TSTP Solution File: FLD041-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : FLD041-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n004.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 : Wed Aug 30 22:27:32 EDT 2023

% Result   : Unsatisfiable 17.87s 18.01s
% Output   : CNFRefutation 17.93s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   32
% Syntax   : Number of formulae    :  129 (  48 unt;  11 typ;   0 def)
%            Number of atoms       :  231 (   0 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :  230 ( 117   ~; 113   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   7   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :  114 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    add: ( $i * $i ) > $i ).

tff(decl_23,type,
    equalish: ( $i * $i ) > $o ).

tff(decl_24,type,
    defined: $i > $o ).

tff(decl_25,type,
    additive_identity: $i ).

tff(decl_26,type,
    additive_inverse: $i > $i ).

tff(decl_27,type,
    multiply: ( $i * $i ) > $i ).

tff(decl_28,type,
    multiplicative_identity: $i ).

tff(decl_29,type,
    multiplicative_inverse: $i > $i ).

tff(decl_30,type,
    less_or_equal: ( $i * $i ) > $o ).

tff(decl_31,type,
    a: $i ).

tff(decl_32,type,
    b: $i ).

cnf(existence_of_identity_multiplication,axiom,
    ( equalish(multiply(multiplicative_identity,X1),X1)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_identity_multiplication) ).

cnf(well_definedness_of_additive_identity,axiom,
    defined(additive_identity),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_identity) ).

cnf(existence_of_inverse_multiplication,axiom,
    ( equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity)
    | equalish(X1,additive_identity)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_multiplication) ).

cnf(b_is_defined,hypothesis,
    defined(b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).

cnf(b_not_equal_to_additive_identity_4,negated_conjecture,
    ~ equalish(b,additive_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_not_equal_to_additive_identity_4) ).

cnf(transitivity_of_equality,axiom,
    ( equalish(X1,X2)
    | ~ equalish(X1,X3)
    | ~ equalish(X3,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).

cnf(compatibility_of_equality_and_multiplication,axiom,
    ( equalish(multiply(X1,X2),multiply(X3,X2))
    | ~ defined(X2)
    | ~ equalish(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_multiplication) ).

cnf(symmetry_of_equality,axiom,
    ( equalish(X1,X2)
    | ~ equalish(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).

cnf(commutativity_multiplication,axiom,
    ( equalish(multiply(X1,X2),multiply(X2,X1))
    | ~ defined(X1)
    | ~ defined(X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',commutativity_multiplication) ).

cnf(well_definedness_of_multiplicative_identity,axiom,
    defined(multiplicative_identity),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_identity) ).

cnf(reflexivity_of_equality,axiom,
    ( equalish(X1,X1)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',reflexivity_of_equality) ).

cnf(a_is_defined,hypothesis,
    defined(a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).

cnf(existence_of_identity_addition,axiom,
    ( equalish(add(additive_identity,X1),X1)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_identity_addition) ).

cnf(multiply_equals_additive_identity_5,negated_conjecture,
    equalish(multiply(a,b),additive_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_equals_additive_identity_5) ).

cnf(distributivity,axiom,
    ( equalish(add(multiply(X1,X2),multiply(X3,X2)),multiply(add(X1,X3),X2))
    | ~ defined(X1)
    | ~ defined(X3)
    | ~ defined(X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',distributivity) ).

cnf(commutativity_addition,axiom,
    ( equalish(add(X1,X2),add(X2,X1))
    | ~ defined(X1)
    | ~ defined(X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',commutativity_addition) ).

cnf(well_definedness_of_multiplication,axiom,
    ( defined(multiply(X1,X2))
    | ~ defined(X1)
    | ~ defined(X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplication) ).

cnf(well_definedness_of_multiplicative_inverse,axiom,
    ( defined(multiplicative_inverse(X1))
    | equalish(X1,additive_identity)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_inverse) ).

cnf(compatibility_of_equality_and_addition,axiom,
    ( equalish(add(X1,X2),add(X3,X2))
    | ~ defined(X2)
    | ~ equalish(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_addition) ).

cnf(associativity_multiplication,axiom,
    ( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3))
    | ~ defined(X1)
    | ~ defined(X2)
    | ~ defined(X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',associativity_multiplication) ).

cnf(a_not_equal_to_additive_identity_3,negated_conjecture,
    ~ equalish(a,additive_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_equal_to_additive_identity_3) ).

cnf(c_0_21,axiom,
    ( equalish(multiply(multiplicative_identity,X1),X1)
    | ~ defined(X1) ),
    existence_of_identity_multiplication ).

cnf(c_0_22,axiom,
    defined(additive_identity),
    well_definedness_of_additive_identity ).

cnf(c_0_23,axiom,
    ( equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity)
    | equalish(X1,additive_identity)
    | ~ defined(X1) ),
    existence_of_inverse_multiplication ).

cnf(c_0_24,hypothesis,
    defined(b),
    b_is_defined ).

cnf(c_0_25,negated_conjecture,
    ~ equalish(b,additive_identity),
    b_not_equal_to_additive_identity_4 ).

cnf(c_0_26,axiom,
    ( equalish(X1,X2)
    | ~ equalish(X1,X3)
    | ~ equalish(X3,X2) ),
    transitivity_of_equality ).

cnf(c_0_27,plain,
    equalish(multiply(multiplicative_identity,additive_identity),additive_identity),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_28,axiom,
    ( equalish(multiply(X1,X2),multiply(X3,X2))
    | ~ defined(X2)
    | ~ equalish(X1,X3) ),
    compatibility_of_equality_and_multiplication ).

cnf(c_0_29,hypothesis,
    equalish(multiply(b,multiplicative_inverse(b)),multiplicative_identity),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).

cnf(c_0_30,axiom,
    ( equalish(X1,X2)
    | ~ equalish(X2,X1) ),
    symmetry_of_equality ).

cnf(c_0_31,plain,
    ( equalish(X1,additive_identity)
    | ~ equalish(X1,multiply(multiplicative_identity,additive_identity)) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_32,hypothesis,
    ( equalish(multiply(multiply(b,multiplicative_inverse(b)),X1),multiply(multiplicative_identity,X1))
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_33,hypothesis,
    equalish(multiplicative_identity,multiply(b,multiplicative_inverse(b))),
    inference(spm,[status(thm)],[c_0_30,c_0_29]) ).

cnf(c_0_34,hypothesis,
    equalish(multiply(multiply(b,multiplicative_inverse(b)),additive_identity),additive_identity),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_22])]) ).

cnf(c_0_35,hypothesis,
    ( equalish(X1,multiply(b,multiplicative_inverse(b)))
    | ~ equalish(X1,multiplicative_identity) ),
    inference(spm,[status(thm)],[c_0_26,c_0_33]) ).

cnf(c_0_36,hypothesis,
    ( equalish(X1,additive_identity)
    | ~ equalish(X1,multiply(multiply(b,multiplicative_inverse(b)),additive_identity)) ),
    inference(spm,[status(thm)],[c_0_26,c_0_34]) ).

cnf(c_0_37,hypothesis,
    ( equalish(multiply(X1,X2),multiply(multiply(b,multiplicative_inverse(b)),X2))
    | ~ defined(X2)
    | ~ equalish(X1,multiplicative_identity) ),
    inference(spm,[status(thm)],[c_0_28,c_0_35]) ).

cnf(c_0_38,axiom,
    ( equalish(multiply(X1,X2),multiply(X2,X1))
    | ~ defined(X1)
    | ~ defined(X2) ),
    commutativity_multiplication ).

cnf(c_0_39,axiom,
    defined(multiplicative_identity),
    well_definedness_of_multiplicative_identity ).

cnf(c_0_40,hypothesis,
    ( equalish(multiply(X1,additive_identity),additive_identity)
    | ~ equalish(X1,multiplicative_identity) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_22])]) ).

cnf(c_0_41,plain,
    ( equalish(multiply(X1,multiplicative_identity),multiply(multiplicative_identity,X1))
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_42,axiom,
    ( equalish(X1,X1)
    | ~ defined(X1) ),
    reflexivity_of_equality ).

cnf(c_0_43,hypothesis,
    ( equalish(X1,additive_identity)
    | ~ equalish(X1,multiply(X2,additive_identity))
    | ~ equalish(X2,multiplicative_identity) ),
    inference(spm,[status(thm)],[c_0_26,c_0_40]) ).

cnf(c_0_44,plain,
    equalish(multiply(additive_identity,multiplicative_identity),multiply(multiplicative_identity,additive_identity)),
    inference(spm,[status(thm)],[c_0_41,c_0_22]) ).

cnf(c_0_45,plain,
    equalish(multiplicative_identity,multiplicative_identity),
    inference(spm,[status(thm)],[c_0_42,c_0_39]) ).

cnf(c_0_46,hypothesis,
    defined(a),
    a_is_defined ).

cnf(c_0_47,hypothesis,
    ( equalish(multiply(X1,b),multiply(b,X1))
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_38,c_0_24]) ).

cnf(c_0_48,hypothesis,
    equalish(multiply(additive_identity,multiplicative_identity),additive_identity),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).

cnf(c_0_49,axiom,
    ( equalish(add(additive_identity,X1),X1)
    | ~ defined(X1) ),
    existence_of_identity_addition ).

cnf(c_0_50,hypothesis,
    equalish(multiply(multiplicative_identity,a),a),
    inference(spm,[status(thm)],[c_0_21,c_0_46]) ).

cnf(c_0_51,hypothesis,
    equalish(multiply(a,b),multiply(b,a)),
    inference(spm,[status(thm)],[c_0_47,c_0_46]) ).

cnf(c_0_52,hypothesis,
    equalish(additive_identity,multiply(additive_identity,multiplicative_identity)),
    inference(spm,[status(thm)],[c_0_30,c_0_48]) ).

cnf(c_0_53,negated_conjecture,
    equalish(multiply(a,b),additive_identity),
    multiply_equals_additive_identity_5 ).

cnf(c_0_54,hypothesis,
    equalish(add(additive_identity,a),a),
    inference(spm,[status(thm)],[c_0_49,c_0_46]) ).

cnf(c_0_55,hypothesis,
    ( equalish(X1,a)
    | ~ equalish(X1,multiply(multiplicative_identity,a)) ),
    inference(spm,[status(thm)],[c_0_26,c_0_50]) ).

cnf(c_0_56,hypothesis,
    equalish(multiply(b,a),multiply(a,b)),
    inference(spm,[status(thm)],[c_0_30,c_0_51]) ).

cnf(c_0_57,hypothesis,
    ( equalish(X1,multiply(additive_identity,multiplicative_identity))
    | ~ equalish(X1,additive_identity) ),
    inference(spm,[status(thm)],[c_0_26,c_0_52]) ).

cnf(c_0_58,negated_conjecture,
    ( equalish(X1,additive_identity)
    | ~ equalish(X1,multiply(a,b)) ),
    inference(spm,[status(thm)],[c_0_26,c_0_53]) ).

cnf(c_0_59,negated_conjecture,
    equalish(additive_identity,multiply(a,b)),
    inference(spm,[status(thm)],[c_0_30,c_0_53]) ).

cnf(c_0_60,hypothesis,
    ( equalish(multiply(add(additive_identity,a),X1),multiply(a,X1))
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_28,c_0_54]) ).

cnf(c_0_61,axiom,
    ( equalish(add(multiply(X1,X2),multiply(X3,X2)),multiply(add(X1,X3),X2))
    | ~ defined(X1)
    | ~ defined(X3)
    | ~ defined(X2) ),
    distributivity ).

cnf(c_0_62,axiom,
    ( equalish(add(X1,X2),add(X2,X1))
    | ~ defined(X1)
    | ~ defined(X2) ),
    commutativity_addition ).

cnf(c_0_63,axiom,
    ( defined(multiply(X1,X2))
    | ~ defined(X1)
    | ~ defined(X2) ),
    well_definedness_of_multiplication ).

cnf(c_0_64,hypothesis,
    equalish(multiply(multiply(b,multiplicative_inverse(b)),a),a),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_32]),c_0_46])]) ).

cnf(c_0_65,axiom,
    ( defined(multiplicative_inverse(X1))
    | equalish(X1,additive_identity)
    | ~ defined(X1) ),
    well_definedness_of_multiplicative_inverse ).

cnf(c_0_66,hypothesis,
    ( equalish(X1,multiply(a,b))
    | ~ equalish(X1,multiply(b,a)) ),
    inference(spm,[status(thm)],[c_0_26,c_0_56]) ).

cnf(c_0_67,hypothesis,
    ( equalish(multiply(additive_identity,multiplicative_identity),X1)
    | ~ equalish(X1,additive_identity) ),
    inference(spm,[status(thm)],[c_0_30,c_0_57]) ).

cnf(c_0_68,negated_conjecture,
    equalish(multiply(b,a),additive_identity),
    inference(spm,[status(thm)],[c_0_58,c_0_56]) ).

cnf(c_0_69,negated_conjecture,
    ( equalish(X1,multiply(a,b))
    | ~ equalish(X1,additive_identity) ),
    inference(spm,[status(thm)],[c_0_26,c_0_59]) ).

cnf(c_0_70,negated_conjecture,
    equalish(multiply(add(additive_identity,a),b),additive_identity),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_60]),c_0_24])]) ).

cnf(c_0_71,plain,
    ( equalish(X1,multiply(add(X2,X3),X4))
    | ~ defined(X3)
    | ~ defined(X4)
    | ~ defined(X2)
    | ~ equalish(X1,add(multiply(X2,X4),multiply(X3,X4))) ),
    inference(spm,[status(thm)],[c_0_26,c_0_61]) ).

cnf(c_0_72,plain,
    ( equalish(add(X1,multiply(X2,X3)),add(multiply(X2,X3),X1))
    | ~ defined(X1)
    | ~ defined(X3)
    | ~ defined(X2) ),
    inference(spm,[status(thm)],[c_0_62,c_0_63]) ).

cnf(c_0_73,hypothesis,
    ( equalish(X1,a)
    | ~ equalish(X1,multiply(multiply(b,multiplicative_inverse(b)),a)) ),
    inference(spm,[status(thm)],[c_0_26,c_0_64]) ).

cnf(c_0_74,plain,
    ( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X2,X3),X1))
    | ~ defined(X1)
    | ~ defined(X3)
    | ~ defined(X2) ),
    inference(spm,[status(thm)],[c_0_38,c_0_63]) ).

cnf(c_0_75,hypothesis,
    defined(multiplicative_inverse(b)),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_24]),c_0_25]) ).

cnf(c_0_76,hypothesis,
    equalish(multiply(additive_identity,multiplicative_identity),multiply(a,b)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68])]) ).

cnf(c_0_77,negated_conjecture,
    ( equalish(multiply(a,b),X1)
    | ~ equalish(X1,additive_identity) ),
    inference(spm,[status(thm)],[c_0_30,c_0_69]) ).

cnf(c_0_78,axiom,
    ( equalish(add(X1,X2),add(X3,X2))
    | ~ defined(X2)
    | ~ equalish(X1,X3) ),
    compatibility_of_equality_and_addition ).

cnf(c_0_79,negated_conjecture,
    ( equalish(X1,additive_identity)
    | ~ equalish(X1,multiply(add(additive_identity,a),b)) ),
    inference(spm,[status(thm)],[c_0_26,c_0_70]) ).

cnf(c_0_80,plain,
    ( equalish(add(multiply(X1,X2),multiply(X3,X2)),multiply(add(X3,X1),X2))
    | ~ defined(X1)
    | ~ defined(X2)
    | ~ defined(X3) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_63]) ).

cnf(c_0_81,hypothesis,
    equalish(multiply(a,multiply(b,multiplicative_inverse(b))),a),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_46]),c_0_75]),c_0_24])]) ).

cnf(c_0_82,axiom,
    ( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3))
    | ~ defined(X1)
    | ~ defined(X2)
    | ~ defined(X3) ),
    associativity_multiplication ).

cnf(c_0_83,hypothesis,
    equalish(multiply(a,b),multiply(additive_identity,multiplicative_identity)),
    inference(spm,[status(thm)],[c_0_30,c_0_76]) ).

cnf(c_0_84,hypothesis,
    equalish(a,multiply(multiplicative_identity,a)),
    inference(spm,[status(thm)],[c_0_30,c_0_50]) ).

cnf(c_0_85,negated_conjecture,
    ( equalish(multiply(a,b),a)
    | ~ equalish(multiply(multiplicative_identity,a),additive_identity) ),
    inference(spm,[status(thm)],[c_0_55,c_0_77]) ).

cnf(c_0_86,negated_conjecture,
    ( equalish(add(multiply(a,b),X1),add(additive_identity,X1))
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_78,c_0_53]) ).

cnf(c_0_87,negated_conjecture,
    equalish(add(multiply(a,b),multiply(additive_identity,b)),additive_identity),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_46]),c_0_24]),c_0_22])]) ).

cnf(c_0_88,hypothesis,
    equalish(multiply(additive_identity,multiply(b,multiplicative_inverse(b))),additive_identity),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_74]),c_0_22]),c_0_75]),c_0_24])]) ).

cnf(c_0_89,hypothesis,
    ( equalish(X1,a)
    | ~ equalish(X1,multiply(a,multiply(b,multiplicative_inverse(b)))) ),
    inference(spm,[status(thm)],[c_0_26,c_0_81]) ).

cnf(c_0_90,plain,
    ( equalish(multiply(multiply(X1,X2),X3),multiply(X1,multiply(X2,X3)))
    | ~ defined(X3)
    | ~ defined(X2)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_30,c_0_82]) ).

cnf(c_0_91,hypothesis,
    ( equalish(X1,multiply(additive_identity,multiplicative_identity))
    | ~ equalish(X1,multiply(a,b)) ),
    inference(spm,[status(thm)],[c_0_26,c_0_83]) ).

cnf(c_0_92,hypothesis,
    ( equalish(X1,multiply(multiplicative_identity,a))
    | ~ equalish(X1,a) ),
    inference(spm,[status(thm)],[c_0_26,c_0_84]) ).

cnf(c_0_93,negated_conjecture,
    ( equalish(a,multiply(a,b))
    | ~ equalish(multiply(multiplicative_identity,a),additive_identity) ),
    inference(spm,[status(thm)],[c_0_30,c_0_85]) ).

cnf(c_0_94,negated_conjecture,
    ~ equalish(a,additive_identity),
    a_not_equal_to_additive_identity_3 ).

cnf(c_0_95,negated_conjecture,
    ( equalish(X1,add(additive_identity,X2))
    | ~ defined(X2)
    | ~ equalish(X1,add(multiply(a,b),X2)) ),
    inference(spm,[status(thm)],[c_0_26,c_0_86]) ).

cnf(c_0_96,negated_conjecture,
    equalish(additive_identity,add(multiply(a,b),multiply(additive_identity,b))),
    inference(spm,[status(thm)],[c_0_30,c_0_87]) ).

cnf(c_0_97,hypothesis,
    ( equalish(X1,additive_identity)
    | ~ equalish(X1,multiply(additive_identity,multiply(b,multiplicative_inverse(b)))) ),
    inference(spm,[status(thm)],[c_0_26,c_0_88]) ).

cnf(c_0_98,hypothesis,
    equalish(multiply(multiply(a,b),multiplicative_inverse(b)),a),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_75]),c_0_24]),c_0_46])]) ).

cnf(c_0_99,hypothesis,
    ( equalish(X1,X2)
    | ~ equalish(X1,multiply(additive_identity,multiplicative_identity))
    | ~ equalish(X2,additive_identity) ),
    inference(spm,[status(thm)],[c_0_26,c_0_67]) ).

cnf(c_0_100,hypothesis,
    equalish(multiply(b,a),multiply(additive_identity,multiplicative_identity)),
    inference(spm,[status(thm)],[c_0_91,c_0_56]) ).

cnf(c_0_101,negated_conjecture,
    ( equalish(X1,additive_identity)
    | ~ equalish(X1,multiply(b,a)) ),
    inference(spm,[status(thm)],[c_0_26,c_0_68]) ).

cnf(c_0_102,hypothesis,
    ( equalish(multiply(multiplicative_identity,a),X1)
    | ~ equalish(X1,a) ),
    inference(spm,[status(thm)],[c_0_30,c_0_92]) ).

cnf(c_0_103,negated_conjecture,
    ~ equalish(multiply(multiplicative_identity,a),additive_identity),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_93]),c_0_94]) ).

cnf(c_0_104,plain,
    ( equalish(add(additive_identity,multiply(X1,X2)),multiply(X1,X2))
    | ~ defined(X2)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_49,c_0_63]) ).

cnf(c_0_105,negated_conjecture,
    ( equalish(additive_identity,add(additive_identity,multiply(additive_identity,b)))
    | ~ defined(multiply(additive_identity,b)) ),
    inference(spm,[status(thm)],[c_0_95,c_0_96]) ).

cnf(c_0_106,hypothesis,
    equalish(multiply(multiply(additive_identity,b),multiplicative_inverse(b)),additive_identity),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_90]),c_0_75]),c_0_24]),c_0_22])]) ).

cnf(c_0_107,hypothesis,
    ( equalish(X1,a)
    | ~ equalish(X1,multiply(multiply(a,b),multiplicative_inverse(b))) ),
    inference(spm,[status(thm)],[c_0_26,c_0_98]) ).

cnf(c_0_108,hypothesis,
    ( equalish(multiply(b,a),X1)
    | ~ equalish(X1,additive_identity) ),
    inference(spm,[status(thm)],[c_0_99,c_0_100]) ).

cnf(c_0_109,hypothesis,
    ~ equalish(multiply(b,a),a),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_103]) ).

cnf(c_0_110,plain,
    ( equalish(X1,multiply(X2,X3))
    | ~ defined(X3)
    | ~ defined(X2)
    | ~ equalish(X1,add(additive_identity,multiply(X2,X3))) ),
    inference(spm,[status(thm)],[c_0_26,c_0_104]) ).

cnf(c_0_111,negated_conjecture,
    equalish(additive_identity,add(additive_identity,multiply(additive_identity,b))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_63]),c_0_24]),c_0_22])]) ).

cnf(c_0_112,hypothesis,
    ( equalish(X1,additive_identity)
    | ~ equalish(X1,multiply(multiply(additive_identity,b),multiplicative_inverse(b))) ),
    inference(spm,[status(thm)],[c_0_26,c_0_106]) ).

cnf(c_0_113,negated_conjecture,
    ( equalish(multiply(multiply(a,b),X1),multiply(X2,X1))
    | ~ defined(X1)
    | ~ equalish(X2,additive_identity) ),
    inference(spm,[status(thm)],[c_0_28,c_0_77]) ).

cnf(c_0_114,hypothesis,
    ~ equalish(multiply(multiply(a,b),multiplicative_inverse(b)),additive_identity),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109]) ).

cnf(c_0_115,negated_conjecture,
    equalish(additive_identity,multiply(additive_identity,b)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_24]),c_0_22])]) ).

cnf(c_0_116,negated_conjecture,
    ~ equalish(multiply(additive_identity,b),additive_identity),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_75])]),c_0_114]) ).

cnf(c_0_117,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_115]),c_0_116]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.16  % Problem    : FLD041-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.18  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.17/0.38  % Computer : n004.cluster.edu
% 0.17/0.38  % Model    : x86_64 x86_64
% 0.17/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38  % Memory   : 8042.1875MB
% 0.17/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38  % CPULimit   : 300
% 0.17/0.38  % WCLimit    : 300
% 0.17/0.38  % DateTime   : Sun Aug 27 23:57:08 EDT 2023
% 0.17/0.38  % CPUTime  : 
% 0.24/0.64  start to proof: theBenchmark
% 17.87/18.01  % Version  : CSE_E---1.5
% 17.87/18.01  % Problem  : theBenchmark.p
% 17.87/18.01  % Proof found
% 17.87/18.01  % SZS status Theorem for theBenchmark.p
% 17.87/18.01  % SZS output start Proof
% See solution above
% 17.93/18.02  % Total time : 17.291000 s
% 17.93/18.02  % SZS output end Proof
% 17.93/18.02  % Total time : 17.295000 s
%------------------------------------------------------------------------------