TSTP Solution File: FLD035-3 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : FLD035-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n032.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 22:27:29 EDT 2023

% Result   : Unsatisfiable 0.17s 0.75s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   27
% Syntax   : Number of formulae    :   51 (  22 unt;  14 typ;   0 def)
%            Number of atoms       :   69 (   0 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   65 (  33   ~;  32   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    2 (   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   :   47 (   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,
    u: $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/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).

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

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

cnf(product_6,negated_conjecture,
    product(b,c,u),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_6) ).

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

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

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

cnf(not_sum_7,negated_conjecture,
    ~ sum(additive_identity,c,additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_7) ).

cnf(product_5,negated_conjecture,
    product(a,c,u),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_5) ).

cnf(u_is_defined,hypothesis,
    defined(u),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_is_defined) ).

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

cnf(not_product_8,negated_conjecture,
    ~ product(multiplicative_identity,a,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_8) ).

cnf(c_0_13,axiom,
    ( product(X1,X2,X3)
    | ~ product(X1,X4,X5)
    | ~ product(X4,X6,X2)
    | ~ product(X5,X6,X3) ),
    associativity_multiplication_1 ).

cnf(c_0_14,axiom,
    ( product(multiplicative_identity,X1,X1)
    | ~ defined(X1) ),
    existence_of_identity_multiplication ).

cnf(c_0_15,axiom,
    ( product(X1,X2,X3)
    | ~ product(X2,X1,X3) ),
    commutativity_multiplication ).

cnf(c_0_16,plain,
    ( product(X1,X2,X3)
    | ~ product(X1,X4,multiplicative_identity)
    | ~ product(X4,X3,X2)
    | ~ defined(X3) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_17,axiom,
    ( product(multiplicative_inverse(X1),X1,multiplicative_identity)
    | sum(additive_identity,X1,additive_identity)
    | ~ defined(X1) ),
    existence_of_inverse_multiplication ).

cnf(c_0_18,negated_conjecture,
    product(b,c,u),
    product_6 ).

cnf(c_0_19,axiom,
    ( product(X1,X2,X3)
    | ~ product(X4,X5,X1)
    | ~ product(X5,X2,X6)
    | ~ product(X4,X6,X3) ),
    associativity_multiplication_2 ).

cnf(c_0_20,plain,
    ( product(X1,multiplicative_identity,X1)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_15,c_0_14]) ).

cnf(c_0_21,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_16,c_0_17]) ).

cnf(c_0_22,negated_conjecture,
    product(c,b,u),
    inference(spm,[status(thm)],[c_0_15,c_0_18]) ).

cnf(c_0_23,hypothesis,
    defined(b),
    b_is_defined ).

cnf(c_0_24,hypothesis,
    defined(c),
    c_is_defined ).

cnf(c_0_25,negated_conjecture,
    ~ sum(additive_identity,c,additive_identity),
    not_sum_7 ).

cnf(c_0_26,negated_conjecture,
    product(a,c,u),
    product_5 ).

cnf(c_0_27,plain,
    ( product(X1,multiplicative_identity,X2)
    | ~ product(X3,X4,X2)
    | ~ product(X3,X4,X1)
    | ~ defined(X4) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_28,negated_conjecture,
    product(multiplicative_inverse(c),u,b),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24])]),c_0_25]) ).

cnf(c_0_29,hypothesis,
    defined(u),
    u_is_defined ).

cnf(c_0_30,negated_conjecture,
    product(c,a,u),
    inference(spm,[status(thm)],[c_0_15,c_0_26]) ).

cnf(c_0_31,hypothesis,
    defined(a),
    a_is_defined ).

cnf(c_0_32,negated_conjecture,
    ( product(X1,multiplicative_identity,b)
    | ~ product(multiplicative_inverse(c),u,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).

cnf(c_0_33,negated_conjecture,
    product(multiplicative_inverse(c),u,a),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_30]),c_0_31]),c_0_24])]),c_0_25]) ).

cnf(c_0_34,negated_conjecture,
    product(a,multiplicative_identity,b),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_35,negated_conjecture,
    ~ product(multiplicative_identity,a,b),
    not_product_8 ).

cnf(c_0_36,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_34]),c_0_35]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : FLD035-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.11  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.31  % Computer : n032.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit   : 300
% 0.11/0.31  % WCLimit    : 300
% 0.11/0.31  % DateTime   : Sun Aug 27 23:36:30 EDT 2023
% 0.11/0.31  % CPUTime  : 
% 0.17/0.49  start to proof: theBenchmark
% 0.17/0.75  % Version  : CSE_E---1.5
% 0.17/0.75  % Problem  : theBenchmark.p
% 0.17/0.75  % Proof found
% 0.17/0.75  % SZS status Theorem for theBenchmark.p
% 0.17/0.75  % SZS output start Proof
% See solution above
% 0.17/0.75  % Total time : 0.253000 s
% 0.17/0.75  % SZS output end Proof
% 0.17/0.75  % Total time : 0.256000 s
%------------------------------------------------------------------------------