TSTP Solution File: BOO006-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : BOO006-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n022.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 18:05:42 EDT 2023

% Result   : Unsatisfiable 0.18s 0.56s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   36 (  17 unt;   8 typ;   0 def)
%            Number of atoms       :   50 (   7 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   46 (  24   ~;  22   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   5   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   61 (   2 sgn;   0   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    multiply: ( $i * $i ) > $i ).

tff(decl_25,type,
    product: ( $i * $i * $i ) > $o ).

tff(decl_26,type,
    additive_identity: $i ).

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

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

tff(decl_29,type,
    x: $i ).

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/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity4) ).

cnf(additive_identity1,axiom,
    sum(additive_identity,X1,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_identity1) ).

cnf(additive_identity2,axiom,
    sum(X1,additive_identity,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_identity2) ).

cnf(multiplicative_inverse1,axiom,
    product(inverse(X1),X1,additive_identity),
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse1) ).

cnf(multiplication_is_well_defined,axiom,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplication_is_well_defined) ).

cnf(closure_of_multiplication,axiom,
    product(X1,X2,multiply(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',closure_of_multiplication) ).

cnf(commutativity_of_multiplication,axiom,
    ( product(X2,X1,X3)
    | ~ product(X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',commutativity_of_multiplication) ).

cnf(prove_equations,negated_conjecture,
    ~ product(x,additive_identity,additive_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equations) ).

cnf(c_0_8,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_9,axiom,
    sum(additive_identity,X1,X1),
    additive_identity1 ).

cnf(c_0_10,plain,
    ( product(X1,X2,X3)
    | ~ product(X4,X2,additive_identity)
    | ~ product(X5,X2,X3)
    | ~ sum(X4,X5,X1) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_11,axiom,
    sum(X1,additive_identity,X1),
    additive_identity2 ).

cnf(c_0_12,plain,
    ( product(X1,X2,X3)
    | ~ product(X1,X2,additive_identity)
    | ~ product(additive_identity,X2,X3) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_13,axiom,
    product(inverse(X1),X1,additive_identity),
    multiplicative_inverse1 ).

cnf(c_0_14,axiom,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    multiplication_is_well_defined ).

cnf(c_0_15,axiom,
    product(X1,X2,multiply(X1,X2)),
    closure_of_multiplication ).

cnf(c_0_16,axiom,
    ( product(X2,X1,X3)
    | ~ product(X1,X2,X3) ),
    commutativity_of_multiplication ).

cnf(c_0_17,plain,
    ( product(inverse(X1),X1,X2)
    | ~ product(additive_identity,X1,X2) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_18,plain,
    ( X1 = multiply(X2,X3)
    | ~ product(X2,X3,X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_19,plain,
    product(X1,X2,multiply(X2,X1)),
    inference(spm,[status(thm)],[c_0_16,c_0_15]) ).

cnf(c_0_20,plain,
    ( X1 = additive_identity
    | ~ product(inverse(X2),X2,X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_13]) ).

cnf(c_0_21,plain,
    product(inverse(X1),X1,multiply(additive_identity,X1)),
    inference(spm,[status(thm)],[c_0_17,c_0_15]) ).

cnf(c_0_22,plain,
    multiply(X1,X2) = multiply(X2,X1),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_23,plain,
    multiply(X1,inverse(X1)) = additive_identity,
    inference(spm,[status(thm)],[c_0_20,c_0_19]) ).

cnf(c_0_24,plain,
    multiply(additive_identity,X1) = additive_identity,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_21]),c_0_22]),c_0_23]) ).

cnf(c_0_25,negated_conjecture,
    ~ product(x,additive_identity,additive_identity),
    prove_equations ).

cnf(c_0_26,plain,
    product(X1,additive_identity,additive_identity),
    inference(spm,[status(thm)],[c_0_19,c_0_24]) ).

cnf(c_0_27,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : BOO006-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.33  % Computer : n022.cluster.edu
% 0.15/0.33  % Model    : x86_64 x86_64
% 0.15/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33  % Memory   : 8042.1875MB
% 0.15/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33  % CPULimit   : 300
% 0.15/0.33  % WCLimit    : 300
% 0.15/0.33  % DateTime   : Sun Aug 27 08:11:39 EDT 2023
% 0.15/0.33  % CPUTime  : 
% 0.18/0.54  start to proof: theBenchmark
% 0.18/0.56  % Version  : CSE_E---1.5
% 0.18/0.56  % Problem  : theBenchmark.p
% 0.18/0.56  % Proof found
% 0.18/0.56  % SZS status Theorem for theBenchmark.p
% 0.18/0.56  % SZS output start Proof
% See solution above
% 0.18/0.56  % Total time : 0.010000 s
% 0.18/0.56  % SZS output end Proof
% 0.18/0.56  % Total time : 0.013000 s
%------------------------------------------------------------------------------