TSTP Solution File: FLD013-5 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : FLD013-5 : 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 : n029.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 22:27:17 EDT 2023

% Result   : Unsatisfiable 0.19s 0.58s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   31
% Syntax   : Number of formulae    :   68 (  28 unt;  16 typ;   0 def)
%            Number of atoms       :   97 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   90 (  45   ~;  45   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    1 (   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    :   12 (  12 usr;   8 con; 0-2 aty)
%            Number of variables   :   58 (   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 ).

tff(decl_36,type,
    u: $i ).

tff(decl_37,type,
    v: $i ).

cnf(associativity_addition_1,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X1,X4,X5)
    | ~ sum(X4,X6,X2)
    | ~ sum(X5,X6,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).

cnf(sum_10,negated_conjecture,
    sum(d,b,v),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_10) ).

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

cnf(sum_7,negated_conjecture,
    sum(additive_identity,a,b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_7) ).

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

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

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

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

cnf(sum_8,negated_conjecture,
    sum(additive_identity,c,d),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_8) ).

cnf(well_definedness_of_additive_identity,axiom,
    defined(additive_identity),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).

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

cnf(sum_9,negated_conjecture,
    sum(a,c,u),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_9) ).

cnf(antisymmetry_of_order_relation,axiom,
    ( sum(additive_identity,X1,X2)
    | ~ less_or_equal(X1,X2)
    | ~ less_or_equal(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',antisymmetry_of_order_relation) ).

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

cnf(not_sum_11,negated_conjecture,
    ~ sum(additive_identity,u,v),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_11) ).

cnf(c_0_15,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X1,X4,X5)
    | ~ sum(X4,X6,X2)
    | ~ sum(X5,X6,X3) ),
    associativity_addition_1 ).

cnf(c_0_16,negated_conjecture,
    sum(d,b,v),
    sum_10 ).

cnf(c_0_17,axiom,
    ( less_or_equal(X1,X2)
    | ~ less_or_equal(X3,X4)
    | ~ sum(X3,X5,X1)
    | ~ sum(X4,X5,X2) ),
    compatibility_of_order_relation_and_addition ).

cnf(c_0_18,negated_conjecture,
    sum(additive_identity,a,b),
    sum_7 ).

cnf(c_0_19,axiom,
    ( less_or_equal(X1,X2)
    | less_or_equal(X2,X1)
    | ~ defined(X1)
    | ~ defined(X2) ),
    totality_of_order_relation ).

cnf(c_0_20,negated_conjecture,
    ( sum(X1,X2,v)
    | ~ sum(X3,b,X2)
    | ~ sum(X1,X3,d) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_21,axiom,
    ( sum(additive_identity,X1,X1)
    | ~ defined(X1) ),
    existence_of_identity_addition ).

cnf(c_0_22,hypothesis,
    defined(b),
    b_is_defined ).

cnf(c_0_23,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X2,X1,X3) ),
    commutativity_addition ).

cnf(c_0_24,negated_conjecture,
    sum(additive_identity,c,d),
    sum_8 ).

cnf(c_0_25,negated_conjecture,
    ( less_or_equal(X1,b)
    | ~ less_or_equal(X2,additive_identity)
    | ~ sum(X2,a,X1) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_26,plain,
    ( less_or_equal(X1,X1)
    | ~ defined(X1) ),
    inference(ef,[status(thm)],[c_0_19]) ).

cnf(c_0_27,axiom,
    defined(additive_identity),
    well_definedness_of_additive_identity ).

cnf(c_0_28,negated_conjecture,
    ( sum(X1,b,v)
    | ~ sum(X1,additive_identity,d) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).

cnf(c_0_29,negated_conjecture,
    sum(c,additive_identity,d),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_30,negated_conjecture,
    ( less_or_equal(X1,b)
    | ~ sum(additive_identity,a,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).

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

cnf(c_0_32,plain,
    ( less_or_equal(X1,X2)
    | ~ less_or_equal(X3,additive_identity)
    | ~ defined(X2)
    | ~ sum(X3,X2,X1) ),
    inference(spm,[status(thm)],[c_0_17,c_0_21]) ).

cnf(c_0_33,negated_conjecture,
    sum(a,c,u),
    sum_9 ).

cnf(c_0_34,negated_conjecture,
    sum(c,b,v),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_35,axiom,
    ( sum(additive_identity,X1,X2)
    | ~ less_or_equal(X1,X2)
    | ~ less_or_equal(X2,X1) ),
    antisymmetry_of_order_relation ).

cnf(c_0_36,negated_conjecture,
    less_or_equal(a,b),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_21]),c_0_31])]) ).

cnf(c_0_37,plain,
    ( less_or_equal(X1,X2)
    | ~ defined(X2)
    | ~ sum(additive_identity,X2,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_26]),c_0_27])]) ).

cnf(c_0_38,negated_conjecture,
    ( sum(X1,X2,u)
    | ~ sum(X3,c,X2)
    | ~ sum(X1,X3,a) ),
    inference(spm,[status(thm)],[c_0_15,c_0_33]) ).

cnf(c_0_39,negated_conjecture,
    sum(b,c,v),
    inference(spm,[status(thm)],[c_0_23,c_0_34]) ).

cnf(c_0_40,negated_conjecture,
    ( sum(additive_identity,b,a)
    | ~ less_or_equal(b,a) ),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_41,negated_conjecture,
    less_or_equal(b,a),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_18]),c_0_31])]) ).

cnf(c_0_42,negated_conjecture,
    ( less_or_equal(X1,u)
    | ~ less_or_equal(X2,a)
    | ~ sum(X2,c,X1) ),
    inference(spm,[status(thm)],[c_0_17,c_0_33]) ).

cnf(c_0_43,negated_conjecture,
    ( sum(X1,v,u)
    | ~ sum(X1,b,a) ),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_44,negated_conjecture,
    sum(additive_identity,b,a),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]) ).

cnf(c_0_45,negated_conjecture,
    ( less_or_equal(X1,u)
    | ~ sum(b,c,X1) ),
    inference(spm,[status(thm)],[c_0_42,c_0_41]) ).

cnf(c_0_46,negated_conjecture,
    sum(additive_identity,v,u),
    inference(spm,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_47,hypothesis,
    defined(v),
    v_is_defined ).

cnf(c_0_48,negated_conjecture,
    less_or_equal(v,u),
    inference(spm,[status(thm)],[c_0_45,c_0_39]) ).

cnf(c_0_49,negated_conjecture,
    less_or_equal(u,v),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_46]),c_0_47])]) ).

cnf(c_0_50,negated_conjecture,
    ~ sum(additive_identity,u,v),
    not_sum_11 ).

cnf(c_0_51,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_48]),c_0_49])]),c_0_50]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : FLD013-5 : 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
% 0.13/0.34  % Computer : n029.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Aug 28 00:43:11 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.58  % Version  : CSE_E---1.5
% 0.19/0.58  % Problem  : theBenchmark.p
% 0.19/0.58  % Proof found
% 0.19/0.58  % SZS status Theorem for theBenchmark.p
% 0.19/0.58  % SZS output start Proof
% See solution above
% 0.19/0.59  % Total time : 0.015000 s
% 0.19/0.59  % SZS output end Proof
% 0.19/0.59  % Total time : 0.018000 s
%------------------------------------------------------------------------------