TSTP Solution File: KLE167+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : KLE167+1 : TPTP v8.1.2. Released v4.0.0.
% 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 : n025.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 10:44:58 EDT 2023

% Result   : Theorem 17.75s 7.25s
% Output   : CNFRefutation 17.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   26
% Syntax   : Number of formulae    :  111 (  69 unt;  11 typ;   0 def)
%            Number of atoms       :  132 (  72 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   65 (  33   ~;  27   |;   1   &)
%                                         (   1 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   5   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :  147 (; 147   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ leq > multiplication > addition > #nlpp > strong_iteration > star > zero > one > #skF_2 > #skF_3 > #skF_1 > #skF_4

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

tff(leq,type,
    leq: ( $i * $i ) > $o ).

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

tff(f_60,axiom,
    ! [A] : ( addition(A,A) = A ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',idempotence) ).

tff(f_102,axiom,
    ! [A,B] :
      ( leq(A,B)
    <=> ( addition(A,B) = B ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).

tff(f_54,axiom,
    ! [A,B] : ( addition(A,B) = addition(B,A) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).

tff(f_58,axiom,
    ! [A] : ( addition(A,zero) = A ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_identity) ).

tff(f_80,axiom,
    ! [A] : ( addition(one,multiplication(star(A),A)) = star(A) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_unfold2) ).

tff(f_56,axiom,
    ! [C,B,A] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).

tff(f_78,axiom,
    ! [A] : ( addition(one,multiplication(A,star(A))) = star(A) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_unfold1) ).

tff(f_65,axiom,
    ! [A] : ( multiplication(A,one) = A ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).

tff(f_70,axiom,
    ! [A,B,C] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',distributivity1) ).

tff(f_75,axiom,
    ! [A] : ( multiplication(zero,A) = zero ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).

tff(f_88,axiom,
    ! [A,B,C] :
      ( leq(addition(multiplication(C,A),B),C)
     => leq(multiplication(B,star(A)),C) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_induction2) ).

tff(f_67,axiom,
    ! [A] : ( multiplication(one,A) = A ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).

tff(f_72,axiom,
    ! [A,B,C] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',distributivity2) ).

tff(f_84,axiom,
    ! [A,B,C] :
      ( leq(addition(multiplication(A,C),B),C)
     => leq(multiplication(star(A),B),C) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_induction1) ).

tff(f_111,negated_conjecture,
    ~ ! [X0,X1] :
        ( ( ( multiplication(X0,X1) = zero )
         => leq(multiplication(X0,star(X1)),X0) )
        & leq(X0,multiplication(X0,star(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

tff(c_8,plain,
    ! [A_7] : ( addition(A_7,A_7) = A_7 ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_38,plain,
    ! [A_33,B_34] :
      ( leq(A_33,B_34)
      | ( addition(A_33,B_34) != B_34 ) ),
    inference(cnfTransformation,[status(thm)],[f_102]) ).

tff(c_116,plain,
    ! [B_40,A_41] : ( addition(B_40,A_41) = addition(A_41,B_40) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_6,plain,
    ! [A_6] : ( addition(A_6,zero) = A_6 ),
    inference(cnfTransformation,[status(thm)],[f_58]) ).

tff(c_132,plain,
    ! [A_41] : ( addition(zero,A_41) = A_41 ),
    inference(superposition,[status(thm),theory(equality)],[c_116,c_6]) ).

tff(c_24,plain,
    ! [A_21] : ( addition(one,multiplication(star(A_21),A_21)) = star(A_21) ),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_376,plain,
    ! [A_52,B_53,C_54] : ( addition(addition(A_52,B_53),C_54) = addition(A_52,addition(B_53,C_54)) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_466,plain,
    ! [A_55,C_56] : ( addition(A_55,addition(A_55,C_56)) = addition(A_55,C_56) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_376]) ).

tff(c_520,plain,
    ! [A_21] : ( addition(one,multiplication(star(A_21),A_21)) = addition(one,star(A_21)) ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_466]) ).

tff(c_556,plain,
    ! [A_21] : ( addition(one,star(A_21)) = star(A_21) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_520]) ).

tff(c_22,plain,
    ! [A_20] : ( addition(one,multiplication(A_20,star(A_20))) = star(A_20) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_2,plain,
    ! [B_2,A_1] : ( addition(B_2,A_1) = addition(A_1,B_2) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_1416,plain,
    ! [C_94,A_95,B_96] : ( addition(C_94,addition(A_95,B_96)) = addition(A_95,addition(B_96,C_94)) ),
    inference(superposition,[status(thm),theory(equality)],[c_376,c_2]) ).

tff(c_3038,plain,
    ! [A_114,C_115] : ( addition(A_114,addition(A_114,C_115)) = addition(C_115,A_114) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_1416]) ).

tff(c_3219,plain,
    ! [A_20] : ( addition(multiplication(A_20,star(A_20)),one) = addition(one,star(A_20)) ),
    inference(superposition,[status(thm),theory(equality)],[c_22,c_3038]) ).

tff(c_3286,plain,
    ! [A_20] : ( addition(multiplication(A_20,star(A_20)),one) = star(A_20) ),
    inference(demodulation,[status(thm),theory(equality)],[c_556,c_3219]) ).

tff(c_12,plain,
    ! [A_11] : ( multiplication(A_11,one) = A_11 ),
    inference(cnfTransformation,[status(thm)],[f_65]) ).

tff(c_923,plain,
    ! [A_69,B_70,C_71] : ( addition(multiplication(A_69,B_70),multiplication(A_69,C_71)) = multiplication(A_69,addition(B_70,C_71)) ),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_984,plain,
    ! [A_11,B_70] : ( multiplication(A_11,addition(B_70,one)) = addition(multiplication(A_11,B_70),A_11) ),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_923]) ).

tff(c_20,plain,
    ! [A_19] : ( multiplication(zero,A_19) = zero ),
    inference(cnfTransformation,[status(thm)],[f_75]) ).

tff(c_1076,plain,
    ! [B_74,A_75,C_76] :
      ( leq(multiplication(B_74,star(A_75)),C_76)
      | ~ leq(addition(multiplication(C_76,A_75),B_74),C_76) ),
    inference(cnfTransformation,[status(thm)],[f_88]) ).

tff(c_1113,plain,
    ! [B_74,A_19] :
      ( leq(multiplication(B_74,star(A_19)),zero)
      | ~ leq(addition(zero,B_74),zero) ),
    inference(superposition,[status(thm),theory(equality)],[c_20,c_1076]) ).

tff(c_1301,plain,
    ! [B_90,A_91] :
      ( leq(multiplication(B_90,star(A_91)),zero)
      | ~ leq(B_90,zero) ),
    inference(demodulation,[status(thm),theory(equality)],[c_132,c_1113]) ).

tff(c_36,plain,
    ! [A_33,B_34] :
      ( ( addition(A_33,B_34) = B_34 )
      | ~ leq(A_33,B_34) ),
    inference(cnfTransformation,[status(thm)],[f_102]) ).

tff(c_1304,plain,
    ! [B_90,A_91] :
      ( ( addition(multiplication(B_90,star(A_91)),zero) = zero )
      | ~ leq(B_90,zero) ),
    inference(resolution,[status(thm)],[c_1301,c_36]) ).

tff(c_1324,plain,
    ! [B_92,A_93] :
      ( ( multiplication(B_92,star(A_93)) = zero )
      | ~ leq(B_92,zero) ),
    inference(demodulation,[status(thm),theory(equality)],[c_132,c_2,c_1304]) ).

tff(c_1362,plain,
    ! [A_93] :
      ( ( star(A_93) = addition(one,zero) )
      | ~ leq(A_93,zero) ),
    inference(superposition,[status(thm),theory(equality)],[c_1324,c_22]) ).

tff(c_1799,plain,
    ! [A_98] :
      ( ( star(A_98) = one )
      | ~ leq(A_98,zero) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_1362]) ).

tff(c_1814,plain,
    ! [A_33] :
      ( ( star(A_33) = one )
      | ( addition(A_33,zero) != zero ) ),
    inference(resolution,[status(thm)],[c_38,c_1799]) ).

tff(c_1822,plain,
    star(zero) = one,
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_1814]) ).

tff(c_2336,plain,
    ! [A_105,B_106] : ( multiplication(A_105,addition(B_106,one)) = addition(multiplication(A_105,B_106),A_105) ),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_923]) ).

tff(c_2464,plain,
    ! [A_105] : ( addition(multiplication(A_105,zero),A_105) = multiplication(A_105,one) ),
    inference(superposition,[status(thm),theory(equality)],[c_132,c_2336]) ).

tff(c_2521,plain,
    ! [A_105] : ( addition(multiplication(A_105,zero),A_105) = A_105 ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_2464]) ).

tff(c_1095,plain,
    ! [B_74,A_75,B_34] :
      ( leq(multiplication(B_74,star(A_75)),B_34)
      | ( addition(addition(multiplication(B_34,A_75),B_74),B_34) != B_34 ) ),
    inference(resolution,[status(thm)],[c_38,c_1076]) ).

tff(c_19383,plain,
    ! [B_320,A_321,B_322] :
      ( leq(multiplication(B_320,star(A_321)),B_322)
      | ( addition(B_322,addition(multiplication(B_322,A_321),B_320)) != B_322 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_1095]) ).

tff(c_19481,plain,
    ! [A_105] :
      ( leq(multiplication(A_105,star(zero)),A_105)
      | ( addition(A_105,A_105) != A_105 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_2521,c_19383]) ).

tff(c_19590,plain,
    ! [A_105] : leq(A_105,A_105),
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_12,c_1822,c_19481]) ).

tff(c_2760,plain,
    ! [A_109,A_110] : ( addition(A_109,addition(A_110,A_109)) = addition(A_110,A_109) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_1416]) ).

tff(c_1677,plain,
    ! [A_41,C_94] : ( addition(zero,addition(A_41,C_94)) = addition(C_94,A_41) ),
    inference(superposition,[status(thm),theory(equality)],[c_132,c_1416]) ).

tff(c_2769,plain,
    ! [A_110,A_109] : ( addition(addition(A_110,A_109),A_109) = addition(zero,addition(A_110,A_109)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2760,c_1677]) ).

tff(c_2952,plain,
    ! [A_110,A_109] : ( addition(addition(A_110,A_109),A_109) = addition(A_110,A_109) ),
    inference(demodulation,[status(thm),theory(equality)],[c_132,c_2769]) ).

tff(c_745,plain,
    ! [A_66,B_67] : ( addition(A_66,addition(B_67,A_66)) = addition(A_66,B_67) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_466]) ).

tff(c_819,plain,
    ! [A_21] : ( addition(multiplication(star(A_21),A_21),star(A_21)) = addition(multiplication(star(A_21),A_21),one) ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_745]) ).

tff(c_6620,plain,
    ! [A_147] : ( addition(multiplication(star(A_147),A_147),star(A_147)) = star(A_147) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_2,c_819]) ).

tff(c_6648,plain,
    ! [A_147] : ( multiplication(star(A_147),addition(A_147,one)) = star(A_147) ),
    inference(superposition,[status(thm),theory(equality)],[c_6620,c_984]) ).

tff(c_388,plain,
    ! [C_54,A_52,B_53] : ( addition(C_54,addition(A_52,B_53)) = addition(A_52,addition(B_53,C_54)) ),
    inference(superposition,[status(thm),theory(equality)],[c_376,c_2]) ).

tff(c_6755,plain,
    ! [A_148] : ( multiplication(star(A_148),addition(A_148,one)) = star(A_148) ),
    inference(superposition,[status(thm),theory(equality)],[c_6620,c_984]) ).

tff(c_14,plain,
    ! [A_12] : ( multiplication(one,A_12) = A_12 ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_655,plain,
    ! [A_62,C_63,B_64] : ( addition(multiplication(A_62,C_63),multiplication(B_64,C_63)) = multiplication(addition(A_62,B_64),C_63) ),
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_695,plain,
    ! [A_62,A_12] : ( multiplication(addition(A_62,one),A_12) = addition(multiplication(A_62,A_12),A_12) ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_655]) ).

tff(c_6761,plain,
    ! [A_148] : ( multiplication(addition(star(A_148),one),addition(A_148,one)) = addition(star(A_148),addition(A_148,one)) ),
    inference(superposition,[status(thm),theory(equality)],[c_6755,c_695]) ).

tff(c_6871,plain,
    ! [A_148] : ( addition(A_148,star(A_148)) = star(A_148) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6648,c_556,c_388,c_556,c_2,c_6761]) ).

tff(c_1181,plain,
    ! [A_81,B_82,C_83] :
      ( leq(multiplication(star(A_81),B_82),C_83)
      | ~ leq(addition(multiplication(A_81,C_83),B_82),C_83) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_16730,plain,
    ! [A_291,C_292] :
      ( leq(multiplication(star(A_291),multiplication(A_291,C_292)),C_292)
      | ~ leq(multiplication(A_291,C_292),C_292) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_1181]) ).

tff(c_16815,plain,
    ! [A_11] :
      ( leq(multiplication(star(A_11),A_11),one)
      | ~ leq(multiplication(A_11,one),one) ),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_16730]) ).

tff(c_35123,plain,
    ! [A_453] :
      ( leq(multiplication(star(A_453),A_453),one)
      | ~ leq(A_453,one) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_16815]) ).

tff(c_35210,plain,
    ( leq(star(one),one)
    | ~ leq(one,one) ),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_35123]) ).

tff(c_35236,plain,
    leq(star(one),one),
    inference(demodulation,[status(thm),theory(equality)],[c_19590,c_35210]) ).

tff(c_35243,plain,
    addition(star(one),one) = one,
    inference(resolution,[status(thm)],[c_35236,c_36]) ).

tff(c_530,plain,
    ! [A_1,B_2] : ( addition(A_1,addition(B_2,A_1)) = addition(A_1,B_2) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_466]) ).

tff(c_2098,plain,
    ! [A_102,C_103] : ( addition(zero,addition(A_102,C_103)) = addition(C_103,A_102) ),
    inference(superposition,[status(thm),theory(equality)],[c_132,c_1416]) ).

tff(c_2177,plain,
    ! [B_2,A_1] : ( addition(addition(B_2,A_1),A_1) = addition(zero,addition(A_1,B_2)) ),
    inference(superposition,[status(thm),theory(equality)],[c_530,c_2098]) ).

tff(c_2263,plain,
    ! [B_2,A_1] : ( addition(addition(B_2,A_1),A_1) = addition(A_1,B_2) ),
    inference(demodulation,[status(thm),theory(equality)],[c_132,c_2177]) ).

tff(c_35323,plain,
    addition(one,star(one)) = addition(one,one),
    inference(superposition,[status(thm),theory(equality)],[c_35243,c_2263]) ).

tff(c_35409,plain,
    star(one) = one,
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_6871,c_35323]) ).

tff(c_1111,plain,
    ! [B_74,A_11] :
      ( leq(multiplication(B_74,star(one)),A_11)
      | ~ leq(addition(A_11,B_74),A_11) ),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_1076]) ).

tff(c_35431,plain,
    ! [B_74,A_11] :
      ( leq(multiplication(B_74,one),A_11)
      | ~ leq(addition(A_11,B_74),A_11) ),
    inference(demodulation,[status(thm),theory(equality)],[c_35409,c_1111]) ).

tff(c_38713,plain,
    ! [B_468,A_469] :
      ( leq(B_468,A_469)
      | ~ leq(addition(A_469,B_468),A_469) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_35431]) ).

tff(c_38812,plain,
    ! [A_109,A_110] :
      ( leq(A_109,addition(A_110,A_109))
      | ~ leq(addition(A_110,A_109),addition(A_110,A_109)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2952,c_38713]) ).

tff(c_39070,plain,
    ! [A_473,A_474] : leq(A_473,addition(A_474,A_473)),
    inference(demodulation,[status(thm),theory(equality)],[c_19590,c_38812]) ).

tff(c_45137,plain,
    ! [A_525,B_526] : leq(A_525,multiplication(A_525,addition(B_526,one))),
    inference(superposition,[status(thm),theory(equality)],[c_984,c_39070]) ).

tff(c_45216,plain,
    ! [A_525,A_20] : leq(A_525,multiplication(A_525,star(A_20))),
    inference(superposition,[status(thm),theory(equality)],[c_3286,c_45137]) ).

tff(c_42,plain,
    ( ( multiplication('#skF_3','#skF_4') = zero )
    | ~ leq('#skF_1',multiplication('#skF_1',star('#skF_2'))) ),
    inference(cnfTransformation,[status(thm)],[f_111]) ).

tff(c_212,plain,
    ~ leq('#skF_1',multiplication('#skF_1',star('#skF_2'))),
    inference(splitLeft,[status(thm)],[c_42]) ).

tff(c_45483,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_45216,c_212]) ).

tff(c_45484,plain,
    multiplication('#skF_3','#skF_4') = zero,
    inference(splitRight,[status(thm)],[c_42]) ).

tff(c_46836,plain,
    ! [B_568,A_569,C_570] :
      ( leq(multiplication(B_568,star(A_569)),C_570)
      | ~ leq(addition(multiplication(C_570,A_569),B_568),C_570) ),
    inference(cnfTransformation,[status(thm)],[f_88]) ).

tff(c_46873,plain,
    ! [B_568] :
      ( leq(multiplication(B_568,star('#skF_4')),'#skF_3')
      | ~ leq(addition(zero,B_568),'#skF_3') ),
    inference(superposition,[status(thm),theory(equality)],[c_45484,c_46836]) ).

tff(c_46958,plain,
    ! [B_574] :
      ( leq(multiplication(B_574,star('#skF_4')),'#skF_3')
      | ~ leq(B_574,'#skF_3') ),
    inference(demodulation,[status(thm),theory(equality)],[c_132,c_46873]) ).

tff(c_45485,plain,
    leq('#skF_1',multiplication('#skF_1',star('#skF_2'))),
    inference(splitRight,[status(thm)],[c_42]) ).

tff(c_40,plain,
    ( ~ leq(multiplication('#skF_3',star('#skF_4')),'#skF_3')
    | ~ leq('#skF_1',multiplication('#skF_1',star('#skF_2'))) ),
    inference(cnfTransformation,[status(thm)],[f_111]) ).

tff(c_45556,plain,
    ~ leq(multiplication('#skF_3',star('#skF_4')),'#skF_3'),
    inference(demodulation,[status(thm),theory(equality)],[c_45485,c_40]) ).

tff(c_46982,plain,
    ~ leq('#skF_3','#skF_3'),
    inference(resolution,[status(thm)],[c_46958,c_45556]) ).

tff(c_46987,plain,
    addition('#skF_3','#skF_3') != '#skF_3',
    inference(resolution,[status(thm)],[c_38,c_46982]) ).

tff(c_46991,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_46987]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : KLE167+1 : TPTP v8.1.2. Released v4.0.0.
% 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
% 0.13/0.36  % Computer : n025.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit : 300
% 0.13/0.36  % WCLimit  : 300
% 0.13/0.36  % DateTime : Thu Aug  3 23:41:05 EDT 2023
% 0.13/0.36  % CPUTime  : 
% 17.75/7.25  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.75/7.26  
% 17.75/7.26  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.86/7.30  
% 17.86/7.30  Inference rules
% 17.86/7.30  ----------------------
% 17.86/7.30  #Ref     : 0
% 17.86/7.30  #Sup     : 12272
% 17.86/7.30  #Fact    : 0
% 17.86/7.30  #Define  : 0
% 17.86/7.30  #Split   : 9
% 17.86/7.30  #Chain   : 0
% 17.86/7.30  #Close   : 0
% 17.86/7.30  
% 17.86/7.30  Ordering : KBO
% 17.86/7.30  
% 17.86/7.30  Simplification rules
% 17.86/7.30  ----------------------
% 17.86/7.30  #Subsume      : 3601
% 17.86/7.30  #Demod        : 11360
% 17.86/7.30  #Tautology    : 3863
% 17.86/7.30  #SimpNegUnit  : 304
% 17.86/7.30  #BackRed      : 34
% 17.86/7.30  
% 17.86/7.30  #Partial instantiations: 0
% 17.86/7.30  #Strategies tried      : 1
% 17.86/7.30  
% 17.86/7.30  Timing (in seconds)
% 17.86/7.30  ----------------------
% 17.86/7.30  Preprocessing        : 0.52
% 17.86/7.30  Parsing              : 0.28
% 17.86/7.30  CNF conversion       : 0.03
% 17.86/7.30  Main loop            : 5.62
% 17.86/7.30  Inferencing          : 1.00
% 17.86/7.30  Reduction            : 3.17
% 17.86/7.30  Demodulation         : 2.71
% 17.86/7.30  BG Simplification    : 0.10
% 17.86/7.30  Subsumption          : 0.99
% 17.86/7.30  Abstraction          : 0.14
% 17.86/7.30  MUC search           : 0.00
% 17.86/7.30  Cooper               : 0.00
% 17.86/7.30  Total                : 6.20
% 17.86/7.31  Index Insertion      : 0.00
% 17.86/7.31  Index Deletion       : 0.00
% 17.86/7.31  Index Matching       : 0.00
% 17.86/7.31  BG Taut test         : 0.00
%------------------------------------------------------------------------------