TSTP Solution File: BOO014-3 by E-SAT---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1
% Problem  : BOO014-3 : TPTP v8.1.2. Bugfixed v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n023.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 2400s
% WCLimit  : 300s
% DateTime : Tue Oct 10 17:18:31 EDT 2023

% Result   : Unsatisfiable 9.00s 1.55s
% Output   : CNFRefutation 9.00s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   36
%            Number of leaves      :   24
% Syntax   : Number of clauses     :  151 (  89 unt;   0 nHn; 104 RR)
%            Number of literals    :  281 (  46 equ; 134 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :  285 (  14 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(distributivity8,axiom,
    ( sum(X6,X2,X7)
    | ~ sum(X1,X2,X3)
    | ~ sum(X4,X2,X5)
    | ~ product(X1,X4,X6)
    | ~ product(X3,X5,X7) ),
    file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',distributivity8) ).

cnf(multiplicative_identity1,axiom,
    product(multiplicative_identity,X1,X1),
    file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',multiplicative_identity1) ).

cnf(multiplicative_identity2,axiom,
    product(X1,multiplicative_identity,X1),
    file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',multiplicative_identity2) ).

cnf(addition_is_well_defined,axiom,
    ( X3 = X4
    | ~ sum(X1,X2,X3)
    | ~ sum(X1,X2,X4) ),
    file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',addition_is_well_defined) ).

cnf(additive_inverse1,axiom,
    sum(inverse(X1),X1,multiplicative_identity),
    file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',additive_inverse1) ).

cnf(closure_of_addition,axiom,
    sum(X1,X2,add(X1,X2)),
    file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',closure_of_addition) ).

cnf(commutativity_of_addition,axiom,
    ( sum(X2,X1,X3)
    | ~ sum(X1,X2,X3) ),
    file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',commutativity_of_addition) ).

cnf(inverse_is_self_cancelling,axiom,
    inverse(inverse(X1)) = X1,
    file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',inverse_is_self_cancelling) ).

cnf(distributivity1,axiom,
    ( sum(X3,X5,X7)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X5)
    | ~ sum(X2,X4,X6)
    | ~ product(X1,X6,X7) ),
    file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',distributivity1) ).

cnf(multiplication_is_well_defined,axiom,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',multiplication_is_well_defined) ).

cnf(closure_of_multiplication,axiom,
    product(X1,X2,multiply(X1,X2)),
    file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',closure_of_multiplication) ).

cnf(commutativity_of_multiplication,axiom,
    ( product(X2,X1,X3)
    | ~ product(X1,X2,X3) ),
    file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',commutativity_of_multiplication) ).

cnf(additive_identity2,axiom,
    sum(X1,additive_identity,X1),
    file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',additive_identity2) ).

cnf(x_inverse_times_y_inverse,hypothesis,
    product(inverse(x),inverse(y),x_inverse_times_y_inverse),
    file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',x_inverse_times_y_inverse) ).

cnf(distributivity7,axiom,
    ( product(X3,X5,X7)
    | ~ sum(X1,X2,X3)
    | ~ sum(X4,X2,X5)
    | ~ product(X1,X4,X6)
    | ~ sum(X6,X2,X7) ),
    file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',distributivity7) ).

cnf(additive_identity1,axiom,
    sum(additive_identity,X1,X1),
    file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',additive_identity1) ).

cnf(additive_inverse2,axiom,
    sum(X1,inverse(X1),multiplicative_identity),
    file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',additive_inverse2) ).

cnf(x_plus_y,hypothesis,
    sum(x,y,x_plus_y),
    file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',x_plus_y) ).

cnf(multiplicative_inverse1,axiom,
    product(inverse(X1),X1,additive_identity),
    file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',multiplicative_inverse1) ).

cnf(distributivity6,axiom,
    ( sum(X1,X6,X7)
    | ~ sum(X1,X2,X3)
    | ~ sum(X1,X4,X5)
    | ~ product(X2,X4,X6)
    | ~ product(X3,X5,X7) ),
    file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',distributivity6) ).

cnf(distributivity4,axiom,
    ( product(X6,X2,X7)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X5)
    | ~ sum(X1,X4,X6)
    | ~ sum(X3,X5,X7) ),
    file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',distributivity4) ).

cnf(multiplicative_inverse2,axiom,
    product(X1,inverse(X1),additive_identity),
    file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',multiplicative_inverse2) ).

cnf(inverse_is_unique,axiom,
    ( X2 = X3
    | ~ sum(X1,X2,multiplicative_identity)
    | ~ sum(X1,X3,multiplicative_identity)
    | ~ product(X1,X2,additive_identity)
    | ~ product(X1,X3,additive_identity) ),
    file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',inverse_is_unique) ).

cnf(prove_equation,negated_conjecture,
    inverse(x_plus_y) != x_inverse_times_y_inverse,
    file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',prove_equation) ).

cnf(c_0_24,axiom,
    ( sum(X6,X2,X7)
    | ~ sum(X1,X2,X3)
    | ~ sum(X4,X2,X5)
    | ~ product(X1,X4,X6)
    | ~ product(X3,X5,X7) ),
    distributivity8 ).

cnf(c_0_25,axiom,
    product(multiplicative_identity,X1,X1),
    multiplicative_identity1 ).

cnf(c_0_26,plain,
    ( sum(X1,X2,X3)
    | ~ product(X4,X5,X1)
    | ~ sum(X4,X2,multiplicative_identity)
    | ~ sum(X5,X2,X3) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_27,axiom,
    product(X1,multiplicative_identity,X1),
    multiplicative_identity2 ).

cnf(c_0_28,axiom,
    ( X3 = X4
    | ~ sum(X1,X2,X3)
    | ~ sum(X1,X2,X4) ),
    addition_is_well_defined ).

cnf(c_0_29,axiom,
    sum(inverse(X1),X1,multiplicative_identity),
    additive_inverse1 ).

cnf(c_0_30,plain,
    ( sum(X1,X2,X3)
    | ~ sum(X1,X2,multiplicative_identity)
    | ~ sum(multiplicative_identity,X2,X3) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_31,axiom,
    sum(X1,X2,add(X1,X2)),
    closure_of_addition ).

cnf(c_0_32,axiom,
    ( sum(X2,X1,X3)
    | ~ sum(X1,X2,X3) ),
    commutativity_of_addition ).

cnf(c_0_33,plain,
    ( X1 = multiplicative_identity
    | ~ sum(inverse(X2),X2,X1) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_34,plain,
    ( sum(inverse(X1),X1,X2)
    | ~ sum(multiplicative_identity,X1,X2) ),
    inference(spm,[status(thm)],[c_0_30,c_0_29]) ).

cnf(c_0_35,plain,
    ( X1 = add(X2,X3)
    | ~ sum(X2,X3,X1) ),
    inference(spm,[status(thm)],[c_0_28,c_0_31]) ).

cnf(c_0_36,plain,
    sum(X1,X2,add(X2,X1)),
    inference(spm,[status(thm)],[c_0_32,c_0_31]) ).

cnf(c_0_37,plain,
    add(inverse(X1),X1) = multiplicative_identity,
    inference(spm,[status(thm)],[c_0_33,c_0_31]) ).

cnf(c_0_38,axiom,
    inverse(inverse(X1)) = X1,
    inverse_is_self_cancelling ).

cnf(c_0_39,plain,
    sum(inverse(X1),X1,add(multiplicative_identity,X1)),
    inference(spm,[status(thm)],[c_0_34,c_0_31]) ).

cnf(c_0_40,plain,
    add(X1,X2) = add(X2,X1),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_41,plain,
    add(X1,inverse(X1)) = multiplicative_identity,
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_42,axiom,
    ( sum(X3,X5,X7)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X5)
    | ~ sum(X2,X4,X6)
    | ~ product(X1,X6,X7) ),
    distributivity1 ).

cnf(c_0_43,plain,
    add(multiplicative_identity,X1) = multiplicative_identity,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_39]),c_0_40]),c_0_41]) ).

cnf(c_0_44,plain,
    ( sum(X1,X2,X3)
    | ~ product(X3,X4,X2)
    | ~ product(X3,X5,X1)
    | ~ sum(X5,X4,multiplicative_identity) ),
    inference(spm,[status(thm)],[c_0_42,c_0_27]) ).

cnf(c_0_45,plain,
    sum(X1,multiplicative_identity,multiplicative_identity),
    inference(spm,[status(thm)],[c_0_36,c_0_43]) ).

cnf(c_0_46,axiom,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    multiplication_is_well_defined ).

cnf(c_0_47,axiom,
    product(X1,X2,multiply(X1,X2)),
    closure_of_multiplication ).

cnf(c_0_48,axiom,
    ( product(X2,X1,X3)
    | ~ product(X1,X2,X3) ),
    commutativity_of_multiplication ).

cnf(c_0_49,axiom,
    sum(X1,additive_identity,X1),
    additive_identity2 ).

cnf(c_0_50,plain,
    ( sum(X1,X2,X2)
    | ~ product(X2,X3,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_27]),c_0_45])]) ).

cnf(c_0_51,plain,
    ( X1 = multiply(X2,X3)
    | ~ product(X2,X3,X1) ),
    inference(spm,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_52,plain,
    product(X1,X2,multiply(X2,X1)),
    inference(spm,[status(thm)],[c_0_48,c_0_47]) ).

cnf(c_0_53,plain,
    ( X1 = X2
    | ~ sum(X2,additive_identity,X1) ),
    inference(spm,[status(thm)],[c_0_28,c_0_49]) ).

cnf(c_0_54,plain,
    sum(multiply(X1,X2),X1,X1),
    inference(spm,[status(thm)],[c_0_50,c_0_47]) ).

cnf(c_0_55,hypothesis,
    product(inverse(x),inverse(y),x_inverse_times_y_inverse),
    x_inverse_times_y_inverse ).

cnf(c_0_56,axiom,
    ( product(X3,X5,X7)
    | ~ sum(X1,X2,X3)
    | ~ sum(X4,X2,X5)
    | ~ product(X1,X4,X6)
    | ~ sum(X6,X2,X7) ),
    distributivity7 ).

cnf(c_0_57,plain,
    multiply(X1,X2) = multiply(X2,X1),
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_58,plain,
    multiply(additive_identity,X1) = additive_identity,
    inference(spm,[status(thm)],[c_0_53,c_0_54]) ).

cnf(c_0_59,hypothesis,
    product(inverse(y),inverse(x),x_inverse_times_y_inverse),
    inference(spm,[status(thm)],[c_0_48,c_0_55]) ).

cnf(c_0_60,plain,
    ( product(X1,X2,X3)
    | ~ sum(multiply(X4,X5),X6,X3)
    | ~ sum(X5,X6,X2)
    | ~ sum(X4,X6,X1) ),
    inference(spm,[status(thm)],[c_0_56,c_0_47]) ).

cnf(c_0_61,axiom,
    sum(additive_identity,X1,X1),
    additive_identity1 ).

cnf(c_0_62,plain,
    multiply(X1,additive_identity) = additive_identity,
    inference(spm,[status(thm)],[c_0_57,c_0_58]) ).

cnf(c_0_63,hypothesis,
    sum(x_inverse_times_y_inverse,inverse(y),inverse(y)),
    inference(spm,[status(thm)],[c_0_50,c_0_59]) ).

cnf(c_0_64,plain,
    ( product(X1,X2,X3)
    | ~ sum(additive_identity,X2,X3)
    | ~ sum(X4,X2,X1) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]) ).

cnf(c_0_65,hypothesis,
    sum(inverse(y),x_inverse_times_y_inverse,inverse(y)),
    inference(spm,[status(thm)],[c_0_32,c_0_63]) ).

cnf(c_0_66,plain,
    ( X1 = X2
    | ~ sum(additive_identity,X2,X1) ),
    inference(spm,[status(thm)],[c_0_28,c_0_61]) ).

cnf(c_0_67,hypothesis,
    ( product(inverse(y),x_inverse_times_y_inverse,X1)
    | ~ sum(additive_identity,x_inverse_times_y_inverse,X1) ),
    inference(spm,[status(thm)],[c_0_64,c_0_65]) ).

cnf(c_0_68,plain,
    add(additive_identity,X1) = X1,
    inference(spm,[status(thm)],[c_0_66,c_0_31]) ).

cnf(c_0_69,plain,
    ( sum(X1,X2,X3)
    | ~ product(X4,X5,X1)
    | ~ sum(X5,X2,multiplicative_identity)
    | ~ sum(X4,X2,X3) ),
    inference(spm,[status(thm)],[c_0_24,c_0_27]) ).

cnf(c_0_70,hypothesis,
    product(inverse(y),x_inverse_times_y_inverse,x_inverse_times_y_inverse),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_31]),c_0_68]) ).

cnf(c_0_71,hypothesis,
    ( sum(x_inverse_times_y_inverse,X1,X2)
    | ~ sum(inverse(y),X1,X2)
    | ~ sum(x_inverse_times_y_inverse,X1,multiplicative_identity) ),
    inference(spm,[status(thm)],[c_0_69,c_0_70]) ).

cnf(c_0_72,axiom,
    sum(X1,inverse(X1),multiplicative_identity),
    additive_inverse2 ).

cnf(c_0_73,hypothesis,
    ( sum(x_inverse_times_y_inverse,inverse(x_inverse_times_y_inverse),X1)
    | ~ sum(inverse(y),inverse(x_inverse_times_y_inverse),X1) ),
    inference(spm,[status(thm)],[c_0_71,c_0_72]) ).

cnf(c_0_74,hypothesis,
    sum(x_inverse_times_y_inverse,inverse(x_inverse_times_y_inverse),add(inverse(y),inverse(x_inverse_times_y_inverse))),
    inference(spm,[status(thm)],[c_0_73,c_0_31]) ).

cnf(c_0_75,plain,
    ( sum(X1,X2,multiply(X3,X4))
    | ~ product(X5,X6,X1)
    | ~ sum(X6,X2,X4)
    | ~ sum(X5,X2,X3) ),
    inference(spm,[status(thm)],[c_0_24,c_0_47]) ).

cnf(c_0_76,hypothesis,
    add(inverse(y),inverse(x_inverse_times_y_inverse)) = multiplicative_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_74]),c_0_41]) ).

cnf(c_0_77,plain,
    ( X1 = X2
    | ~ product(X2,multiplicative_identity,X1) ),
    inference(spm,[status(thm)],[c_0_46,c_0_27]) ).

cnf(c_0_78,hypothesis,
    ( sum(x_inverse_times_y_inverse,X1,multiply(X2,X3))
    | ~ sum(inverse(y),X1,X3)
    | ~ sum(inverse(x),X1,X2) ),
    inference(spm,[status(thm)],[c_0_75,c_0_55]) ).

cnf(c_0_79,hypothesis,
    sum(inverse(y),inverse(x_inverse_times_y_inverse),multiplicative_identity),
    inference(spm,[status(thm)],[c_0_31,c_0_76]) ).

cnf(c_0_80,plain,
    multiply(X1,multiplicative_identity) = X1,
    inference(spm,[status(thm)],[c_0_77,c_0_47]) ).

cnf(c_0_81,hypothesis,
    ( sum(x_inverse_times_y_inverse,inverse(x_inverse_times_y_inverse),X1)
    | ~ sum(inverse(x),inverse(x_inverse_times_y_inverse),X1) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]) ).

cnf(c_0_82,hypothesis,
    sum(x,y,x_plus_y),
    x_plus_y ).

cnf(c_0_83,plain,
    ( product(add(X1,X2),X2,X3)
    | ~ sum(additive_identity,X2,X3) ),
    inference(spm,[status(thm)],[c_0_64,c_0_31]) ).

cnf(c_0_84,axiom,
    product(inverse(X1),X1,additive_identity),
    multiplicative_inverse1 ).

cnf(c_0_85,hypothesis,
    sum(x_inverse_times_y_inverse,inverse(x_inverse_times_y_inverse),add(inverse(x),inverse(x_inverse_times_y_inverse))),
    inference(spm,[status(thm)],[c_0_81,c_0_31]) ).

cnf(c_0_86,hypothesis,
    sum(y,x,x_plus_y),
    inference(spm,[status(thm)],[c_0_32,c_0_82]) ).

cnf(c_0_87,plain,
    add(X1,multiply(X1,X2)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_54]),c_0_40]) ).

cnf(c_0_88,plain,
    product(add(X1,X2),X2,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_31]),c_0_68]) ).

cnf(c_0_89,plain,
    ( sum(additive_identity,X1,X2)
    | ~ sum(inverse(X3),X1,multiplicative_identity)
    | ~ sum(X3,X1,X2) ),
    inference(spm,[status(thm)],[c_0_26,c_0_84]) ).

cnf(c_0_90,hypothesis,
    add(inverse(x),inverse(x_inverse_times_y_inverse)) = multiplicative_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_85]),c_0_41]) ).

cnf(c_0_91,hypothesis,
    ( product(x_plus_y,x,X1)
    | ~ sum(additive_identity,x,X1) ),
    inference(spm,[status(thm)],[c_0_64,c_0_86]) ).

cnf(c_0_92,plain,
    add(X1,multiply(X2,X1)) = X1,
    inference(spm,[status(thm)],[c_0_87,c_0_57]) ).

cnf(c_0_93,plain,
    multiply(X1,add(X2,X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_88]),c_0_57]) ).

cnf(c_0_94,plain,
    ( sum(additive_identity,X1,add(X2,X1))
    | ~ sum(inverse(X2),X1,multiplicative_identity) ),
    inference(spm,[status(thm)],[c_0_89,c_0_31]) ).

cnf(c_0_95,hypothesis,
    sum(inverse(x),inverse(x_inverse_times_y_inverse),multiplicative_identity),
    inference(spm,[status(thm)],[c_0_31,c_0_90]) ).

cnf(c_0_96,hypothesis,
    product(x_plus_y,x,x),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_31]),c_0_68]) ).

cnf(c_0_97,plain,
    sum(X1,multiply(X2,X1),X1),
    inference(spm,[status(thm)],[c_0_31,c_0_92]) ).

cnf(c_0_98,plain,
    multiply(X1,add(X1,X2)) = X1,
    inference(spm,[status(thm)],[c_0_93,c_0_40]) ).

cnf(c_0_99,hypothesis,
    sum(additive_identity,inverse(x_inverse_times_y_inverse),add(x,inverse(x_inverse_times_y_inverse))),
    inference(spm,[status(thm)],[c_0_94,c_0_95]) ).

cnf(c_0_100,hypothesis,
    sum(additive_identity,inverse(x_inverse_times_y_inverse),add(y,inverse(x_inverse_times_y_inverse))),
    inference(spm,[status(thm)],[c_0_94,c_0_79]) ).

cnf(c_0_101,hypothesis,
    ( sum(x,X1,multiply(X2,X3))
    | ~ sum(x,X1,X3)
    | ~ sum(x_plus_y,X1,X2) ),
    inference(spm,[status(thm)],[c_0_75,c_0_96]) ).

cnf(c_0_102,plain,
    sum(add(X1,X2),X1,add(X1,X2)),
    inference(spm,[status(thm)],[c_0_97,c_0_98]) ).

cnf(c_0_103,hypothesis,
    add(x,inverse(x_inverse_times_y_inverse)) = inverse(x_inverse_times_y_inverse),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_99]),c_0_68]) ).

cnf(c_0_104,hypothesis,
    add(y,inverse(x_inverse_times_y_inverse)) = inverse(x_inverse_times_y_inverse),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_100]),c_0_68]) ).

cnf(c_0_105,hypothesis,
    ( sum(x,inverse(x),X1)
    | ~ sum(x_plus_y,inverse(x),X1) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_72]),c_0_80]) ).

cnf(c_0_106,hypothesis,
    ( product(X1,x_plus_y,X2)
    | ~ sum(multiply(X3,y),x,X2)
    | ~ sum(X3,x,X1) ),
    inference(spm,[status(thm)],[c_0_60,c_0_86]) ).

cnf(c_0_107,hypothesis,
    sum(inverse(x_inverse_times_y_inverse),x,inverse(x_inverse_times_y_inverse)),
    inference(spm,[status(thm)],[c_0_102,c_0_103]) ).

cnf(c_0_108,hypothesis,
    multiply(y,inverse(x_inverse_times_y_inverse)) = y,
    inference(spm,[status(thm)],[c_0_98,c_0_104]) ).

cnf(c_0_109,hypothesis,
    ( X1 = x_plus_y
    | ~ sum(x,y,X1) ),
    inference(spm,[status(thm)],[c_0_28,c_0_82]) ).

cnf(c_0_110,axiom,
    ( sum(X1,X6,X7)
    | ~ sum(X1,X2,X3)
    | ~ sum(X1,X4,X5)
    | ~ product(X2,X4,X6)
    | ~ product(X3,X5,X7) ),
    distributivity6 ).

cnf(c_0_111,hypothesis,
    sum(x,inverse(x),add(x_plus_y,inverse(x))),
    inference(spm,[status(thm)],[c_0_105,c_0_31]) ).

cnf(c_0_112,axiom,
    ( product(X6,X2,X7)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X5)
    | ~ sum(X1,X4,X6)
    | ~ sum(X3,X5,X7) ),
    distributivity4 ).

cnf(c_0_113,axiom,
    product(X1,inverse(X1),additive_identity),
    multiplicative_inverse2 ).

cnf(c_0_114,hypothesis,
    ( product(inverse(x_inverse_times_y_inverse),x_plus_y,X1)
    | ~ sum(y,x,X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_57]),c_0_108]) ).

cnf(c_0_115,hypothesis,
    add(x,y) = x_plus_y,
    inference(spm,[status(thm)],[c_0_109,c_0_31]) ).

cnf(c_0_116,plain,
    ( sum(X1,X2,multiply(X3,X4))
    | ~ product(X5,X6,X2)
    | ~ sum(X1,X6,X4)
    | ~ sum(X1,X5,X3) ),
    inference(spm,[status(thm)],[c_0_110,c_0_47]) ).

cnf(c_0_117,hypothesis,
    add(x_plus_y,inverse(x)) = multiplicative_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_111]),c_0_41]) ).

cnf(c_0_118,plain,
    ( product(X1,inverse(X2),X3)
    | ~ product(X4,inverse(X2),X5)
    | ~ sum(X5,additive_identity,X3)
    | ~ sum(X4,X2,X1) ),
    inference(spm,[status(thm)],[c_0_112,c_0_113]) ).

cnf(c_0_119,hypothesis,
    product(inverse(x_inverse_times_y_inverse),x_plus_y,x_plus_y),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_31]),c_0_40]),c_0_115]) ).

cnf(c_0_120,hypothesis,
    ( sum(X1,x_inverse_times_y_inverse,multiply(X2,X3))
    | ~ sum(X1,inverse(x),X3)
    | ~ sum(X1,inverse(y),X2) ),
    inference(spm,[status(thm)],[c_0_116,c_0_59]) ).

cnf(c_0_121,hypothesis,
    sum(x_plus_y,inverse(x),multiplicative_identity),
    inference(spm,[status(thm)],[c_0_31,c_0_117]) ).

cnf(c_0_122,plain,
    ( product(X1,inverse(X2),X3)
    | ~ sum(multiply(X4,inverse(X2)),additive_identity,X3)
    | ~ sum(X4,X2,X1) ),
    inference(spm,[status(thm)],[c_0_118,c_0_47]) ).

cnf(c_0_123,hypothesis,
    sum(x_plus_y,inverse(x_inverse_times_y_inverse),inverse(x_inverse_times_y_inverse)),
    inference(spm,[status(thm)],[c_0_50,c_0_119]) ).

cnf(c_0_124,plain,
    ( X1 = additive_identity
    | ~ product(inverse(X2),X2,X1) ),
    inference(spm,[status(thm)],[c_0_46,c_0_84]) ).

cnf(c_0_125,hypothesis,
    ( sum(x_plus_y,x_inverse_times_y_inverse,X1)
    | ~ sum(x_plus_y,inverse(y),X1) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_80]) ).

cnf(c_0_126,hypothesis,
    ( product(inverse(x_inverse_times_y_inverse),x_inverse_times_y_inverse,X1)
    | ~ sum(multiply(x_plus_y,x_inverse_times_y_inverse),additive_identity,X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_38]),c_0_38]) ).

cnf(c_0_127,plain,
    add(X1,additive_identity) = X1,
    inference(spm,[status(thm)],[c_0_53,c_0_31]) ).

cnf(c_0_128,plain,
    multiply(inverse(X1),X1) = additive_identity,
    inference(spm,[status(thm)],[c_0_124,c_0_47]) ).

cnf(c_0_129,hypothesis,
    sum(x_plus_y,x_inverse_times_y_inverse,add(x_plus_y,inverse(y))),
    inference(spm,[status(thm)],[c_0_125,c_0_31]) ).

cnf(c_0_130,hypothesis,
    ( product(x_plus_y,y,X1)
    | ~ sum(additive_identity,y,X1) ),
    inference(spm,[status(thm)],[c_0_64,c_0_82]) ).

cnf(c_0_131,hypothesis,
    product(inverse(x_inverse_times_y_inverse),x_inverse_times_y_inverse,multiply(x_plus_y,x_inverse_times_y_inverse)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_31]),c_0_127]) ).

cnf(c_0_132,plain,
    multiply(X1,inverse(X1)) = additive_identity,
    inference(spm,[status(thm)],[c_0_128,c_0_38]) ).

cnf(c_0_133,plain,
    ( sum(multiply(X1,X2),X3,multiply(X4,X5))
    | ~ sum(X2,X3,X5)
    | ~ sum(X1,X3,X4) ),
    inference(spm,[status(thm)],[c_0_75,c_0_47]) ).

cnf(c_0_134,hypothesis,
    add(x_plus_y,inverse(y)) = add(x_plus_y,x_inverse_times_y_inverse),
    inference(spm,[status(thm)],[c_0_35,c_0_129]) ).

cnf(c_0_135,hypothesis,
    product(x_plus_y,y,y),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_31]),c_0_68]) ).

cnf(c_0_136,axiom,
    ( X2 = X3
    | ~ sum(X1,X2,multiplicative_identity)
    | ~ sum(X1,X3,multiplicative_identity)
    | ~ product(X1,X2,additive_identity)
    | ~ product(X1,X3,additive_identity) ),
    inverse_is_unique ).

cnf(c_0_137,hypothesis,
    multiply(x_plus_y,x_inverse_times_y_inverse) = additive_identity,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_131]),c_0_57]),c_0_132]) ).

cnf(c_0_138,plain,
    ( sum(multiply(X1,inverse(X2)),X2,X3)
    | ~ sum(X1,X2,X3) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_29]),c_0_80]) ).

cnf(c_0_139,hypothesis,
    sum(x_plus_y,inverse(y),add(x_plus_y,x_inverse_times_y_inverse)),
    inference(spm,[status(thm)],[c_0_31,c_0_134]) ).

cnf(c_0_140,hypothesis,
    multiply(y,x_plus_y) = y,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_135]),c_0_57]) ).

cnf(c_0_141,plain,
    ( sum(X1,X2,X3)
    | ~ product(X4,X5,X2)
    | ~ sum(X1,X4,multiplicative_identity)
    | ~ sum(X1,X5,X3) ),
    inference(spm,[status(thm)],[c_0_110,c_0_25]) ).

cnf(c_0_142,plain,
    ( X1 = inverse(X2)
    | ~ product(X2,X1,additive_identity)
    | ~ sum(X2,X1,multiplicative_identity) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_113]),c_0_72])]) ).

cnf(c_0_143,hypothesis,
    product(x_plus_y,x_inverse_times_y_inverse,additive_identity),
    inference(spm,[status(thm)],[c_0_47,c_0_137]) ).

cnf(c_0_144,negated_conjecture,
    inverse(x_plus_y) != x_inverse_times_y_inverse,
    prove_equation ).

cnf(c_0_145,hypothesis,
    sum(y,inverse(y),add(x_plus_y,x_inverse_times_y_inverse)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_38]),c_0_57]),c_0_140]) ).

cnf(c_0_146,hypothesis,
    ( sum(X1,x_inverse_times_y_inverse,X2)
    | ~ sum(X1,inverse(y),multiplicative_identity)
    | ~ sum(X1,inverse(x),X2) ),
    inference(spm,[status(thm)],[c_0_141,c_0_59]) ).

cnf(c_0_147,hypothesis,
    ~ sum(x_plus_y,x_inverse_times_y_inverse,multiplicative_identity),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_144]) ).

cnf(c_0_148,hypothesis,
    add(x_plus_y,x_inverse_times_y_inverse) = multiplicative_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_145]),c_0_41]) ).

cnf(c_0_149,hypothesis,
    ~ sum(x_plus_y,inverse(y),multiplicative_identity),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_121]),c_0_147]) ).

cnf(c_0_150,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_148]),c_0_149]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : BOO014-3 : TPTP v8.1.2. Bugfixed v2.2.0.
% 0.00/0.09  % Command    : run_E %s %d THM
% 0.09/0.29  % Computer : n023.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit   : 2400
% 0.09/0.29  % WCLimit    : 300
% 0.09/0.29  % DateTime   : Mon Oct  2 20:54:07 EDT 2023
% 0.09/0.29  % CPUTime    : 
% 0.13/0.39  Running first-order model finding
% 0.13/0.39  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p
% 9.00/1.55  # Version: 3.1pre001
% 9.00/1.55  # Preprocessing class: FSMSSMSSSSSNFFN.
% 9.00/1.55  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.00/1.55  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 9.00/1.55  # Starting new_bool_3 with 300s (1) cores
% 9.00/1.55  # Starting new_bool_1 with 300s (1) cores
% 9.00/1.55  # Starting sh5l with 300s (1) cores
% 9.00/1.55  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 22477 completed with status 0
% 9.00/1.55  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 9.00/1.55  # Preprocessing class: FSMSSMSSSSSNFFN.
% 9.00/1.55  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.00/1.55  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 9.00/1.55  # No SInE strategy applied
% 9.00/1.55  # Search class: FHUSM-FFMF21-SFFFFFNN
% 9.00/1.55  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 9.00/1.55  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 811s (1) cores
% 9.00/1.55  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 9.00/1.55  # Starting new_bool_3 with 136s (1) cores
% 9.00/1.55  # Starting new_bool_1 with 136s (1) cores
% 9.00/1.55  # Starting sh5l with 136s (1) cores
% 9.00/1.55  # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with pid 22481 completed with status 0
% 9.00/1.55  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d
% 9.00/1.55  # Preprocessing class: FSMSSMSSSSSNFFN.
% 9.00/1.55  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.00/1.55  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 9.00/1.55  # No SInE strategy applied
% 9.00/1.55  # Search class: FHUSM-FFMF21-SFFFFFNN
% 9.00/1.55  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 9.00/1.55  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 811s (1) cores
% 9.00/1.55  # Preprocessing time       : 0.001 s
% 9.00/1.55  # Presaturation interreduction done
% 9.00/1.55  
% 9.00/1.55  # Proof found!
% 9.00/1.55  # SZS status Unsatisfiable
% 9.00/1.55  # SZS output start CNFRefutation
% See solution above
% 9.00/1.55  # Parsed axioms                        : 27
% 9.00/1.55  # Removed by relevancy pruning/SinE    : 0
% 9.00/1.55  # Initial clauses                      : 27
% 9.00/1.55  # Removed in clause preprocessing      : 0
% 9.00/1.55  # Initial clauses in saturation        : 27
% 9.00/1.55  # Processed clauses                    : 14594
% 9.00/1.55  # ...of these trivial                  : 585
% 9.00/1.55  # ...subsumed                          : 10203
% 9.00/1.55  # ...remaining for further processing  : 3806
% 9.00/1.55  # Other redundant clauses eliminated   : 0
% 9.00/1.55  # Clauses deleted for lack of memory   : 0
% 9.00/1.55  # Backward-subsumed                    : 131
% 9.00/1.55  # Backward-rewritten                   : 282
% 9.00/1.55  # Generated clauses                    : 60867
% 9.00/1.55  # ...of the previous two non-redundant : 49294
% 9.00/1.55  # ...aggressively subsumed             : 0
% 9.00/1.55  # Contextual simplify-reflections      : 0
% 9.00/1.55  # Paramodulations                      : 60867
% 9.00/1.55  # Factorizations                       : 0
% 9.00/1.55  # NegExts                              : 0
% 9.00/1.55  # Equation resolutions                 : 0
% 9.00/1.55  # Total rewrite steps                  : 32527
% 9.00/1.55  # Propositional unsat checks           : 0
% 9.00/1.55  #    Propositional check models        : 0
% 9.00/1.55  #    Propositional check unsatisfiable : 0
% 9.00/1.55  #    Propositional clauses             : 0
% 9.00/1.55  #    Propositional clauses after purity: 0
% 9.00/1.55  #    Propositional unsat core size     : 0
% 9.00/1.55  #    Propositional preprocessing time  : 0.000
% 9.00/1.55  #    Propositional encoding time       : 0.000
% 9.00/1.55  #    Propositional solver time         : 0.000
% 9.00/1.55  #    Success case prop preproc time    : 0.000
% 9.00/1.55  #    Success case prop encoding time   : 0.000
% 9.00/1.55  #    Success case prop solver time     : 0.000
% 9.00/1.55  # Current number of processed clauses  : 3366
% 9.00/1.55  #    Positive orientable unit clauses  : 278
% 9.00/1.55  #    Positive unorientable unit clauses: 2
% 9.00/1.55  #    Negative unit clauses             : 3
% 9.00/1.55  #    Non-unit-clauses                  : 3083
% 9.00/1.55  # Current number of unprocessed clauses: 34066
% 9.00/1.55  # ...number of literals in the above   : 78062
% 9.00/1.55  # Current number of archived formulas  : 0
% 9.00/1.55  # Current number of archived clauses   : 440
% 9.00/1.55  # Clause-clause subsumption calls (NU) : 1786670
% 9.00/1.55  # Rec. Clause-clause subsumption calls : 1248722
% 9.00/1.55  # Non-unit clause-clause subsumptions  : 10326
% 9.00/1.55  # Unit Clause-clause subsumption calls : 4146
% 9.00/1.55  # Rewrite failures with RHS unbound    : 0
% 9.00/1.55  # BW rewrite match attempts            : 1104
% 9.00/1.55  # BW rewrite match successes           : 92
% 9.00/1.55  # Condensation attempts                : 0
% 9.00/1.55  # Condensation successes               : 0
% 9.00/1.55  # Termbank termtop insertions          : 902644
% 9.00/1.55  
% 9.00/1.55  # -------------------------------------------------
% 9.00/1.55  # User time                : 1.120 s
% 9.00/1.55  # System time              : 0.027 s
% 9.00/1.55  # Total time               : 1.147 s
% 9.00/1.55  # Maximum resident set size: 1640 pages
% 9.00/1.55  
% 9.00/1.55  # -------------------------------------------------
% 9.00/1.55  # User time                : 5.685 s
% 9.00/1.55  # System time              : 0.065 s
% 9.00/1.55  # Total time               : 5.749 s
% 9.00/1.55  # Maximum resident set size: 1692 pages
% 9.00/1.55  % E---3.1 exiting
%------------------------------------------------------------------------------