TSTP Solution File: KLE040+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : KLE040+2 : 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 : n026.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 10:44:44 EDT 2023

% Result   : Theorem 41.90s 28.53s
% Output   : CNFRefutation 41.90s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   23
% Syntax   : Number of formulae    :  108 (  78 unt;   8 typ;   0 def)
%            Number of atoms       :  122 (  73 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   48 (  26   ~;  18   |;   1   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :  141 (; 141   !;   0   ?;   0   :)

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

%Foreground sorts:

%Background operators:

%Foreground operators:
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_1',type,
    '#skF_1': $i ).

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

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

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

tff(f_65,axiom,
    ! [A] : ( multiplication(one,A) = A ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_left_identity) ).

tff(f_86,axiom,
    ! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_unfold_left) ).

tff(f_52,axiom,
    ! [A,B] : ( addition(A,B) = addition(B,A) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_commutativity) ).

tff(f_95,axiom,
    ! [A,B,C] :
      ( leq(addition(multiplication(A,B),C),A)
     => leq(multiplication(C,star(B)),A) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_induction_right) ).

tff(f_58,axiom,
    ! [A] : ( addition(A,A) = A ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_idempotence) ).

tff(f_70,axiom,
    ! [A,B,C] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',left_distributivity) ).

tff(f_54,axiom,
    ! [C,B,A] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_associativity) ).

tff(f_84,axiom,
    ! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_unfold_right) ).

tff(f_80,axiom,
    ! [A,B] :
      ( leq(A,B)
    <=> ( addition(A,B) = B ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',order) ).

tff(f_63,axiom,
    ! [A] : ( multiplication(A,one) = A ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_right_identity) ).

tff(f_56,axiom,
    ! [A] : ( addition(A,zero) = A ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_identity) ).

tff(f_75,axiom,
    ! [A] : ( multiplication(zero,A) = zero ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',left_annihilation) ).

tff(f_91,axiom,
    ! [A,B,C] :
      ( leq(addition(multiplication(A,B),C),B)
     => leq(multiplication(star(A),C),B) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_induction_left) ).

tff(f_68,axiom,
    ! [A,B,C] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',right_distributivity) ).

tff(f_102,negated_conjecture,
    ~ ! [X0] :
        ( leq(multiplication(star(X0),star(X0)),star(X0))
        & leq(star(X0),multiplication(star(X0),star(X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

tff(c_14,plain,
    ! [A_12] : ( multiplication(one,A_12) = A_12 ),
    inference(cnfTransformation,[status(thm)],[f_65]) ).

tff(c_30,plain,
    ! [A_24] : leq(addition(one,multiplication(star(A_24),A_24)),star(A_24)),
    inference(cnfTransformation,[status(thm)],[f_86]) ).

tff(c_2,plain,
    ! [B_2,A_1] : ( addition(B_2,A_1) = addition(A_1,B_2) ),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_10526,plain,
    ! [C_189,B_190,A_191] :
      ( leq(multiplication(C_189,star(B_190)),A_191)
      | ~ leq(addition(multiplication(A_191,B_190),C_189),A_191) ),
    inference(cnfTransformation,[status(thm)],[f_95]) ).

tff(c_21895,plain,
    ! [B_292,B_293,A_294] :
      ( leq(multiplication(B_292,star(B_293)),A_294)
      | ~ leq(addition(B_292,multiplication(A_294,B_293)),A_294) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_10526]) ).

tff(c_21958,plain,
    ! [A_24] : leq(multiplication(one,star(A_24)),star(A_24)),
    inference(resolution,[status(thm)],[c_30,c_21895]) ).

tff(c_21999,plain,
    ! [A_24] : leq(star(A_24),star(A_24)),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_21958]) ).

tff(c_8,plain,
    ! [A_7] : ( addition(A_7,A_7) = A_7 ),
    inference(cnfTransformation,[status(thm)],[f_58]) ).

tff(c_9624,plain,
    ! [A_179,C_180,B_181] : ( addition(multiplication(A_179,C_180),multiplication(B_181,C_180)) = multiplication(addition(A_179,B_181),C_180) ),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_12622,plain,
    ! [A_225,A_226] : ( multiplication(addition(A_225,one),A_226) = addition(multiplication(A_225,A_226),A_226) ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_9624]) ).

tff(c_12822,plain,
    ! [A_1,A_226] : ( multiplication(addition(one,A_1),A_226) = addition(multiplication(A_1,A_226),A_226) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_12622]) ).

tff(c_9704,plain,
    ! [B_181,A_12] : ( multiplication(addition(one,B_181),A_12) = addition(A_12,multiplication(B_181,A_12)) ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_9624]) ).

tff(c_4,plain,
    ! [A_5,B_4,C_3] : ( addition(addition(A_5,B_4),C_3) = addition(A_5,addition(B_4,C_3)) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_8093,plain,
    ! [A_152] : leq(addition(one,multiplication(A_152,star(A_152))),star(A_152)),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_24,plain,
    ! [A_21,B_22] :
      ( ( addition(A_21,B_22) = B_22 )
      | ~ leq(A_21,B_22) ),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_14358,plain,
    ! [A_242] : ( addition(addition(one,multiplication(A_242,star(A_242))),star(A_242)) = star(A_242) ),
    inference(resolution,[status(thm)],[c_8093,c_24]) ).

tff(c_14455,plain,
    ! [A_242] : ( addition(one,addition(multiplication(A_242,star(A_242)),star(A_242))) = star(A_242) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_14358]) ).

tff(c_14491,plain,
    ! [A_242] : ( addition(one,multiplication(addition(one,A_242),star(A_242))) = star(A_242) ),
    inference(demodulation,[status(thm),theory(equality)],[c_9704,c_2,c_14455]) ).

tff(c_14678,plain,
    ! [A_247] : ( addition(one,multiplication(addition(one,A_247),star(A_247))) = star(A_247) ),
    inference(demodulation,[status(thm),theory(equality)],[c_9704,c_2,c_14455]) ).

tff(c_8160,plain,
    ! [A_154,B_155,C_156] : ( addition(addition(A_154,B_155),C_156) = addition(A_154,addition(B_155,C_156)) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_8224,plain,
    ! [A_7,C_156] : ( addition(A_7,addition(A_7,C_156)) = addition(A_7,C_156) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_8160]) ).

tff(c_14740,plain,
    ! [A_247] : ( addition(one,multiplication(addition(one,A_247),star(A_247))) = addition(one,star(A_247)) ),
    inference(superposition,[status(thm),theory(equality)],[c_14678,c_8224]) ).

tff(c_14832,plain,
    ! [A_248] : ( addition(one,star(A_248)) = star(A_248) ),
    inference(demodulation,[status(thm),theory(equality)],[c_14491,c_14740]) ).

tff(c_26,plain,
    ! [A_21,B_22] :
      ( leq(A_21,B_22)
      | ( addition(A_21,B_22) != B_22 ) ),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_12,plain,
    ! [A_11] : ( multiplication(A_11,one) = A_11 ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_135,plain,
    ! [B_37,A_38] : ( addition(B_37,A_38) = addition(A_38,B_37) ),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_6,plain,
    ! [A_6] : ( addition(A_6,zero) = A_6 ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_151,plain,
    ! [A_38] : ( addition(zero,A_38) = A_38 ),
    inference(superposition,[status(thm),theory(equality)],[c_135,c_6]) ).

tff(c_22,plain,
    ! [A_20] : ( multiplication(zero,A_20) = zero ),
    inference(cnfTransformation,[status(thm)],[f_75]) ).

tff(c_10799,plain,
    ! [A_199,C_200,B_201] :
      ( leq(multiplication(star(A_199),C_200),B_201)
      | ~ leq(addition(multiplication(A_199,B_201),C_200),B_201) ),
    inference(cnfTransformation,[status(thm)],[f_91]) ).

tff(c_10848,plain,
    ! [C_200,A_20] :
      ( leq(multiplication(star(zero),C_200),A_20)
      | ~ leq(addition(zero,C_200),A_20) ),
    inference(superposition,[status(thm),theory(equality)],[c_22,c_10799]) ).

tff(c_10977,plain,
    ! [C_205,A_206] :
      ( leq(multiplication(star(zero),C_205),A_206)
      | ~ leq(C_205,A_206) ),
    inference(demodulation,[status(thm),theory(equality)],[c_151,c_10848]) ).

tff(c_10997,plain,
    ! [A_207] :
      ( leq(star(zero),A_207)
      | ~ leq(one,A_207) ),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_10977]) ).

tff(c_11143,plain,
    ! [A_212] :
      ( ( addition(star(zero),A_212) = A_212 )
      | ~ leq(one,A_212) ),
    inference(resolution,[status(thm)],[c_10997,c_24]) ).

tff(c_8265,plain,
    ! [A_157,C_158] : ( addition(A_157,addition(A_157,C_158)) = addition(A_157,C_158) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_8160]) ).

tff(c_8314,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_8265]) ).

tff(c_8573,plain,
    ! [C_167,A_168,B_169] : ( addition(C_167,addition(A_168,B_169)) = addition(A_168,addition(B_169,C_167)) ),
    inference(superposition,[status(thm),theory(equality)],[c_8160,c_2]) ).

tff(c_8991,plain,
    ! [A_172,C_173] : ( addition(A_172,addition(A_172,C_173)) = addition(C_173,A_172) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_8573]) ).

tff(c_9073,plain,
    ! [B_2,A_1] : ( addition(addition(B_2,A_1),A_1) = addition(A_1,addition(A_1,B_2)) ),
    inference(superposition,[status(thm),theory(equality)],[c_8314,c_8991]) ).

tff(c_9139,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_8224,c_9073]) ).

tff(c_11162,plain,
    ! [A_212] :
      ( ( addition(A_212,star(zero)) = addition(A_212,A_212) )
      | ~ leq(one,A_212) ),
    inference(superposition,[status(thm),theory(equality)],[c_11143,c_9139]) ).

tff(c_11288,plain,
    ! [A_213] :
      ( ( addition(A_213,star(zero)) = A_213 )
      | ~ leq(one,A_213) ),
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_11162]) ).

tff(c_8104,plain,
    leq(addition(one,zero),star(zero)),
    inference(superposition,[status(thm),theory(equality)],[c_22,c_8093]) ).

tff(c_8106,plain,
    leq(one,star(zero)),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_8104]) ).

tff(c_8110,plain,
    addition(one,star(zero)) = star(zero),
    inference(resolution,[status(thm)],[c_8106,c_24]) ).

tff(c_11368,plain,
    ( ( star(zero) = one )
    | ~ leq(one,one) ),
    inference(superposition,[status(thm),theory(equality)],[c_11288,c_8110]) ).

tff(c_11462,plain,
    ~ leq(one,one),
    inference(splitLeft,[status(thm)],[c_11368]) ).

tff(c_11465,plain,
    addition(one,one) != one,
    inference(resolution,[status(thm)],[c_26,c_11462]) ).

tff(c_11469,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_11465]) ).

tff(c_11470,plain,
    star(zero) = one,
    inference(splitRight,[status(thm)],[c_11368]) ).

tff(c_11272,plain,
    ! [A_212] :
      ( ( addition(A_212,star(zero)) = A_212 )
      | ~ leq(one,A_212) ),
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_11162]) ).

tff(c_11767,plain,
    ! [A_217] :
      ( ( addition(A_217,one) = A_217 )
      | ~ leq(one,A_217) ),
    inference(demodulation,[status(thm),theory(equality)],[c_11470,c_11272]) ).

tff(c_11782,plain,
    ! [B_22] :
      ( ( addition(B_22,one) = B_22 )
      | ( addition(one,B_22) != B_22 ) ),
    inference(resolution,[status(thm)],[c_26,c_11767]) ).

tff(c_14912,plain,
    ! [A_248] : ( addition(star(A_248),one) = star(A_248) ),
    inference(superposition,[status(thm),theory(equality)],[c_14832,c_11782]) ).

tff(c_158124,plain,
    ! [B_937,C_938,A_939] : ( addition(addition(B_937,C_938),A_939) = addition(C_938,addition(A_939,B_937)) ),
    inference(superposition,[status(thm),theory(equality)],[c_8573,c_2]) ).

tff(c_8105,plain,
    ! [A_152] : ( addition(addition(one,multiplication(A_152,star(A_152))),star(A_152)) = star(A_152) ),
    inference(resolution,[status(thm)],[c_8093,c_24]) ).

tff(c_158371,plain,
    ! [A_152] : ( addition(multiplication(A_152,star(A_152)),addition(star(A_152),one)) = star(A_152) ),
    inference(superposition,[status(thm),theory(equality)],[c_158124,c_8105]) ).

tff(c_158893,plain,
    ! [A_152] : ( multiplication(addition(one,A_152),star(A_152)) = star(A_152) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12822,c_14912,c_158371]) ).

tff(c_12029,plain,
    ! [B_220,A_221] : ( multiplication(addition(one,B_220),A_221) = addition(A_221,multiplication(B_220,A_221)) ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_9624]) ).

tff(c_182107,plain,
    ! [A_1059,B_1060] : ( addition(A_1059,multiplication(addition(one,B_1060),A_1059)) = addition(A_1059,multiplication(B_1060,A_1059)) ),
    inference(superposition,[status(thm),theory(equality)],[c_12029,c_8224]) ).

tff(c_182529,plain,
    ! [A_152] : ( addition(star(A_152),multiplication(A_152,star(A_152))) = addition(star(A_152),star(A_152)) ),
    inference(superposition,[status(thm),theory(equality)],[c_158893,c_182107]) ).

tff(c_197353,plain,
    ! [A_1120] : ( addition(star(A_1120),multiplication(A_1120,star(A_1120))) = star(A_1120) ),
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_182529]) ).

tff(c_10834,plain,
    ! [A_199,A_1,B_201] :
      ( leq(multiplication(star(A_199),A_1),B_201)
      | ~ leq(addition(A_1,multiplication(A_199,B_201)),B_201) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_10799]) ).

tff(c_197473,plain,
    ! [A_1120] :
      ( leq(multiplication(star(A_1120),star(A_1120)),star(A_1120))
      | ~ leq(star(A_1120),star(A_1120)) ),
    inference(superposition,[status(thm),theory(equality)],[c_197353,c_10834]) ).

tff(c_197803,plain,
    ! [A_1120] : leq(multiplication(star(A_1120),star(A_1120)),star(A_1120)),
    inference(demodulation,[status(thm),theory(equality)],[c_21999,c_197473]) ).

tff(c_706,plain,
    ! [A_59,B_60,C_61] : ( addition(multiplication(A_59,B_60),multiplication(A_59,C_61)) = multiplication(A_59,addition(B_60,C_61)) ),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_758,plain,
    ! [A_11,C_61] : ( multiplication(A_11,addition(one,C_61)) = addition(A_11,multiplication(A_11,C_61)) ),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_706]) ).

tff(c_269,plain,
    ! [A_45] : leq(addition(one,multiplication(star(A_45),A_45)),star(A_45)),
    inference(cnfTransformation,[status(thm)],[f_86]) ).

tff(c_7741,plain,
    ! [A_146] : ( addition(addition(one,multiplication(star(A_146),A_146)),star(A_146)) = star(A_146) ),
    inference(resolution,[status(thm)],[c_269,c_24]) ).

tff(c_7851,plain,
    ! [A_146] : ( addition(one,addition(multiplication(star(A_146),A_146),star(A_146))) = star(A_146) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_7741]) ).

tff(c_7890,plain,
    ! [A_146] : ( addition(one,multiplication(star(A_146),addition(one,A_146))) = star(A_146) ),
    inference(demodulation,[status(thm),theory(equality)],[c_758,c_2,c_7851]) ).

tff(c_7893,plain,
    ! [A_147] : ( addition(one,multiplication(star(A_147),addition(one,A_147))) = star(A_147) ),
    inference(demodulation,[status(thm),theory(equality)],[c_758,c_2,c_7851]) ).

tff(c_364,plain,
    ! [A_49,B_50,C_51] : ( addition(addition(A_49,B_50),C_51) = addition(A_49,addition(B_50,C_51)) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_425,plain,
    ! [A_7,C_51] : ( addition(A_7,addition(A_7,C_51)) = addition(A_7,C_51) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_364]) ).

tff(c_7967,plain,
    ! [A_147] : ( addition(one,multiplication(star(A_147),addition(one,A_147))) = addition(one,star(A_147)) ),
    inference(superposition,[status(thm),theory(equality)],[c_7893,c_425]) ).

tff(c_8059,plain,
    ! [A_147] : ( addition(one,star(A_147)) = star(A_147) ),
    inference(demodulation,[status(thm),theory(equality)],[c_7890,c_7967]) ).

tff(c_460,plain,
    ! [A_52,C_53,B_54] : ( addition(multiplication(A_52,C_53),multiplication(B_54,C_53)) = multiplication(addition(A_52,B_54),C_53) ),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_504,plain,
    ! [B_54,A_12] : ( multiplication(addition(one,B_54),A_12) = addition(A_12,multiplication(B_54,A_12)) ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_460]) ).

tff(c_36,plain,
    ( ~ leq(multiplication(star('#skF_2'),star('#skF_2')),star('#skF_2'))
    | ~ leq(star('#skF_1'),multiplication(star('#skF_1'),star('#skF_1'))) ),
    inference(cnfTransformation,[status(thm)],[f_102]) ).

tff(c_230,plain,
    ~ leq(star('#skF_1'),multiplication(star('#skF_1'),star('#skF_1'))),
    inference(splitLeft,[status(thm)],[c_36]) ).

tff(c_242,plain,
    addition(star('#skF_1'),multiplication(star('#skF_1'),star('#skF_1'))) != multiplication(star('#skF_1'),star('#skF_1')),
    inference(resolution,[status(thm)],[c_26,c_230]) ).

tff(c_3552,plain,
    multiplication(addition(one,star('#skF_1')),star('#skF_1')) != multiplication(star('#skF_1'),star('#skF_1')),
    inference(demodulation,[status(thm),theory(equality)],[c_504,c_242]) ).

tff(c_8073,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_8059,c_3552]) ).

tff(c_8074,plain,
    ~ leq(multiplication(star('#skF_2'),star('#skF_2')),star('#skF_2')),
    inference(splitRight,[status(thm)],[c_36]) ).

tff(c_198126,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_197803,c_8074]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : KLE040+2 : 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
% 0.14/0.35  % Computer : n026.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
% 0.21/0.35  % CPULimit : 300
% 0.21/0.35  % WCLimit  : 300
% 0.21/0.35  % DateTime : Thu Aug  3 23:38:32 EDT 2023
% 0.21/0.35  % CPUTime  : 
% 41.90/28.53  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 41.90/28.55  
% 41.90/28.55  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 41.90/28.59  
% 41.90/28.59  Inference rules
% 41.90/28.59  ----------------------
% 41.90/28.59  #Ref     : 6
% 41.90/28.59  #Sup     : 50309
% 41.90/28.59  #Fact    : 0
% 41.90/28.59  #Define  : 0
% 41.90/28.59  #Split   : 19
% 41.90/28.59  #Chain   : 0
% 41.90/28.59  #Close   : 0
% 41.90/28.59  
% 41.90/28.59  Ordering : KBO
% 41.90/28.59  
% 41.90/28.59  Simplification rules
% 41.90/28.59  ----------------------
% 41.90/28.59  #Subsume      : 18935
% 41.90/28.59  #Demod        : 54361
% 41.90/28.59  #Tautology    : 10916
% 41.90/28.59  #SimpNegUnit  : 596
% 41.90/28.59  #BackRed      : 78
% 41.90/28.59  
% 41.90/28.59  #Partial instantiations: 0
% 41.90/28.59  #Strategies tried      : 1
% 41.90/28.59  
% 41.90/28.59  Timing (in seconds)
% 41.90/28.59  ----------------------
% 41.90/28.60  Preprocessing        : 0.50
% 41.90/28.60  Parsing              : 0.27
% 41.90/28.60  CNF conversion       : 0.03
% 41.90/28.60  Main loop            : 27.00
% 41.90/28.60  Inferencing          : 2.93
% 41.90/28.60  Reduction            : 17.62
% 41.90/28.60  Demodulation         : 15.94
% 41.90/28.60  BG Simplification    : 0.33
% 41.90/28.60  Subsumption          : 4.50
% 41.90/28.60  Abstraction          : 0.61
% 41.90/28.60  MUC search           : 0.00
% 41.90/28.60  Cooper               : 0.00
% 41.90/28.60  Total                : 27.58
% 41.90/28.60  Index Insertion      : 0.00
% 41.90/28.60  Index Deletion       : 0.00
% 41.90/28.60  Index Matching       : 0.00
% 41.90/28.60  BG Taut test         : 0.00
%------------------------------------------------------------------------------