TSTP Solution File: FLD066-3 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : FLD066-3 : 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 : 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 22:27:47 EDT 2023

% Result   : Unsatisfiable 0.12s 0.61s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   31
% Syntax   : Number of formulae    :   71 (  27 unt;  15 typ;   0 def)
%            Number of atoms       :  116 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  119 (  59   ~;  60   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 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    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :   80 (   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 ).

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

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_6,negated_conjecture,
    sum(a,c,u),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_6) ).

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

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

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

cnf(not_less_or_equal_9,negated_conjecture,
    ~ less_or_equal(a,b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_9) ).

cnf(associativity_addition_2,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X4,X5,X1)
    | ~ sum(X5,X2,X6)
    | ~ sum(X4,X6,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).

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(less_or_equal_8,negated_conjecture,
    less_or_equal(u,v),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_8) ).

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

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

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

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

cnf(c_0_16,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_17,negated_conjecture,
    sum(a,c,u),
    sum_6 ).

cnf(c_0_18,negated_conjecture,
    ( less_or_equal(X1,u)
    | ~ less_or_equal(X2,a)
    | ~ sum(X2,c,X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

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,hypothesis,
    defined(a),
    a_is_defined ).

cnf(c_0_21,negated_conjecture,
    ( less_or_equal(a,X1)
    | less_or_equal(X2,u)
    | ~ defined(X1)
    | ~ sum(X1,c,X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).

cnf(c_0_22,negated_conjecture,
    sum(b,c,v),
    sum_7 ).

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

cnf(c_0_24,negated_conjecture,
    ~ less_or_equal(a,b),
    not_less_or_equal_9 ).

cnf(c_0_25,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X4,X5,X1)
    | ~ sum(X5,X2,X6)
    | ~ sum(X4,X6,X3) ),
    associativity_addition_2 ).

cnf(c_0_26,axiom,
    ( sum(additive_identity,X1,X2)
    | ~ less_or_equal(X1,X2)
    | ~ less_or_equal(X2,X1) ),
    antisymmetry_of_order_relation ).

cnf(c_0_27,negated_conjecture,
    less_or_equal(v,u),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]),c_0_24]) ).

cnf(c_0_28,negated_conjecture,
    less_or_equal(u,v),
    less_or_equal_8 ).

cnf(c_0_29,negated_conjecture,
    ( sum(X1,c,X2)
    | ~ sum(X3,u,X2)
    | ~ sum(X3,a,X1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_17]) ).

cnf(c_0_30,negated_conjecture,
    sum(additive_identity,u,v),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).

cnf(c_0_31,axiom,
    ( sum(additive_identity,X1,X1)
    | ~ defined(X1) ),
    existence_of_identity_addition ).

cnf(c_0_32,negated_conjecture,
    ( sum(X1,c,v)
    | ~ sum(additive_identity,a,X1) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_33,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X1,X4,X5)
    | ~ sum(X4,X6,X2)
    | ~ sum(X5,X6,X3) ),
    associativity_addition_1 ).

cnf(c_0_34,plain,
    ( less_or_equal(X1,X2)
    | ~ less_or_equal(X3,additive_identity)
    | ~ defined(X2)
    | ~ sum(X3,X2,X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_31]) ).

cnf(c_0_35,plain,
    ( less_or_equal(X1,X1)
    | ~ defined(X1) ),
    inference(ef,[status(thm)],[c_0_19]) ).

cnf(c_0_36,axiom,
    defined(additive_identity),
    well_definedness_of_additive_identity ).

cnf(c_0_37,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X2,X1,X3) ),
    commutativity_addition ).

cnf(c_0_38,negated_conjecture,
    sum(a,c,v),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_31]),c_0_20])]) ).

cnf(c_0_39,plain,
    ( sum(X1,X2,X3)
    | ~ defined(X3)
    | ~ sum(X1,X4,additive_identity)
    | ~ sum(X4,X3,X2) ),
    inference(spm,[status(thm)],[c_0_33,c_0_31]) ).

cnf(c_0_40,axiom,
    ( sum(additive_inverse(X1),X1,additive_identity)
    | ~ defined(X1) ),
    existence_of_inverse_addition ).

cnf(c_0_41,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_34,c_0_35]),c_0_36])]) ).

cnf(c_0_42,plain,
    ( sum(X1,additive_identity,X1)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_37,c_0_31]) ).

cnf(c_0_43,negated_conjecture,
    sum(c,a,v),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_44,plain,
    ( sum(additive_inverse(X1),X2,X3)
    | ~ defined(X3)
    | ~ defined(X1)
    | ~ sum(X1,X3,X2) ),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_45,negated_conjecture,
    sum(c,b,v),
    inference(spm,[status(thm)],[c_0_37,c_0_22]) ).

cnf(c_0_46,hypothesis,
    defined(c),
    c_is_defined ).

cnf(c_0_47,plain,
    less_or_equal(additive_identity,additive_identity),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_36])]) ).

cnf(c_0_48,negated_conjecture,
    ( sum(X1,a,X2)
    | ~ sum(X3,v,X2)
    | ~ sum(X3,c,X1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_43]) ).

cnf(c_0_49,negated_conjecture,
    sum(additive_inverse(c),v,b),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_23]),c_0_46])]) ).

cnf(c_0_50,plain,
    sum(additive_identity,additive_identity,additive_identity),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_47]),c_0_47])]) ).

cnf(c_0_51,negated_conjecture,
    ( sum(X1,a,b)
    | ~ sum(additive_inverse(c),c,X1) ),
    inference(spm,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_52,plain,
    ( sum(additive_identity,X1,X2)
    | ~ defined(X2)
    | ~ sum(additive_identity,X2,X1) ),
    inference(spm,[status(thm)],[c_0_39,c_0_50]) ).

cnf(c_0_53,negated_conjecture,
    sum(additive_identity,a,b),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_40]),c_0_46])]) ).

cnf(c_0_54,negated_conjecture,
    sum(additive_identity,b,a),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_20])]) ).

cnf(c_0_55,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_54]),c_0_23])]),c_0_24]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : FLD066-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.09  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.08/0.28  % Computer : n032.cluster.edu
% 0.08/0.28  % Model    : x86_64 x86_64
% 0.08/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28  % Memory   : 8042.1875MB
% 0.08/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28  % CPULimit   : 300
% 0.08/0.28  % WCLimit    : 300
% 0.08/0.28  % DateTime   : Mon Aug 28 00:33:15 EDT 2023
% 0.08/0.28  % CPUTime  : 
% 0.12/0.43  start to proof: theBenchmark
% 0.12/0.61  % Version  : CSE_E---1.5
% 0.12/0.61  % Problem  : theBenchmark.p
% 0.12/0.61  % Proof found
% 0.12/0.61  % SZS status Theorem for theBenchmark.p
% 0.12/0.61  % SZS output start Proof
% See solution above
% 0.12/0.62  % Total time : 0.175000 s
% 0.12/0.62  % SZS output end Proof
% 0.12/0.62  % Total time : 0.177000 s
%------------------------------------------------------------------------------