TSTP Solution File: KLE148+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : KLE148+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 : n003.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 10:44:56 EDT 2023

% Result   : Theorem 34.71s 21.33s
% Output   : CNFRefutation 34.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   28
% Syntax   : Number of formulae    :  124 (  84 unt;  11 typ;   0 def)
%            Number of atoms       :  143 (  88 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   62 (  32   ~;  25   |;   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   :  164 (; 164   !;   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_65,axiom,
    ! [A] : ( multiplication(A,one) = A ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).

tff(f_91,axiom,
    ! [A] : ( strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).

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_75,axiom,
    ! [A] : ( multiplication(zero,A) = zero ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).

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_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_102,axiom,
    ! [A,B] :
      ( leq(A,B)
    <=> ( addition(A,B) = B ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).

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_78,axiom,
    ! [A] : ( addition(one,multiplication(A,star(A))) = star(A) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_unfold1) ).

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_80,axiom,
    ! [A] : ( addition(one,multiplication(star(A),A)) = star(A) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_unfold2) ).

tff(f_63,axiom,
    ! [A,B,C] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_associativity) ).

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,strong_iteration(X1)),X0) )
        & leq(X0,multiplication(X0,strong_iteration(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_12,plain,
    ! [A_11] : ( multiplication(A_11,one) = A_11 ),
    inference(cnfTransformation,[status(thm)],[f_65]) ).

tff(c_30,plain,
    ! [A_28] : ( addition(multiplication(A_28,strong_iteration(A_28)),one) = strong_iteration(A_28) ),
    inference(cnfTransformation,[status(thm)],[f_91]) ).

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_20,plain,
    ! [A_19] : ( multiplication(zero,A_19) = zero ),
    inference(cnfTransformation,[status(thm)],[f_75]) ).

tff(c_272,plain,
    ! [A_49] : ( addition(multiplication(A_49,strong_iteration(A_49)),one) = strong_iteration(A_49) ),
    inference(cnfTransformation,[status(thm)],[f_91]) ).

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_278,plain,
    ! [A_49] : ( addition(one,multiplication(A_49,strong_iteration(A_49))) = strong_iteration(A_49) ),
    inference(superposition,[status(thm),theory(equality)],[c_272,c_2]) ).

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_499,plain,
    ! [A_49] : ( addition(one,multiplication(A_49,strong_iteration(A_49))) = addition(one,strong_iteration(A_49)) ),
    inference(superposition,[status(thm),theory(equality)],[c_278,c_466]) ).

tff(c_549,plain,
    ! [A_49] : ( addition(one,strong_iteration(A_49)) = strong_iteration(A_49) ),
    inference(demodulation,[status(thm),theory(equality)],[c_278,c_499]) ).

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_981,plain,
    ! [A_11,C_71] : ( multiplication(A_11,addition(one,C_71)) = addition(A_11,multiplication(A_11,C_71)) ),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_923]) ).

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_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_22,plain,
    ! [A_20] : ( addition(one,multiplication(A_20,star(A_20))) = star(A_20) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_1359,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_1792,plain,
    ! [A_98] :
      ( ( star(A_98) = one )
      | ~ leq(A_98,zero) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_1359]) ).

tff(c_1807,plain,
    ! [A_33] :
      ( ( star(A_33) = one )
      | ( addition(A_33,zero) != zero ) ),
    inference(resolution,[status(thm)],[c_38,c_1792]) ).

tff(c_1815,plain,
    star(zero) = one,
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_1807]) ).

tff(c_3381,plain,
    ! [A_115,B_116] : ( multiplication(A_115,addition(B_116,one)) = addition(multiplication(A_115,B_116),A_115) ),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_923]) ).

tff(c_3532,plain,
    ! [A_115] : ( addition(multiplication(A_115,zero),A_115) = multiplication(A_115,one) ),
    inference(superposition,[status(thm),theory(equality)],[c_132,c_3381]) ).

tff(c_3591,plain,
    ! [A_115] : ( addition(multiplication(A_115,zero),A_115) = A_115 ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_3532]) ).

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_18616,plain,
    ! [B_307,A_308,B_309] :
      ( leq(multiplication(B_307,star(A_308)),B_309)
      | ( addition(B_309,addition(multiplication(B_309,A_308),B_307)) != B_309 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_1095]) ).

tff(c_18695,plain,
    ! [A_115] :
      ( leq(multiplication(A_115,star(zero)),A_115)
      | ( addition(A_115,A_115) != A_115 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_3591,c_18616]) ).

tff(c_18804,plain,
    ! [A_115] : leq(A_115,A_115),
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_12,c_1815,c_18695]) ).

tff(c_453,plain,
    ! [A_7,C_54] : ( addition(A_7,addition(A_7,C_54)) = addition(A_7,C_54) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_376]) ).

tff(c_1409,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_1854,plain,
    ! [A_100,C_101] : ( addition(A_100,addition(A_100,C_101)) = addition(C_101,A_100) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_1409]) ).

tff(c_1959,plain,
    ! [A_7,C_54] : ( addition(addition(A_7,C_54),A_7) = addition(A_7,addition(A_7,C_54)) ),
    inference(superposition,[status(thm),theory(equality)],[c_453,c_1854]) ).

tff(c_2032,plain,
    ! [A_7,C_54] : ( addition(addition(A_7,C_54),A_7) = addition(A_7,C_54) ),
    inference(demodulation,[status(thm),theory(equality)],[c_453,c_1959]) ).

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

tff(c_2652,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_1409]) ).

tff(c_2830,plain,
    ! [A_20] : ( addition(multiplication(A_20,star(A_20)),star(A_20)) = addition(one,multiplication(A_20,star(A_20))) ),
    inference(superposition,[status(thm),theory(equality)],[c_22,c_2652]) ).

tff(c_7119,plain,
    ! [A_151] : ( addition(multiplication(A_151,star(A_151)),star(A_151)) = star(A_151) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_2830]) ).

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_7125,plain,
    ! [A_151] : ( multiplication(addition(A_151,one),star(A_151)) = star(A_151) ),
    inference(superposition,[status(thm),theory(equality)],[c_7119,c_695]) ).

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_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_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_56]) ).

tff(c_7248,plain,
    ! [A_152] : ( multiplication(addition(A_152,one),star(A_152)) = star(A_152) ),
    inference(superposition,[status(thm),theory(equality)],[c_7119,c_695]) ).

tff(c_7260,plain,
    ! [A_152] : ( multiplication(addition(A_152,one),addition(one,star(A_152))) = addition(addition(A_152,one),star(A_152)) ),
    inference(superposition,[status(thm),theory(equality)],[c_7248,c_981]) ).

tff(c_7399,plain,
    ! [A_153] : ( addition(A_153,star(A_153)) = star(A_153) ),
    inference(demodulation,[status(thm),theory(equality)],[c_7125,c_556,c_4,c_556,c_7260]) ).

tff(c_1670,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_1409]) ).

tff(c_7439,plain,
    ! [A_153] : ( addition(star(A_153),A_153) = addition(zero,star(A_153)) ),
    inference(superposition,[status(thm),theory(equality)],[c_7399,c_1670]) ).

tff(c_7521,plain,
    ! [A_153] : ( addition(star(A_153),A_153) = star(A_153) ),
    inference(demodulation,[status(thm),theory(equality)],[c_132,c_7439]) ).

tff(c_10,plain,
    ! [A_8,B_9,C_10] : ( multiplication(multiplication(A_8,B_9),C_10) = multiplication(A_8,multiplication(B_9,C_10)) ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_1109,plain,
    ! [C_76,A_75] :
      ( leq(multiplication(multiplication(C_76,A_75),star(A_75)),C_76)
      | ~ leq(multiplication(C_76,A_75),C_76) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_1076]) ).

tff(c_16595,plain,
    ! [C_287,A_288] :
      ( leq(multiplication(C_287,multiplication(A_288,star(A_288))),C_287)
      | ~ leq(multiplication(C_287,A_288),C_287) ),
    inference(demodulation,[status(thm),theory(equality)],[c_10,c_1109]) ).

tff(c_16659,plain,
    ! [A_288] :
      ( leq(multiplication(A_288,star(A_288)),one)
      | ~ leq(multiplication(one,A_288),one) ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_16595]) ).

tff(c_34300,plain,
    ! [A_462] :
      ( leq(multiplication(A_462,star(A_462)),one)
      | ~ leq(A_462,one) ),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_16659]) ).

tff(c_34360,plain,
    ( leq(star(one),one)
    | ~ leq(one,one) ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_34300]) ).

tff(c_34378,plain,
    leq(star(one),one),
    inference(demodulation,[status(thm),theory(equality)],[c_18804,c_34360]) ).

tff(c_34387,plain,
    addition(star(one),one) = one,
    inference(resolution,[status(thm)],[c_34378,c_36]) ).

tff(c_2661,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_2652,c_1670]) ).

tff(c_2855,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_2661]) ).

tff(c_34467,plain,
    addition(star(one),one) = addition(one,one),
    inference(superposition,[status(thm),theory(equality)],[c_34387,c_2855]) ).

tff(c_34565,plain,
    star(one) = one,
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_7521,c_34467]) ).

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_1208,plain,
    ! [B_82,A_12] :
      ( leq(multiplication(star(one),B_82),A_12)
      | ~ leq(addition(A_12,B_82),A_12) ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_1181]) ).

tff(c_34585,plain,
    ! [B_82,A_12] :
      ( leq(multiplication(one,B_82),A_12)
      | ~ leq(addition(A_12,B_82),A_12) ),
    inference(demodulation,[status(thm),theory(equality)],[c_34565,c_1208]) ).

tff(c_37001,plain,
    ! [B_474,A_475] :
      ( leq(B_474,A_475)
      | ~ leq(addition(A_475,B_474),A_475) ),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_34585]) ).

tff(c_37109,plain,
    ! [A_7,C_54] :
      ( leq(A_7,addition(A_7,C_54))
      | ~ leq(addition(A_7,C_54),addition(A_7,C_54)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2032,c_37001]) ).

tff(c_37576,plain,
    ! [A_481,C_482] : leq(A_481,addition(A_481,C_482)),
    inference(demodulation,[status(thm),theory(equality)],[c_18804,c_37109]) ).

tff(c_45784,plain,
    ! [A_548,C_549] : leq(A_548,multiplication(A_548,addition(one,C_549))),
    inference(superposition,[status(thm),theory(equality)],[c_981,c_37576]) ).

tff(c_45879,plain,
    ! [A_548,A_49] : leq(A_548,multiplication(A_548,strong_iteration(A_49))),
    inference(superposition,[status(thm),theory(equality)],[c_549,c_45784]) ).

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

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

tff(c_46135,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_45879,c_212]) ).

tff(c_46136,plain,
    multiplication('#skF_3','#skF_4') = zero,
    inference(splitRight,[status(thm)],[c_42]) ).

tff(c_46575,plain,
    ! [A_570,B_571,C_572] : ( multiplication(multiplication(A_570,B_571),C_572) = multiplication(A_570,multiplication(B_571,C_572)) ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_46606,plain,
    ! [C_572] : ( multiplication('#skF_3',multiplication('#skF_4',C_572)) = multiplication(zero,C_572) ),
    inference(superposition,[status(thm),theory(equality)],[c_46136,c_46575]) ).

tff(c_46625,plain,
    ! [C_572] : ( multiplication('#skF_3',multiplication('#skF_4',C_572)) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_20,c_46606]) ).

tff(c_47010,plain,
    ! [A_581,B_582,C_583] : ( addition(multiplication(A_581,B_582),multiplication(A_581,C_583)) = multiplication(A_581,addition(B_582,C_583)) ),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_47042,plain,
    ! [C_572,C_583] : ( multiplication('#skF_3',addition(multiplication('#skF_4',C_572),C_583)) = addition(zero,multiplication('#skF_3',C_583)) ),
    inference(superposition,[status(thm),theory(equality)],[c_46625,c_47010]) ).

tff(c_134510,plain,
    ! [C_1201,C_1202] : ( multiplication('#skF_3',addition(multiplication('#skF_4',C_1201),C_1202)) = multiplication('#skF_3',C_1202) ),
    inference(demodulation,[status(thm),theory(equality)],[c_132,c_47042]) ).

tff(c_134895,plain,
    multiplication('#skF_3',strong_iteration('#skF_4')) = multiplication('#skF_3',one),
    inference(superposition,[status(thm),theory(equality)],[c_30,c_134510]) ).

tff(c_134986,plain,
    multiplication('#skF_3',strong_iteration('#skF_4')) = '#skF_3',
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_134895]) ).

tff(c_46137,plain,
    leq('#skF_1',multiplication('#skF_1',strong_iteration('#skF_2'))),
    inference(splitRight,[status(thm)],[c_42]) ).

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

tff(c_46145,plain,
    ~ leq(multiplication('#skF_3',strong_iteration('#skF_4')),'#skF_3'),
    inference(demodulation,[status(thm),theory(equality)],[c_46137,c_40]) ).

tff(c_46148,plain,
    addition(multiplication('#skF_3',strong_iteration('#skF_4')),'#skF_3') != '#skF_3',
    inference(resolution,[status(thm)],[c_38,c_46145]) ).

tff(c_46150,plain,
    addition('#skF_3',multiplication('#skF_3',strong_iteration('#skF_4'))) != '#skF_3',
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_46148]) ).

tff(c_134990,plain,
    addition('#skF_3','#skF_3') != '#skF_3',
    inference(demodulation,[status(thm),theory(equality)],[c_134986,c_46150]) ).

tff(c_134994,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_134990]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : KLE148+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15  % 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
% 0.14/0.36  % Computer : n003.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 23:30:08 EDT 2023
% 0.22/0.37  % CPUTime  : 
% 34.71/21.33  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.80/21.35  
% 34.80/21.35  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 34.80/21.39  
% 34.80/21.39  Inference rules
% 34.80/21.39  ----------------------
% 34.80/21.39  #Ref     : 0
% 34.80/21.39  #Sup     : 34827
% 34.80/21.39  #Fact    : 0
% 34.80/21.39  #Define  : 0
% 34.80/21.39  #Split   : 27
% 34.80/21.39  #Chain   : 0
% 34.80/21.39  #Close   : 0
% 34.80/21.39  
% 34.80/21.39  Ordering : KBO
% 34.80/21.39  
% 34.80/21.39  Simplification rules
% 34.80/21.39  ----------------------
% 34.80/21.39  #Subsume      : 8456
% 34.80/21.39  #Demod        : 38517
% 34.80/21.39  #Tautology    : 10796
% 34.80/21.39  #SimpNegUnit  : 599
% 34.80/21.39  #BackRed      : 82
% 34.80/21.39  
% 34.80/21.39  #Partial instantiations: 0
% 34.80/21.39  #Strategies tried      : 1
% 34.80/21.39  
% 34.80/21.39  Timing (in seconds)
% 34.80/21.39  ----------------------
% 34.80/21.40  Preprocessing        : 0.50
% 34.80/21.40  Parsing              : 0.27
% 34.80/21.40  CNF conversion       : 0.03
% 34.80/21.40  Main loop            : 19.74
% 34.80/21.40  Inferencing          : 2.25
% 34.80/21.40  Reduction            : 13.02
% 34.80/21.40  Demodulation         : 11.53
% 34.80/21.40  BG Simplification    : 0.23
% 34.80/21.40  Subsumption          : 3.32
% 34.80/21.40  Abstraction          : 0.40
% 34.80/21.40  MUC search           : 0.00
% 34.80/21.40  Cooper               : 0.00
% 34.80/21.40  Total                : 20.32
% 34.80/21.40  Index Insertion      : 0.00
% 34.80/21.40  Index Deletion       : 0.00
% 34.80/21.40  Index Matching       : 0.00
% 34.80/21.40  BG Taut test         : 0.00
%------------------------------------------------------------------------------