_80,axiom,
    ( implies_2
  <=> ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',implies_2) ).

tff(f_248,axiom,
    modus_ponens,
    file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).

tff(f_60,axiom,
    ( modus_ponens
  <=> ! [X,Y] :
        ( ( is_a_theorem(X)
          & is_a_theorem(implies(X,Y)) )
       => is_a_theorem(Y) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).

tff(f_125,axiom,
    ( kn1
  <=> ! [P] : is_a_theorem(implies(P,and(P,P))) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn1) ).

tff(f_270,axiom,
    op_and,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_and) ).

tff(f_269,axiom,
    op_implies_or,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_implies_or) ).

tff(f_210,axiom,
    ( op_implies_or
   => ! [X,Y] : ( implies(X,Y) = or(not(X),Y) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_or) ).

tff(f_202,axiom,
    ( op_and
   => ! [X,Y] : ( and(X,Y) = not(or(not(X),not(Y))) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_and) ).

tff(f_250,axiom,
    modus_tollens,
    file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_tollens) ).

tff(f_72,axiom,
    ( modus_tollens
  <=> ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_tollens) ).

tff(f_146,axiom,
    ( cn3
  <=> ! [P] : is_a_theorem(implies(implies(not(P),P),P)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',cn3) ).

tff(f_273,negated_conjecture,
    ~ r1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r1) ).

tff(f_151,axiom,
    ( r1
  <=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r1) ).

tff(c_122,plain,
    op_or,
    inference(cnfTransformation,[status(thm)],[f_244]) ).

tff(c_124,plain,
    op_implies_and,
    inference(cnfTransformation,[status(thm)],[f_245]) ).

tff(c_116,plain,
    ! [X_60,Y_61] :
      ( ( not(and(X_60,not(Y_61))) = implies(X_60,Y_61) )
      | ~ op_implies_and ),
    inference(cnfTransformation,[status(thm)],[f_206]) ).

tff(c_171,plain,
    ! [X_60,Y_61] : ( not(and(X_60,not(Y_61))) = implies(X_60,Y_61) ),
    inference(demodulation,[status(thm),theory(equality)],[c_124,c_116]) ).

tff(c_112,plain,
    ! [X_56,Y_57] :
      ( ( not(and(not(X_56),not(Y_57))) = or(X_56,Y_57) )
      | ~ op_or ),
    inference(cnfTransformation,[status(thm)],[f_198]) ).

tff(c_175,plain,
    ! [X_56,Y_57] : ( implies(not(X_56),Y_57) = or(X_56,Y_57) ),
    inference(demodulation,[status(thm),theory(equality)],[c_122,c_171,c_112]) ).

tff(c_1631,plain,
    ! [X_222,Y_223] : ( not(and(X_222,not(Y_223))) = implies(X_222,Y_223) ),
    inference(demodulation,[status(thm),theory(equality)],[c_124,c_116]) ).

tff(c_1649,plain,
    ! [X_222,Y_223,Y_57] : ( or(and(X_222,not(Y_223)),Y_57) = implies(implies(X_222,Y_223),Y_57) ),
    inference(superposition,[status(thm),theory(equality)],[c_1631,c_175]) ).

tff(c_1439,plain,
    ! [X_192,Y_193] : ( implies(not(X_192),Y_193) = or(X_192,Y_193) ),
    inference(demodulation,[status(thm),theory(equality)],[c_122,c_171,c_112]) ).

tff(c_142,plain,
    and_3,
    inference(cnfTransformation,[status(thm)],[f_256]) ).

tff(c_42,plain,
    ! [X_18,Y_19] :
      ( is_a_theorem(implies(X_18,implies(Y_19,and(X_18,Y_19))))
      | ~ and_3 ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_214,plain,
    ! [X_18,Y_19] : is_a_theorem(implies(X_18,implies(Y_19,and(X_18,Y_19)))),
    inference(demodulation,[status(thm),theory(equality)],[c_142,c_42]) ).

tff(c_134,plain,
    implies_2,
    inference(cnfTransformation,[status(thm)],[f_252]) ).

tff(c_26,plain,
    ! [X_9,Y_10] :
      ( is_a_theorem(implies(implies(X_9,implies(X_9,Y_10)),implies(X_9,Y_10)))
      | ~ implies_2 ),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_602,plain,
    ! [X_119,Y_120] : is_a_theorem(implies(implies(X_119,implies(X_119,Y_120)),implies(X_119,Y_120))),
    inference(demodulation,[status(thm),theory(equality)],[c_134,c_26]) ).

tff(c_128,plain,
    modus_ponens,
    inference(cnfTransformation,[status(thm)],[f_248]) ).

tff(c_2,plain,
    ! [Y_2,X_1] :
      ( is_a_theorem(Y_2)
      | ~ is_a_theorem(implies(X_1,Y_2))
      | ~ is_a_theorem(X_1)
      | ~ modus_ponens ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_255,plain,
    ! [Y_2,X_1] :
      ( is_a_theorem(Y_2)
      | ~ is_a_theorem(implies(X_1,Y_2))
      | ~ is_a_theorem(X_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).

tff(c_1314,plain,
    ! [X_179,Y_180] :
      ( is_a_theorem(implies(X_179,Y_180))
      | ~ is_a_theorem(implies(X_179,implies(X_179,Y_180))) ),
    inference(resolution,[status(thm)],[c_602,c_255]) ).

tff(c_1368,plain,
    ! [Y_19] : is_a_theorem(implies(Y_19,and(Y_19,Y_19))),
    inference(resolution,[status(thm)],[c_214,c_1314]) ).

tff(c_68,plain,
    ( kn1
    | ~ is_a_theorem(implies('#skF_33',and('#skF_33','#skF_33'))) ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_259,plain,
    ~ is_a_theorem(implies('#skF_33',and('#skF_33','#skF_33'))),
    inference(splitLeft,[status(thm)],[c_68]) ).

tff(c_1408,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1368,c_259]) ).

tff(c_1409,plain,
    kn1,
    inference(splitRight,[status(thm)],[c_68]) ).

tff(c_70,plain,
    ! [P_33] :
      ( is_a_theorem(implies(P_33,and(P_33,P_33)))
      | ~ kn1 ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_1411,plain,
    ~ kn1,
    inference(splitLeft,[status(thm)],[c_70]) ).

tff(c_1413,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1409,c_1411]) ).

tff(c_1414,plain,
    ! [P_33] : is_a_theorem(implies(P_33,and(P_33,P_33))),
    inference(splitRight,[status(thm)],[c_70]) ).

tff(c_1457,plain,
    ! [X_192] : is_a_theorem(or(X_192,and(not(X_192),not(X_192)))),
    inference(superposition,[status(thm),theory(equality)],[c_1439,c_1414]) ).

tff(c_160,plain,
    op_and,
    inference(cnfTransformation,[status(thm)],[f_270]) ).

tff(c_158,plain,
    op_implies_or,
    inference(cnfTransformation,[status(thm)],[f_269]) ).

tff(c_118,plain,
    ! [X_62,Y_63] :
      ( ( or(not(X_62),Y_63) = implies(X_62,Y_63) )
      | ~ op_implies_or ),
    inference(cnfTransformation,[status(thm)],[f_210]) ).

tff(c_169,plain,
    ! [X_62,Y_63] : ( or(not(X_62),Y_63) = implies(X_62,Y_63) ),
    inference(demodulation,[status(thm),theory(equality)],[c_158,c_118]) ).

tff(c_114,plain,
    ! [X_58,Y_59] :
      ( ( not(or(not(X_58),not(Y_59))) = and(X_58,Y_59) )
      | ~ op_and ),
    inference(cnfTransformation,[status(thm)],[f_202]) ).

tff(c_1662,plain,
    ! [X_224,Y_225] : ( not(implies(X_224,not(Y_225))) = and(X_224,Y_225) ),
    inference(demodulation,[status(thm),theory(equality)],[c_160,c_169,c_114]) ).

tff(c_1699,plain,
    ! [X_56,Y_225] : ( not(or(X_56,not(Y_225))) = and(not(X_56),Y_225) ),
    inference(superposition,[status(thm),theory(equality)],[c_175,c_1662]) ).

tff(c_130,plain,
    modus_tollens,
    inference(cnfTransformation,[status(thm)],[f_250]) ).

tff(c_18,plain,
    ! [Y_6,X_5] :
      ( is_a_theorem(implies(implies(not(Y_6),not(X_5)),implies(X_5,Y_6)))
      | ~ modus_tollens ),
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_1743,plain,
    ! [Y_229,X_230] : is_a_theorem(implies(or(Y_229,not(X_230)),implies(X_230,Y_229))),
    inference(demodulation,[status(thm),theory(equality)],[c_130,c_175,c_18]) ).

tff(c_1755,plain,
    ! [Y_57,X_56] : is_a_theorem(implies(or(Y_57,not(not(X_56))),or(X_56,Y_57))),
    inference(superposition,[status(thm),theory(equality)],[c_175,c_1743]) ).

tff(c_1503,plain,
    ! [Y_200,X_201] :
      ( is_a_theorem(Y_200)
      | ~ is_a_theorem(implies(X_201,Y_200))
      | ~ is_a_theorem(X_201) ),
    inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).

tff(c_2265,plain,
    ! [Y_275,X_276] :
      ( is_a_theorem(Y_275)
      | ~ is_a_theorem(or(X_276,Y_275))
      | ~ is_a_theorem(not(X_276)) ),
    inference(superposition,[status(thm),theory(equality)],[c_175,c_1503]) ).

tff(c_14111,plain,
    ! [Y_798,X_799] :
      ( is_a_theorem(Y_798)
      | ~ is_a_theorem(implies(X_799,Y_798))
      | ~ is_a_theorem(not(not(X_799))) ),
    inference(superposition,[status(thm),theory(equality)],[c_169,c_2265]) ).

tff(c_14173,plain,
    ! [X_56,Y_57] :
      ( is_a_theorem(or(X_56,Y_57))
      | ~ is_a_theorem(not(not(or(Y_57,not(not(X_56)))))) ),
    inference(resolution,[status(thm)],[c_1755,c_14111]) ).

tff(c_14300,plain,
    ! [X_800,Y_801] :
      ( is_a_theorem(or(X_800,Y_801))
      | ~ is_a_theorem(or(Y_801,X_800)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_175,c_171,c_1699,c_14173]) ).

tff(c_14384,plain,
    ! [X_192] : is_a_theorem(or(and(not(X_192),not(X_192)),X_192)),
    inference(resolution,[status(thm)],[c_1457,c_14300]) ).

tff(c_14471,plain,
    ! [X_192] : is_a_theorem(implies(or(X_192,X_192),X_192)),
    inference(demodulation,[status(thm),theory(equality)],[c_175,c_1649,c_14384]) ).

tff(c_88,plain,
    ( cn3
    | ~ is_a_theorem(implies(implies(not('#skF_44'),'#skF_44'),'#skF_44')) ),
    inference(cnfTransformation,[status(thm)],[f_146]) ).

tff(c_178,plain,
    ( cn3
    | ~ is_a_theorem(implies(or('#skF_44','#skF_44'),'#skF_44')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_175,c_88]) ).

tff(c_1479,plain,
    ~ is_a_theorem(implies(or('#skF_44','#skF_44'),'#skF_44')),
    inference(splitLeft,[status(thm)],[c_178]) ).

tff(c_14483,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_14471,c_1479]) ).

tff(c_14484,plain,
    cn3,
    inference(splitRight,[status(thm)],[c_178]) ).

tff(c_90,plain,
    ! [P_44] :
      ( is_a_theorem(implies(implies(not(P_44),P_44),P_44))
      | ~ cn3 ),
    inference(cnfTransformation,[status(thm)],[f_146]) ).

tff(c_177,plain,
    ! [P_44] :
      ( is_a_theorem(implies(or(P_44,P_44),P_44))
      | ~ cn3 ),
    inference(demodulation,[status(thm),theory(equality)],[c_175,c_90]) ).

tff(c_14487,plain,
    ! [P_44] : is_a_theorem(implies(or(P_44,P_44),P_44)),
    inference(demodulation,[status(thm),theory(equality)],[c_14484,c_177]) ).

tff(c_164,plain,
    ~ r1,
    inference(cnfTransformation,[status(thm)],[f_273]) ).

tff(c_92,plain,
    ( r1
    | ~ is_a_theorem(implies(or('#skF_45','#skF_45'),'#skF_45')) ),
    inference(cnfTransformation,[status(thm)],[f_151]) ).

tff(c_176,plain,
    ~ is_a_theorem(implies(or('#skF_45','#skF_45'),'#skF_45')),
    inference(negUnitSimplification,[status(thm)],[c_164,c_92]) ).

tff(c_14491,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_14487,c_176]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem  : LCL454+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.14  % 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
% 0.14/0.35  % Computer : n023.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 14:23:22 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 13.20/4.75  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.36/4.76  
% 13.36/4.76  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.52/4.80  
% 13.52/4.80  Inference rules
% 13.52/4.80  ----------------------
% 13.52/4.80  #Ref     : 0
% 13.52/4.80  #Sup     : 3483
% 13.52/4.80  #Fact    : 0
% 13.52/4.80  #Define  : 0
% 13.52/4.80  #Split   : 24
% 13.52/4.80  #Chain   : 0
% 13.52/4.80  #Close   : 0
% 13.52/4.80  
% 13.52/4.80  Ordering : KBO
% 13.52/4.80  
% 13.52/4.80  Simplification rules
% 13.52/4.80  ----------------------
% 13.52/4.80  #Subsume      : 824
% 13.52/4.80  #Demod        : 2358
% 13.52/4.80  #Tautology    : 698
% 13.52/4.80  #SimpNegUnit  : 81
% 13.52/4.80  #BackRed      : 53
% 13.52/4.80  
% 13.52/4.80  #Partial instantiations: 0
% 13.52/4.80  #Strategies tried      : 1
% 13.52/4.80  
% 13.52/4.80  Timing (in seconds)
% 13.52/4.80  ----------------------
% 13.52/4.80  Preprocessing        : 0.62
% 13.52/4.80  Parsing              : 0.31
% 13.52/4.80  CNF conversion       : 0.05
% 13.52/4.80  Main loop            : 3.02
% 13.52/4.80  Inferencing          : 0.75
% 13.52/4.80  Reduction            : 1.34
% 13.52/4.80  Demodulation         : 1.01
% 13.52/4.80  BG Simplification    : 0.07
% 13.52/4.80  Subsumption          : 0.68
% 13.52/4.80  Abstraction          : 0.07
% 13.52/4.80  MUC search           : 0.00
% 13.52/4.80  Cooper               : 0.00
% 13.52/4.80  Total                : 3.71
% 13.52/4.80  Index Insertion      : 0.00
% 13.52/4.80  Index Deletion       : 0.00
% 13.52/4.80  Index Matching       : 0.00
% 13.52/4.80  BG Taut test         : 0.00
%------------------------------------------------------------------------------