TSTP Solution File: KLE081+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : KLE081+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 : n019.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 10:44:49 EDT 2023

% Result   : Theorem 50.94s 38.05s
% Output   : CNFRefutation 51.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   24
% Syntax   : Number of formulae    :  104 (  95 unt;   8 typ;   0 def)
%            Number of atoms       :   98 (  97 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :    4 (   2   ~;   0   |;   1   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    6 (   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    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :  142 (; 142   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ leq > multiplication > addition > #nlpp > domain > antidomain > zero > one > #skF_1

%Foreground sorts:

%Background operators:

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

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

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

tff(addition,type,
    addition: ( $i * $i ) > $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_77,axiom,
    ! [A] : ( multiplication(zero,A) = zero ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).

tff(f_65,axiom,
    ! [A] : ( multiplication(A,one) = A ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).

tff(f_120,axiom,
    domain(zero) = zero,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain4) ).

tff(f_132,negated_conjecture,
    ~ ! [X0] :
        ( ! [X1] :
            ( ( addition(domain(X1),antidomain(X1)) = one )
            & ( multiplication(domain(X1),antidomain(X1)) = zero ) )
       => ( multiplication(antidomain(X0),X0) = zero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

tff(f_54,axiom,
    ! [A,B] : ( addition(A,B) = addition(B,A) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).

tff(f_58,axiom,
    ! [A] : ( addition(A,zero) = A ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).

tff(f_67,axiom,
    ! [A] : ( multiplication(one,A) = A ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).

tff(f_119,axiom,
    ! [X0] : ( addition(domain(X0),one) = one ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain3) ).

tff(f_115,axiom,
    ! [X0] : ( addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain1) ).

tff(f_117,axiom,
    ! [X0,X1] : ( domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain2) ).

tff(f_122,axiom,
    ! [X0,X1] : ( domain(addition(X0,X1)) = addition(domain(X0),domain(X1)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain5) ).

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/KLE001+0.ax',left_distributivity) ).

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/KLE001+0.ax',right_distributivity) ).

tff(f_60,axiom,
    ! [A] : ( addition(A,A) = A ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).

tff(f_56,axiom,
    ! [C,B,A] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).

tff(f_63,axiom,
    ! [A,B,C] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).

tff(c_22,plain,
    ! [A_20] : ( multiplication(zero,A_20) = zero ),
    inference(cnfTransformation,[status(thm)],[f_77]) ).

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

tff(c_34,plain,
    domain(zero) = zero,
    inference(cnfTransformation,[status(thm)],[f_120]) ).

tff(c_307,plain,
    ! [X1_43] : ( addition(domain(X1_43),antidomain(X1_43)) = one ),
    inference(cnfTransformation,[status(thm)],[f_132]) ).

tff(c_326,plain,
    addition(zero,antidomain(zero)) = one,
    inference(superposition,[status(thm),theory(equality)],[c_34,c_307]) ).

tff(c_158,plain,
    ! [B_38,A_39] : ( addition(B_38,A_39) = addition(A_39,B_38) ),
    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_186,plain,
    ! [A_39] : ( addition(zero,A_39) = A_39 ),
    inference(superposition,[status(thm),theory(equality)],[c_158,c_6]) ).

tff(c_333,plain,
    antidomain(zero) = one,
    inference(superposition,[status(thm),theory(equality)],[c_326,c_186]) ).

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

tff(c_32,plain,
    ! [X0_26] : ( addition(domain(X0_26),one) = one ),
    inference(cnfTransformation,[status(thm)],[f_119]) ).

tff(c_214,plain,
    ! [X0_26] : ( addition(one,domain(X0_26)) = one ),
    inference(superposition,[status(thm),theory(equality)],[c_32,c_158]) ).

tff(c_1452,plain,
    ! [X0_74] : ( addition(X0_74,multiplication(domain(X0_74),X0_74)) = multiplication(domain(X0_74),X0_74) ),
    inference(cnfTransformation,[status(thm)],[f_115]) ).

tff(c_1507,plain,
    multiplication(domain(one),one) = addition(one,domain(one)),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_1452]) ).

tff(c_1520,plain,
    domain(one) = one,
    inference(demodulation,[status(thm),theory(equality)],[c_214,c_12,c_1507]) ).

tff(c_379,plain,
    ! [X0_49,X1_50] : ( domain(multiplication(X0_49,domain(X1_50))) = domain(multiplication(X0_49,X1_50)) ),
    inference(cnfTransformation,[status(thm)],[f_117]) ).

tff(c_408,plain,
    ! [X1_50] : ( domain(multiplication(one,X1_50)) = domain(domain(X1_50)) ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_379]) ).

tff(c_422,plain,
    ! [X1_50] : ( domain(domain(X1_50)) = domain(X1_50) ),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_408]) ).

tff(c_40,plain,
    ! [X1_30] : ( addition(domain(X1_30),antidomain(X1_30)) = one ),
    inference(cnfTransformation,[status(thm)],[f_132]) ).

tff(c_36,plain,
    ! [X0_27,X1_28] : ( addition(domain(X0_27),domain(X1_28)) = domain(addition(X0_27,X1_28)) ),
    inference(cnfTransformation,[status(thm)],[f_122]) ).

tff(c_42,plain,
    ! [X1_30] : ( multiplication(domain(X1_30),antidomain(X1_30)) = zero ),
    inference(cnfTransformation,[status(thm)],[f_132]) ).

tff(c_2660,plain,
    ! [A_90,C_91,B_92] : ( addition(multiplication(A_90,C_91),multiplication(B_92,C_91)) = multiplication(addition(A_90,B_92),C_91) ),
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_2717,plain,
    ! [A_90,X1_30] : ( multiplication(addition(A_90,domain(X1_30)),antidomain(X1_30)) = addition(multiplication(A_90,antidomain(X1_30)),zero) ),
    inference(superposition,[status(thm),theory(equality)],[c_42,c_2660]) ).

tff(c_19740,plain,
    ! [A_221,X1_222] : ( multiplication(addition(A_221,domain(X1_222)),antidomain(X1_222)) = multiplication(A_221,antidomain(X1_222)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_2717]) ).

tff(c_172005,plain,
    ! [X0_659,X1_660] : ( multiplication(domain(addition(X0_659,X1_660)),antidomain(X1_660)) = multiplication(domain(X0_659),antidomain(X1_660)) ),
    inference(superposition,[status(thm),theory(equality)],[c_36,c_19740]) ).

tff(c_172870,plain,
    ! [X1_30] : ( multiplication(domain(domain(X1_30)),antidomain(antidomain(X1_30))) = multiplication(domain(one),antidomain(antidomain(X1_30))) ),
    inference(superposition,[status(thm),theory(equality)],[c_40,c_172005]) ).

tff(c_173128,plain,
    ! [X1_30] : ( multiplication(domain(X1_30),antidomain(antidomain(X1_30))) = antidomain(antidomain(X1_30)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_1520,c_422,c_172870]) ).

tff(c_2100,plain,
    ! [A_82,B_83,C_84] : ( addition(multiplication(A_82,B_83),multiplication(A_82,C_84)) = multiplication(A_82,addition(B_83,C_84)) ),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_2146,plain,
    ! [X1_30,C_84] : ( multiplication(domain(X1_30),addition(antidomain(X1_30),C_84)) = addition(zero,multiplication(domain(X1_30),C_84)) ),
    inference(superposition,[status(thm),theory(equality)],[c_42,c_2100]) ).

tff(c_2195,plain,
    ! [X1_30,C_84] : ( multiplication(domain(X1_30),addition(antidomain(X1_30),C_84)) = multiplication(domain(X1_30),C_84) ),
    inference(demodulation,[status(thm),theory(equality)],[c_186,c_2146]) ).

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_574,plain,
    ! [X0_55,X1_56] : ( addition(domain(X0_55),domain(X1_56)) = domain(addition(X0_55,X1_56)) ),
    inference(cnfTransformation,[status(thm)],[f_122]) ).

tff(c_734,plain,
    ! [X1_60,X0_61] : ( addition(domain(X1_60),domain(X0_61)) = domain(addition(X0_61,X1_60)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_574]) ).

tff(c_762,plain,
    ! [X1_60,X1_50] : ( addition(domain(X1_60),domain(X1_50)) = domain(addition(domain(X1_50),X1_60)) ),
    inference(superposition,[status(thm),theory(equality)],[c_422,c_734]) ).

tff(c_22422,plain,
    ! [X1_237,X1_238] : ( domain(addition(domain(X1_237),X1_238)) = domain(addition(X1_238,X1_237)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_36,c_762]) ).

tff(c_22828,plain,
    ! [X1_30] : ( domain(addition(antidomain(X1_30),X1_30)) = domain(one) ),
    inference(superposition,[status(thm),theory(equality)],[c_40,c_22422]) ).

tff(c_22957,plain,
    ! [X1_239] : ( domain(addition(X1_239,antidomain(X1_239))) = one ),
    inference(demodulation,[status(thm),theory(equality)],[c_1520,c_2,c_22828]) ).

tff(c_30,plain,
    ! [X0_24,X1_25] : ( domain(multiplication(X0_24,domain(X1_25))) = domain(multiplication(X0_24,X1_25)) ),
    inference(cnfTransformation,[status(thm)],[f_117]) ).

tff(c_23152,plain,
    ! [X0_24,X1_239] : ( domain(multiplication(X0_24,addition(X1_239,antidomain(X1_239)))) = domain(multiplication(X0_24,one)) ),
    inference(superposition,[status(thm),theory(equality)],[c_22957,c_30]) ).

tff(c_114271,plain,
    ! [X0_531,X1_532] : ( domain(multiplication(X0_531,addition(X1_532,antidomain(X1_532)))) = domain(X0_531) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_23152]) ).

tff(c_114793,plain,
    ! [X1_30] : ( domain(multiplication(domain(X1_30),antidomain(antidomain(X1_30)))) = domain(domain(X1_30)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2195,c_114271]) ).

tff(c_114991,plain,
    ! [X1_30] : ( domain(multiplication(domain(X1_30),antidomain(antidomain(X1_30)))) = domain(X1_30) ),
    inference(demodulation,[status(thm),theory(equality)],[c_422,c_114793]) ).

tff(c_235860,plain,
    ! [X1_30] : ( domain(antidomain(antidomain(X1_30))) = domain(X1_30) ),
    inference(demodulation,[status(thm),theory(equality)],[c_173128,c_114991]) ).

tff(c_315,plain,
    ! [X1_43] : ( addition(antidomain(X1_43),domain(X1_43)) = one ),
    inference(superposition,[status(thm),theory(equality)],[c_307,c_2]) ).

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

tff(c_1018,plain,
    ! [A_64,B_65,C_66] : ( addition(addition(A_64,B_65),C_66) = addition(A_64,addition(B_65,C_66)) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_1117,plain,
    ! [A_67,C_68] : ( addition(A_67,addition(A_67,C_68)) = addition(A_67,C_68) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_1018]) ).

tff(c_1165,plain,
    ! [X1_43] : ( addition(antidomain(X1_43),domain(X1_43)) = addition(antidomain(X1_43),one) ),
    inference(superposition,[status(thm),theory(equality)],[c_315,c_1117]) ).

tff(c_1208,plain,
    ! [X1_43] : ( addition(one,antidomain(X1_43)) = one ),
    inference(demodulation,[status(thm),theory(equality)],[c_315,c_2,c_1165]) ).

tff(c_11442,plain,
    ! [B_167,A_168] : ( multiplication(addition(one,B_167),A_168) = addition(A_168,multiplication(B_167,A_168)) ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_2660]) ).

tff(c_11678,plain,
    ! [A_168,X1_43] : ( addition(A_168,multiplication(antidomain(X1_43),A_168)) = multiplication(one,A_168) ),
    inference(superposition,[status(thm),theory(equality)],[c_1208,c_11442]) ).

tff(c_11763,plain,
    ! [A_168,X1_43] : ( addition(A_168,multiplication(antidomain(X1_43),A_168)) = A_168 ),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_11678]) ).

tff(c_20288,plain,
    ! [X1_224,C_225] : ( multiplication(domain(X1_224),addition(antidomain(X1_224),C_225)) = multiplication(domain(X1_224),C_225) ),
    inference(demodulation,[status(thm),theory(equality)],[c_186,c_2146]) ).

tff(c_20375,plain,
    ! [X1_224,X1_43] : ( multiplication(domain(X1_224),multiplication(antidomain(X1_43),antidomain(X1_224))) = multiplication(domain(X1_224),antidomain(X1_224)) ),
    inference(superposition,[status(thm),theory(equality)],[c_11763,c_20288]) ).

tff(c_98995,plain,
    ! [X1_490,X1_491] : ( multiplication(domain(X1_490),multiplication(antidomain(X1_491),antidomain(X1_490))) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_42,c_20375]) ).

tff(c_10430,plain,
    ! [A_160,A_161] : ( multiplication(addition(A_160,one),A_161) = addition(multiplication(A_160,A_161),A_161) ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_2660]) ).

tff(c_10688,plain,
    ! [X0_26,A_161] : ( addition(multiplication(domain(X0_26),A_161),A_161) = multiplication(one,A_161) ),
    inference(superposition,[status(thm),theory(equality)],[c_32,c_10430]) ).

tff(c_10753,plain,
    ! [X0_162,A_163] : ( addition(multiplication(domain(X0_162),A_163),A_163) = A_163 ),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_10688]) ).

tff(c_2729,plain,
    ! [A_90,A_12] : ( multiplication(addition(A_90,one),A_12) = addition(multiplication(A_90,A_12),A_12) ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_2660]) ).

tff(c_10760,plain,
    ! [X0_162,A_12] : ( addition(multiplication(multiplication(domain(X0_162),one),A_12),A_12) = multiplication(one,A_12) ),
    inference(superposition,[status(thm),theory(equality)],[c_10753,c_2729]) ).

tff(c_10981,plain,
    ! [A_12,X0_162] : ( addition(A_12,multiplication(domain(X0_162),A_12)) = A_12 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_14,c_12,c_10760]) ).

tff(c_28,plain,
    ! [X0_23] : ( addition(X0_23,multiplication(domain(X0_23),X0_23)) = multiplication(domain(X0_23),X0_23) ),
    inference(cnfTransformation,[status(thm)],[f_115]) ).

tff(c_11281,plain,
    ! [X0_166] : ( multiplication(domain(X0_166),X0_166) = X0_166 ),
    inference(demodulation,[status(thm),theory(equality)],[c_10981,c_28]) ).

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_11341,plain,
    ! [X0_166,C_10] : ( multiplication(domain(X0_166),multiplication(X0_166,C_10)) = multiplication(X0_166,C_10) ),
    inference(superposition,[status(thm),theory(equality)],[c_11281,c_10]) ).

tff(c_100273,plain,
    ! [X1_494] : ( multiplication(antidomain(X1_494),antidomain(antidomain(X1_494))) = zero ),
    inference(superposition,[status(thm),theory(equality)],[c_98995,c_11341]) ).

tff(c_1495,plain,
    ! [X0_24,X1_25] : ( addition(multiplication(X0_24,domain(X1_25)),multiplication(domain(multiplication(X0_24,X1_25)),multiplication(X0_24,domain(X1_25)))) = multiplication(domain(multiplication(X0_24,domain(X1_25))),multiplication(X0_24,domain(X1_25))) ),
    inference(superposition,[status(thm),theory(equality)],[c_30,c_1452]) ).

tff(c_1517,plain,
    ! [X0_24,X1_25] : ( addition(multiplication(X0_24,domain(X1_25)),multiplication(domain(multiplication(X0_24,X1_25)),multiplication(X0_24,domain(X1_25)))) = multiplication(domain(multiplication(X0_24,X1_25)),multiplication(X0_24,domain(X1_25))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_30,c_1495]) ).

tff(c_61205,plain,
    ! [X0_24,X1_25] : ( multiplication(domain(multiplication(X0_24,X1_25)),multiplication(X0_24,domain(X1_25))) = multiplication(X0_24,domain(X1_25)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_10981,c_1517]) ).

tff(c_100311,plain,
    ! [X1_494] : ( multiplication(domain(zero),multiplication(antidomain(X1_494),domain(antidomain(antidomain(X1_494))))) = multiplication(antidomain(X1_494),domain(antidomain(antidomain(X1_494)))) ),
    inference(superposition,[status(thm),theory(equality)],[c_100273,c_61205]) ).

tff(c_100534,plain,
    ! [X1_494] : ( multiplication(antidomain(X1_494),domain(antidomain(antidomain(X1_494)))) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_34,c_100311]) ).

tff(c_236786,plain,
    ! [X1_756] : ( multiplication(antidomain(X1_756),domain(X1_756)) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_235860,c_100534]) ).

tff(c_396,plain,
    ! [X0_49,X1_50] : ( multiplication(domain(multiplication(X0_49,X1_50)),antidomain(multiplication(X0_49,domain(X1_50)))) = zero ),
    inference(superposition,[status(thm),theory(equality)],[c_379,c_42]) ).

tff(c_236998,plain,
    ! [X1_756] : ( multiplication(domain(multiplication(antidomain(X1_756),X1_756)),antidomain(zero)) = zero ),
    inference(superposition,[status(thm),theory(equality)],[c_236786,c_396]) ).

tff(c_237496,plain,
    ! [X1_757] : ( domain(multiplication(antidomain(X1_757),X1_757)) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_333,c_236998]) ).

tff(c_11034,plain,
    ! [X0_23] : ( multiplication(domain(X0_23),X0_23) = X0_23 ),
    inference(demodulation,[status(thm),theory(equality)],[c_10981,c_28]) ).

tff(c_238066,plain,
    ! [X1_757] : ( multiplication(zero,multiplication(antidomain(X1_757),X1_757)) = multiplication(antidomain(X1_757),X1_757) ),
    inference(superposition,[status(thm),theory(equality)],[c_237496,c_11034]) ).

tff(c_238479,plain,
    ! [X1_757] : ( multiplication(antidomain(X1_757),X1_757) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_238066]) ).

tff(c_38,plain,
    multiplication(antidomain('#skF_1'),'#skF_1') != zero,
    inference(cnfTransformation,[status(thm)],[f_132]) ).

tff(c_238552,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_238479,c_38]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : KLE081+1 : 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
% 0.15/0.37  % Computer : n019.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Thu Aug  3 23:32:31 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 50.94/38.05  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 50.94/38.07  
% 50.94/38.07  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 51.11/38.11  
% 51.11/38.11  Inference rules
% 51.11/38.11  ----------------------
% 51.11/38.11  #Ref     : 0
% 51.11/38.11  #Sup     : 60683
% 51.11/38.11  #Fact    : 0
% 51.11/38.11  #Define  : 0
% 51.11/38.11  #Split   : 0
% 51.11/38.11  #Chain   : 0
% 51.11/38.11  #Close   : 0
% 51.11/38.11  
% 51.11/38.11  Ordering : KBO
% 51.11/38.11  
% 51.11/38.11  Simplification rules
% 51.11/38.11  ----------------------
% 51.11/38.11  #Subsume      : 1457
% 51.11/38.11  #Demod        : 115344
% 51.11/38.11  #Tautology    : 37650
% 51.11/38.11  #SimpNegUnit  : 0
% 51.11/38.11  #BackRed      : 49
% 51.11/38.11  
% 51.11/38.11  #Partial instantiations: 0
% 51.11/38.11  #Strategies tried      : 1
% 51.11/38.11  
% 51.11/38.11  Timing (in seconds)
% 51.11/38.11  ----------------------
% 51.11/38.11  Preprocessing        : 0.49
% 51.11/38.11  Parsing              : 0.26
% 51.11/38.11  CNF conversion       : 0.03
% 51.11/38.11  Main loop            : 36.52
% 51.11/38.11  Inferencing          : 2.77
% 51.11/38.11  Reduction            : 25.68
% 51.11/38.11  Demodulation         : 24.26
% 51.11/38.11  BG Simplification    : 0.27
% 51.11/38.11  Subsumption          : 6.22
% 51.11/38.11  Abstraction          : 0.65
% 51.11/38.11  MUC search           : 0.00
% 51.11/38.11  Cooper               : 0.00
% 51.11/38.11  Total                : 37.08
% 51.11/38.11  Index Insertion      : 0.00
% 51.11/38.11  Index Deletion       : 0.00
% 51.11/38.11  Index Matching       : 0.00
% 51.11/38.11  BG Taut test         : 0.00
%------------------------------------------------------------------------------