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iProver---3.9.4.UNS-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : FLD027-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM

% Computer : n016.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep 25 01:15:41 PM UTC 2026

% Result   : Unsatisfiable 181.07s 33.54s
% Output   : CNFRefutation 181.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   87 (  13 unt;   0 def)
%            Number of atoms       :  215 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  254 ( 126   ~; 128   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   78 (   0 sgn  78   !;   0   ?;  60   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,axiom,
    ! [X2,X0,X1] :
      ( ~ defined(X2)
      | ~ defined(X1)
      | ~ defined(X0)
      | equalish(multiply(X0,multiply(X1,X2)),multiply(multiply(X0,X1),X2)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',associativity_multiplication) ).

fof(f6,axiom,
    ! [X0] :
      ( ~ defined(X0)
      | equalish(multiply(multiplicative_identity,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_identity_multiplication) ).

fof(f7,axiom,
    ! [X0] :
      ( equalish(X0,additive_identity)
      | ~ defined(X0)
      | equalish(multiply(X0,multiplicative_inverse(X0)),multiplicative_identity) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_multiplication) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( ~ defined(X1)
      | ~ defined(X0)
      | equalish(multiply(X0,X1),multiply(X1,X0)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',commutativity_multiplication) ).

fof(f13,axiom,
    ! [X0,X1] :
      ( ~ defined(X1)
      | ~ defined(X0)
      | defined(multiply(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplication) ).

fof(f15,axiom,
    ! [X0] :
      ( equalish(X0,additive_identity)
      | ~ defined(X0)
      | defined(multiplicative_inverse(X0)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_inverse) ).

fof(f22,axiom,
    ! [X0,X1] :
      ( ~ equalish(X1,X0)
      | equalish(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).

fof(f23,axiom,
    ! [X2,X0,X1] :
      ( ~ equalish(X2,X1)
      | ~ equalish(X0,X2)
      | equalish(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).

fof(f25,axiom,
    ! [X2,X0,X1] :
      ( ~ equalish(X0,X2)
      | ~ defined(X1)
      | equalish(multiply(X0,X1),multiply(X2,X1)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_multiplication) ).

fof(f28,axiom,
    defined(a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).

fof(f29,axiom,
    defined(b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).

fof(f30,negated_conjecture,
    ~ equalish(a,additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_equal_to_additive_identity_3) ).

fof(f31,negated_conjecture,
    ~ equalish(b,additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_not_equal_to_additive_identity_4) ).

fof(f32,negated_conjecture,
    equalish(multiplicative_inverse(a),multiplicative_inverse(b)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverses_equal) ).

fof(f33,negated_conjecture,
    ~ equalish(a,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_equal_to_b_6) ).

tcf(c_86,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( equalish(multiply(X0,multiply(X1,X2)),multiply(multiply(X0,X1),X2))
      | ~ defined(X2)
      | ~ defined(X1)
      | ~ defined(X0) ),
    inference(cnf_transformation,[],[f5]) ).

tcf(c_87,plain,
    ! [X0: $i] :
      ( equalish(multiply(multiplicative_identity,X0),X0)
      | ~ defined(X0) ),
    inference(cnf_transformation,[],[f6]) ).

tcf(c_88,plain,
    ! [X0: $i] :
      ( equalish(X0,additive_identity)
      | equalish(multiply(X0,multiplicative_inverse(X0)),multiplicative_identity)
      | ~ defined(X0) ),
    inference(cnf_transformation,[],[f7]) ).

tcf(c_89,plain,
    ! [X0: $i,X1: $i] :
      ( equalish(multiply(X0,X1),multiply(X1,X0))
      | ~ defined(X1)
      | ~ defined(X0) ),
    inference(cnf_transformation,[],[f8]) ).

tcf(c_94,plain,
    ! [X0: $i,X1: $i] :
      ( defined(multiply(X0,X1))
      | ~ defined(X1)
      | ~ defined(X0) ),
    inference(cnf_transformation,[],[f13]) ).

tcf(c_96,plain,
    ! [X0: $i] :
      ( equalish(X0,additive_identity)
      | defined(multiplicative_inverse(X0))
      | ~ defined(X0) ),
    inference(cnf_transformation,[],[f15]) ).

tcf(c_103,plain,
    ! [X0: $i,X1: $i] :
      ( equalish(X1,X0)
      | ~ equalish(X0,X1) ),
    inference(cnf_transformation,[],[f22]) ).

tcf(c_104,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( equalish(X0,X2)
      | ~ equalish(X1,X2)
      | ~ equalish(X0,X1) ),
    inference(cnf_transformation,[],[f23]) ).

tcf(c_106,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( equalish(multiply(X0,X2),multiply(X1,X2))
      | ~ defined(X2)
      | ~ equalish(X0,X1) ),
    inference(cnf_transformation,[],[f25]) ).

tcf(c_109,plain,
    defined(a),
    inference(cnf_transformation,[],[f28]) ).

tcf(c_110,plain,
    defined(b),
    inference(cnf_transformation,[],[f29]) ).

tcf(c_111,negated_conjecture,
    ~ equalish(a,additive_identity),
    inference(cnf_transformation,[],[f30]) ).

tcf(c_112,negated_conjecture,
    ~ equalish(b,additive_identity),
    inference(cnf_transformation,[],[f31]) ).

tcf(c_113,negated_conjecture,
    equalish(multiplicative_inverse(a),multiplicative_inverse(b)),
    inference(cnf_transformation,[],[f32]) ).

tcf(c_114,negated_conjecture,
    ~ equalish(a,b),
    inference(cnf_transformation,[],[f33]) ).

tcf(c_291,plain,
    ( equalish(a,additive_identity)
    | defined(multiplicative_inverse(a))
    | ~ defined(a) ),
    inference(instantiation,[status(thm)],[c_96]) ).

tcf(c_292,plain,
    ( equalish(b,additive_identity)
    | defined(multiplicative_inverse(b))
    | ~ defined(b) ),
    inference(instantiation,[status(thm)],[c_96]) ).

tcf(c_293,plain,
    ( equalish(a,additive_identity)
    | equalish(multiply(a,multiplicative_inverse(a)),multiplicative_identity)
    | ~ defined(a) ),
    inference(instantiation,[status(thm)],[c_88]) ).

tcf(c_294,plain,
    ( equalish(b,additive_identity)
    | equalish(multiply(b,multiplicative_inverse(b)),multiplicative_identity)
    | ~ defined(b) ),
    inference(instantiation,[status(thm)],[c_88]) ).

tcf(c_372,plain,
    ! [X0: $i] :
      ( equalish(a,X0)
      | ~ equalish(X0,a) ),
    inference(instantiation,[status(thm)],[c_103]) ).

tcf(c_373,plain,
    ! [X0: $i,X1: $i] :
      ( equalish(a,X1)
      | ~ equalish(a,X0)
      | ~ equalish(X0,X1) ),
    inference(instantiation,[status(thm)],[c_104]) ).

tcf(c_413,plain,
    ( equalish(multiply(multiplicative_identity,b),b)
    | ~ defined(b) ),
    inference(instantiation,[status(thm)],[c_87]) ).

tcf(c_417,plain,
    ! [X0: $i,X1: $i] :
      ( equalish(X0,b)
      | ~ equalish(X1,b)
      | ~ equalish(X0,X1) ),
    inference(instantiation,[status(thm)],[c_104]) ).

tcf(c_474,plain,
    ( equalish(a,multiply(multiplicative_identity,a))
    | ~ equalish(multiply(multiplicative_identity,a),a) ),
    inference(instantiation,[status(thm)],[c_372]) ).

tcf(c_475,plain,
    ( equalish(multiply(multiplicative_identity,a),a)
    | ~ defined(a) ),
    inference(instantiation,[status(thm)],[c_87]) ).

tcf(c_815,plain,
    ! [X0: $i] :
      ( equalish(X0,b)
      | ~ equalish(multiply(multiplicative_identity,b),b)
      | ~ equalish(X0,multiply(multiplicative_identity,b)) ),
    inference(instantiation,[status(thm)],[c_417]) ).

tcf(c_819,plain,
    ! [X0: $i] :
      ( equalish(multiplicative_identity,X0)
      | ~ equalish(X0,multiplicative_identity) ),
    inference(instantiation,[status(thm)],[c_103]) ).

tcf(c_820,plain,
    ! [X0: $i,X1: $i] :
      ( equalish(multiplicative_identity,X1)
      | ~ equalish(multiplicative_identity,X0)
      | ~ equalish(X0,X1) ),
    inference(instantiation,[status(thm)],[c_104]) ).

tcf(c_1034,plain,
    ( equalish(multiply(multiplicative_inverse(b),b),multiply(b,multiplicative_inverse(b)))
    | ~ defined(b)
    | ~ defined(multiplicative_inverse(b)) ),
    inference(instantiation,[status(thm)],[c_89]) ).

tcf(c_1038,plain,
    ! [X0: $i,X1: $i] :
      ( equalish(X1,multiply(b,multiplicative_inverse(b)))
      | ~ equalish(X1,X0)
      | ~ equalish(X0,multiply(b,multiplicative_inverse(b))) ),
    inference(instantiation,[status(thm)],[c_104]) ).

tcf(c_1105,plain,
    ! [X0: $i] :
      ( equalish(a,X0)
      | ~ equalish(a,multiply(multiplicative_identity,a))
      | ~ equalish(multiply(multiplicative_identity,a),X0) ),
    inference(instantiation,[status(thm)],[c_373]) ).

tcf(c_1200,plain,
    ( equalish(multiplicative_identity,multiply(b,multiplicative_inverse(b)))
    | ~ equalish(multiply(b,multiplicative_inverse(b)),multiplicative_identity) ),
    inference(instantiation,[status(thm)],[c_819]) ).

tcf(c_1589,plain,
    ! [X0: $i,X1: $i] :
      ( equalish(X1,multiply(multiplicative_identity,b))
      | ~ equalish(X1,X0)
      | ~ equalish(X0,multiply(multiplicative_identity,b)) ),
    inference(instantiation,[status(thm)],[c_104]) ).

tcf(c_1591,plain,
    ! [X0: $i] :
      ( equalish(multiply(X0,b),multiply(multiplicative_identity,b))
      | ~ defined(b)
      | ~ equalish(X0,multiplicative_identity) ),
    inference(instantiation,[status(thm)],[c_106]) ).

tcf(c_2144,plain,
    ! [X0: $i] :
      ( equalish(multiplicative_identity,X0)
      | ~ equalish(multiplicative_identity,multiply(b,multiplicative_inverse(b)))
      | ~ equalish(multiply(b,multiplicative_inverse(b)),X0) ),
    inference(instantiation,[status(thm)],[c_820]) ).

tcf(c_2542,plain,
    ! [X0: $i] :
      ( equalish(multiply(multiplicative_identity,a),multiply(X0,a))
      | ~ defined(a)
      | ~ equalish(multiplicative_identity,X0) ),
    inference(instantiation,[status(thm)],[c_106]) ).

tcf(c_3255,plain,
    ! [X0: $i] :
      ( equalish(X0,multiply(b,multiplicative_inverse(b)))
      | ~ equalish(X0,multiply(multiplicative_inverse(b),b))
      | ~ equalish(multiply(multiplicative_inverse(b),b),multiply(b,multiplicative_inverse(b))) ),
    inference(instantiation,[status(thm)],[c_1038]) ).

tcf(c_3628,plain,
    ( equalish(multiply(multiply(a,multiplicative_inverse(a)),b),multiply(multiplicative_identity,b))
    | ~ defined(b)
    | ~ equalish(multiply(a,multiplicative_inverse(a)),multiplicative_identity) ),
    inference(instantiation,[status(thm)],[c_1591]) ).

tcf(c_4857,plain,
    ! [X0: $i] :
      ( equalish(X0,multiply(multiplicative_identity,b))
      | ~ equalish(X0,multiply(multiply(a,multiplicative_inverse(a)),b))
      | ~ equalish(multiply(multiply(a,multiplicative_inverse(a)),b),multiply(multiplicative_identity,b)) ),
    inference(instantiation,[status(thm)],[c_1589]) ).

tcf(c_8622,plain,
    ! [X0: $i] :
      ( equalish(multiply(X0,b),multiply(multiplicative_inverse(b),b))
      | ~ defined(b)
      | ~ equalish(X0,multiplicative_inverse(b)) ),
    inference(instantiation,[status(thm)],[c_106]) ).

tcf(c_16278,plain,
    ( equalish(multiply(a,multiply(multiplicative_inverse(a),b)),multiply(multiplicative_identity,b))
    | ~ equalish(multiply(multiply(a,multiplicative_inverse(a)),b),multiply(multiplicative_identity,b))
    | ~ equalish(multiply(a,multiply(multiplicative_inverse(a),b)),multiply(multiply(a,multiplicative_inverse(a)),b)) ),
    inference(instantiation,[status(thm)],[c_4857]) ).

tcf(c_16279,plain,
    ( equalish(multiply(a,multiply(multiplicative_inverse(a),b)),multiply(multiply(a,multiplicative_inverse(a)),b))
    | ~ defined(b)
    | ~ defined(a)
    | ~ defined(multiplicative_inverse(a)) ),
    inference(instantiation,[status(thm)],[c_86]) ).

tcf(c_34624,plain,
    ( equalish(multiply(a,multiply(multiplicative_inverse(a),b)),b)
    | ~ equalish(multiply(multiplicative_identity,b),b)
    | ~ equalish(multiply(a,multiply(multiplicative_inverse(a),b)),multiply(multiplicative_identity,b)) ),
    inference(instantiation,[status(thm)],[c_815]) ).

tcf(c_63091,plain,
    ! [X0: $i,X1: $i] :
      ( equalish(X0,b)
      | ~ equalish(X1,b)
      | ~ equalish(X0,X1) ),
    inference(instantiation,[status(thm)],[c_104]) ).

tcf(c_98237,plain,
    ! [X0: $i] :
      ( equalish(X0,b)
      | ~ equalish(multiply(a,multiply(multiplicative_inverse(a),b)),b)
      | ~ equalish(X0,multiply(a,multiply(multiplicative_inverse(a),b))) ),
    inference(instantiation,[status(thm)],[c_63091]) ).

tcf(c_102253,plain,
    ( equalish(multiply(multiply(multiplicative_inverse(a),b),a),b)
    | ~ equalish(multiply(a,multiply(multiplicative_inverse(a),b)),b)
    | ~ equalish(multiply(multiply(multiplicative_inverse(a),b),a),multiply(a,multiply(multiplicative_inverse(a),b))) ),
    inference(instantiation,[status(thm)],[c_98237]) ).

tcf(c_102254,plain,
    ( equalish(multiply(multiply(multiplicative_inverse(a),b),a),multiply(a,multiply(multiplicative_inverse(a),b)))
    | ~ defined(a)
    | ~ defined(multiply(multiplicative_inverse(a),b)) ),
    inference(instantiation,[status(thm)],[c_89]) ).

tcf(c_153213,plain,
    ! [X0: $i] :
      ( equalish(a,b)
      | ~ equalish(a,X0)
      | ~ equalish(X0,b) ),
    inference(instantiation,[status(thm)],[c_104]) ).

tcf(c_325423,plain,
    ( defined(multiply(multiplicative_inverse(a),b))
    | ~ defined(b)
    | ~ defined(multiplicative_inverse(a)) ),
    inference(instantiation,[status(thm)],[c_94]) ).

tcf(c_334834,plain,
    ( equalish(a,b)
    | ~ equalish(a,multiply(multiply(multiplicative_inverse(a),b),a))
    | ~ equalish(multiply(multiply(multiplicative_inverse(a),b),a),b) ),
    inference(instantiation,[status(thm)],[c_153213]) ).

tcf(c_340132,plain,
    ! [X0: $i,X1: $i] :
      ( equalish(a,X1)
      | ~ equalish(a,X0)
      | ~ equalish(X0,X1) ),
    inference(instantiation,[status(thm)],[c_104]) ).

tcf(c_340163,plain,
    ! [X0: $i,X1: $i] :
      ( equalish(multiplicative_identity,X1)
      | ~ equalish(multiplicative_identity,X0)
      | ~ equalish(X0,X1) ),
    inference(instantiation,[status(thm)],[c_104]) ).

tcf(c_340425,plain,
    ! [X0: $i] :
      ( equalish(multiplicative_identity,X0)
      | ~ equalish(multiplicative_identity,multiply(b,multiplicative_inverse(b)))
      | ~ equalish(multiply(b,multiplicative_inverse(b)),X0) ),
    inference(instantiation,[status(thm)],[c_340163]) ).

tcf(c_340457,plain,
    ! [X0: $i,X1: $i] :
      ( equalish(X1,multiply(b,multiplicative_inverse(b)))
      | ~ equalish(X1,X0)
      | ~ equalish(X0,multiply(b,multiplicative_inverse(b))) ),
    inference(instantiation,[status(thm)],[c_104]) ).

tcf(c_341045,plain,
    ! [X0: $i] :
      ( equalish(a,X0)
      | ~ equalish(a,multiply(multiplicative_identity,a))
      | ~ equalish(multiply(multiplicative_identity,a),X0) ),
    inference(instantiation,[status(thm)],[c_340132]) ).

tcf(c_341140,plain,
    ! [X0: $i] :
      ( equalish(multiplicative_identity,X0)
      | ~ equalish(multiply(b,multiplicative_inverse(b)),X0) ),
    inference(global_subsumption_just,[status(thm)],[c_340425,c_110,c_112,c_294,c_1200,c_2144]) ).

tcf(c_341150,plain,
    ! [X0: $i] :
      ( equalish(multiply(b,multiplicative_inverse(b)),X0)
      | ~ equalish(X0,multiply(b,multiplicative_inverse(b))) ),
    inference(instantiation,[status(thm)],[c_103]) ).

tcf(c_341303,plain,
    ! [X0: $i] :
      ( equalish(X0,multiply(b,multiplicative_inverse(b)))
      | ~ equalish(X0,multiply(multiplicative_inverse(b),b))
      | ~ equalish(multiply(multiplicative_inverse(b),b),multiply(b,multiplicative_inverse(b))) ),
    inference(instantiation,[status(thm)],[c_340457]) ).

tcf(c_342609,plain,
    ! [X0: $i] :
      ( equalish(a,X0)
      | ~ equalish(multiply(multiplicative_identity,a),X0) ),
    inference(global_subsumption_just,[status(thm)],[c_341045,c_109,c_474,c_475,c_1105]) ).

tcf(c_342623,plain,
    ! [X0: $i] :
      ( equalish(a,multiply(X0,a))
      | ~ equalish(multiply(multiplicative_identity,a),multiply(X0,a)) ),
    inference(instantiation,[status(thm)],[c_342609]) ).

tcf(c_342624,plain,
    ! [X0: $i] :
      ( equalish(multiply(multiplicative_identity,a),multiply(X0,a))
      | ~ defined(a)
      | ~ equalish(multiplicative_identity,X0) ),
    inference(instantiation,[status(thm)],[c_106]) ).

tcf(c_343639,plain,
    ! [X0: $i] :
      ( equalish(multiply(X0,b),multiply(multiplicative_inverse(b),b))
      | ~ defined(b)
      | ~ equalish(X0,multiplicative_inverse(b)) ),
    inference(instantiation,[status(thm)],[c_106]) ).

tcf(c_343920,plain,
    ! [X0: $i] :
      ( equalish(X0,multiply(b,multiplicative_inverse(b)))
      | ~ equalish(X0,multiply(multiplicative_inverse(b),b)) ),
    inference(global_subsumption_just,[status(thm)],[c_341303,c_110,c_112,c_292,c_1034,c_3255]) ).

tcf(c_354887,plain,
    ! [X0: $i] :
      ( equalish(multiply(multiplicative_identity,a),multiply(X0,a))
      | ~ equalish(multiplicative_identity,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_342624,c_109,c_2542]) ).

tcf(c_362788,plain,
    ! [X0: $i] :
      ( equalish(multiply(X0,b),multiply(multiplicative_inverse(b),b))
      | ~ equalish(X0,multiplicative_inverse(b)) ),
    inference(global_subsumption_just,[status(thm)],[c_343639,c_110,c_8622]) ).

tcf(c_362791,plain,
    ( equalish(multiply(multiplicative_inverse(a),b),multiply(multiplicative_inverse(b),b))
    | ~ equalish(multiplicative_inverse(a),multiplicative_inverse(b)) ),
    inference(instantiation,[status(thm)],[c_362788]) ).

tcf(c_364030,plain,
    ( equalish(multiply(multiplicative_inverse(a),b),multiply(b,multiplicative_inverse(b)))
    | ~ equalish(multiply(multiplicative_inverse(a),b),multiply(multiplicative_inverse(b),b)) ),
    inference(instantiation,[status(thm)],[c_343920]) ).

tcf(c_365929,plain,
    ( equalish(multiply(b,multiplicative_inverse(b)),multiply(multiplicative_inverse(a),b))
    | ~ equalish(multiply(multiplicative_inverse(a),b),multiply(b,multiplicative_inverse(b))) ),
    inference(instantiation,[status(thm)],[c_341150]) ).

tcf(c_367929,plain,
    ( equalish(multiplicative_identity,multiply(multiplicative_inverse(a),b))
    | ~ equalish(multiply(b,multiplicative_inverse(b)),multiply(multiplicative_inverse(a),b)) ),
    inference(instantiation,[status(thm)],[c_341140]) ).

tcf(c_372013,plain,
    ( equalish(multiply(multiplicative_identity,a),multiply(multiply(multiplicative_inverse(a),b),a))
    | ~ equalish(multiplicative_identity,multiply(multiplicative_inverse(a),b)) ),
    inference(instantiation,[status(thm)],[c_354887]) ).

tcf(c_429936,plain,
    ( equalish(a,multiply(multiply(multiplicative_inverse(a),b),a))
    | ~ equalish(multiply(multiplicative_identity,a),multiply(multiply(multiplicative_inverse(a),b),a)) ),
    inference(instantiation,[status(thm)],[c_342623]) ).

tcf(c_429937,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_429936,c_372013,c_367929,c_365929,c_364030,c_362791,c_334834,c_325423,c_102254,c_102253,c_34624,c_16279,c_16278,c_3628,c_413,c_293,c_291,c_113,c_111,c_114,c_109,c_110]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : FLD027-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.38  % Computer : n016.cluster.edu
% 0.10/0.38  % Model    : x86_64 x86_64
% 0.10/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38  % Memory   : 8046.5625MB
% 0.10/0.38  % OS       : Linux 6.8.0-71-generic
% 0.10/0.38  % CPULimit : 300
% 0.10/0.38  % WCLimit  : 300
% 0.10/0.38  % DateTime : Fri Sep 25 10:47:29 UTC 2026
% 0.10/0.38  % CPUTime  : 
% 0.10/0.38  Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.42  Running first-order theorem proving
% 0.10/0.42  Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.43  
% 0.10/0.43  % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43  
% 0.10/0.43  % Detected problem language: tptp
% 0.10/0.44  % Proving...
% 181.07/33.54  % SZS status Started for theBenchmark.p
% 181.07/33.54  % SZS status Unsatisfiable for theBenchmark.p
% 181.07/33.54  
% 181.07/33.54  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 181.07/33.54  
% 181.07/33.54  % ------  iProver source info
% 181.07/33.54  
% 181.07/33.54  % git: date: 2026-07-19 20:42:38 +0200
% 181.07/33.54  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 181.07/33.54  % git: non_committed_changes: false
% 181.07/33.54  
% 181.07/33.54  % ------ Parsing...% successful
% 181.07/33.54  
% 181.07/33.54  
% 181.07/33.54  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 181.07/33.54  
% 181.07/33.54  % ------ Preprocessing... sf_s  rm: 0 0s  sf_e  pe_s  pe_e % 
% 181.07/33.54  
% 181.07/33.54  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 181.07/33.54  % ------ Proving...
% 181.07/33.54  % ------ Problem Properties 
% 181.07/33.54  
% 181.07/33.54  % 
% 181.07/33.54  % clauses                               33
% 181.07/33.54  % conjectures                           4
% 181.07/33.54  % EPR                                   15
% 181.07/33.54  % Horn                                  30
% 181.07/33.54  % unary                                 9
% 181.07/33.54  % binary                                6
% 181.07/33.54  % lits                                  79
% 181.07/33.54  % lits eq                               0
% 181.07/33.54  % fd_pure                               0
% 181.07/33.54  % fd_pseudo                             0
% 181.07/33.54  % fd_cond                               0
% 181.07/33.54  % fd_pseudo_cond                        0
% 181.07/33.54  % AC symbols                            0
% 181.07/33.54  
% 181.07/33.54  % ------ Input Options Time Limit: Unbounded
% 181.07/33.54  
% 181.07/33.54  
% 181.07/33.54  % ------ 
% 181.07/33.54  % Current options:
% 181.07/33.54  % ------ 
% 181.07/33.54  
% 181.07/33.54  
% 181.07/33.54  % 
% 181.07/33.54  
% 181.07/33.54  % ------ Proving...
% 181.07/33.54  % 
% 181.07/33.54  
% 181.07/33.54  % SZS status Unsatisfiable for theBenchmark.p
% 181.07/33.54  
% 181.07/33.54  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 181.07/33.55  
% 181.07/33.55  
%------------------------------------------------------------------------------