TSTP Solution File: FLD050-3 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : FLD050-3 : 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 : 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 : Wed Aug 30 22:27:37 EDT 2023

% Result   : Unsatisfiable 15.05s 15.16s
% Output   : CNFRefutation 15.05s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   30
% Syntax   : Number of formulae    :   62 (  22 unt;  14 typ;   0 def)
%            Number of atoms       :  106 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  116 (  58   ~;  58   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   15 (   8   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :   68 (   0 sgn;   0   !;   0   ?;   0   :)

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

tff(decl_23,type,
    additive_identity: $i ).

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

tff(decl_25,type,
    additive_inverse: $i > $i ).

tff(decl_26,type,
    product: ( $i * $i * $i ) > $o ).

tff(decl_27,type,
    multiplicative_identity: $i ).

tff(decl_28,type,
    multiplicative_inverse: $i > $i ).

tff(decl_29,type,
    add: ( $i * $i ) > $i ).

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

tff(decl_31,type,
    less_or_equal: ( $i * $i ) > $o ).

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

tff(decl_33,type,
    b: $i ).

tff(decl_34,type,
    c: $i ).

tff(decl_35,type,
    d: $i ).

cnf(associativity_multiplication_1,axiom,
    ( product(X1,X2,X3)
    | ~ product(X1,X4,X5)
    | ~ product(X4,X6,X2)
    | ~ product(X5,X6,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).

cnf(existence_of_identity_multiplication,axiom,
    ( product(multiplicative_identity,X1,X1)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).

cnf(commutativity_multiplication,axiom,
    ( product(X1,X2,X3)
    | ~ product(X2,X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).

cnf(totality_of_multiplication,axiom,
    ( product(X1,X2,multiply(X1,X2))
    | ~ defined(X1)
    | ~ defined(X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_multiplication) ).

cnf(existence_of_inverse_multiplication,axiom,
    ( product(multiplicative_inverse(X1),X1,multiplicative_identity)
    | sum(additive_identity,X1,additive_identity)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).

cnf(product_7,negated_conjecture,
    product(a,d,multiply(b,c)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_7) ).

cnf(associativity_multiplication_2,axiom,
    ( product(X1,X2,X3)
    | ~ product(X4,X5,X1)
    | ~ product(X5,X2,X6)
    | ~ product(X4,X6,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).

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

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

cnf(not_sum_6,negated_conjecture,
    ~ sum(additive_identity,d,additive_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_6) ).

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

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

cnf(well_definedness_of_multiplicative_inverse,axiom,
    ( defined(multiplicative_inverse(X1))
    | sum(additive_identity,X1,additive_identity)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).

cnf(not_product_8,negated_conjecture,
    ~ product(a,multiplicative_inverse(b),multiply(c,multiplicative_inverse(d))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_8) ).

cnf(not_sum_5,negated_conjecture,
    ~ sum(additive_identity,b,additive_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_5) ).

cnf(well_definedness_of_multiplication,axiom,
    ( defined(multiply(X1,X2))
    | ~ defined(X1)
    | ~ defined(X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplication) ).

cnf(c_0_16,axiom,
    ( product(X1,X2,X3)
    | ~ product(X1,X4,X5)
    | ~ product(X4,X6,X2)
    | ~ product(X5,X6,X3) ),
    associativity_multiplication_1 ).

cnf(c_0_17,axiom,
    ( product(multiplicative_identity,X1,X1)
    | ~ defined(X1) ),
    existence_of_identity_multiplication ).

cnf(c_0_18,axiom,
    ( product(X1,X2,X3)
    | ~ product(X2,X1,X3) ),
    commutativity_multiplication ).

cnf(c_0_19,axiom,
    ( product(X1,X2,multiply(X1,X2))
    | ~ defined(X1)
    | ~ defined(X2) ),
    totality_of_multiplication ).

cnf(c_0_20,plain,
    ( product(X1,X2,X3)
    | ~ product(X1,X4,multiplicative_identity)
    | ~ product(X4,X3,X2)
    | ~ defined(X3) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_21,axiom,
    ( product(multiplicative_inverse(X1),X1,multiplicative_identity)
    | sum(additive_identity,X1,additive_identity)
    | ~ defined(X1) ),
    existence_of_inverse_multiplication ).

cnf(c_0_22,negated_conjecture,
    product(a,d,multiply(b,c)),
    product_7 ).

cnf(c_0_23,axiom,
    ( product(X1,X2,X3)
    | ~ product(X4,X5,X1)
    | ~ product(X5,X2,X6)
    | ~ product(X4,X6,X3) ),
    associativity_multiplication_2 ).

cnf(c_0_24,plain,
    ( product(X1,X2,multiply(X2,X1))
    | ~ defined(X1)
    | ~ defined(X2) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_25,plain,
    ( product(multiplicative_inverse(X1),X2,X3)
    | sum(additive_identity,X1,additive_identity)
    | ~ product(X1,X3,X2)
    | ~ defined(X3)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_26,negated_conjecture,
    product(d,a,multiply(b,c)),
    inference(spm,[status(thm)],[c_0_18,c_0_22]) ).

cnf(c_0_27,hypothesis,
    defined(a),
    a_is_defined ).

cnf(c_0_28,hypothesis,
    defined(d),
    d_is_defined ).

cnf(c_0_29,negated_conjecture,
    ~ sum(additive_identity,d,additive_identity),
    not_sum_6 ).

cnf(c_0_30,plain,
    ( product(X1,X2,X3)
    | ~ product(X4,multiply(X2,X5),X3)
    | ~ product(X4,X5,X1)
    | ~ defined(X5)
    | ~ defined(X2) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_31,negated_conjecture,
    product(multiplicative_inverse(d),multiply(b,c),a),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])]),c_0_29]) ).

cnf(c_0_32,hypothesis,
    defined(c),
    c_is_defined ).

cnf(c_0_33,hypothesis,
    defined(b),
    b_is_defined ).

cnf(c_0_34,plain,
    ( product(X1,multiplicative_inverse(X1),multiplicative_identity)
    | sum(additive_identity,X1,additive_identity)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_21]) ).

cnf(c_0_35,negated_conjecture,
    ( product(X1,b,a)
    | ~ product(multiplicative_inverse(d),c,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33])]) ).

cnf(c_0_36,plain,
    ( product(X1,multiplicative_inverse(X2),X3)
    | sum(additive_identity,X2,additive_identity)
    | ~ product(X4,multiplicative_identity,X3)
    | ~ product(X4,X2,X1)
    | ~ defined(X2) ),
    inference(spm,[status(thm)],[c_0_23,c_0_34]) ).

cnf(c_0_37,plain,
    ( product(X1,multiplicative_identity,X1)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_17]) ).

cnf(c_0_38,negated_conjecture,
    ( product(multiply(c,multiplicative_inverse(d)),b,a)
    | ~ defined(multiplicative_inverse(d)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_24]),c_0_32])]) ).

cnf(c_0_39,axiom,
    ( defined(multiplicative_inverse(X1))
    | sum(additive_identity,X1,additive_identity)
    | ~ defined(X1) ),
    well_definedness_of_multiplicative_inverse ).

cnf(c_0_40,plain,
    ( product(X1,multiplicative_inverse(X2),X3)
    | sum(additive_identity,X2,additive_identity)
    | ~ product(X3,X2,X1)
    | ~ defined(X2)
    | ~ defined(X3) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_41,negated_conjecture,
    product(multiply(c,multiplicative_inverse(d)),b,a),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_28])]),c_0_29]) ).

cnf(c_0_42,negated_conjecture,
    ~ product(a,multiplicative_inverse(b),multiply(c,multiplicative_inverse(d))),
    not_product_8 ).

cnf(c_0_43,negated_conjecture,
    ~ sum(additive_identity,b,additive_identity),
    not_sum_5 ).

cnf(c_0_44,negated_conjecture,
    ~ defined(multiply(c,multiplicative_inverse(d))),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_33])]),c_0_42]),c_0_43]) ).

cnf(c_0_45,axiom,
    ( defined(multiply(X1,X2))
    | ~ defined(X1)
    | ~ defined(X2) ),
    well_definedness_of_multiplication ).

cnf(c_0_46,negated_conjecture,
    ~ defined(multiplicative_inverse(d)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_32])]) ).

cnf(c_0_47,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_39]),c_0_28])]),c_0_29]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : FLD050-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n019.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Sun Aug 27 23:13:13 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.18/0.57  start to proof: theBenchmark
% 15.05/15.16  % Version  : CSE_E---1.5
% 15.05/15.16  % Problem  : theBenchmark.p
% 15.05/15.16  % Proof found
% 15.05/15.16  % SZS status Theorem for theBenchmark.p
% 15.05/15.16  % SZS output start Proof
% See solution above
% 15.05/15.17  % Total time : 14.536000 s
% 15.05/15.17  % SZS output end Proof
% 15.05/15.17  % Total time : 14.541000 s
%------------------------------------------------------------------------------