TSTP Solution File: FLD003-1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : FLD003-1 : 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 : n002.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 22:27:11 EDT 2023

% Result   : Unsatisfiable 1.53s 1.67s
% Output   : CNFRefutation 1.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   47 (  10 unt;  11 typ;   0 def)
%            Number of atoms       :   79 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   91 (  48   ~;  43   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   7   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   47 (   1 sgn;   0   !;   0   ?;   0   :)

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

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

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

tff(decl_25,type,
    additive_identity: $i ).

tff(decl_26,type,
    additive_inverse: $i > $i ).

tff(decl_27,type,
    multiply: ( $i * $i ) > $i ).

tff(decl_28,type,
    multiplicative_identity: $i ).

tff(decl_29,type,
    multiplicative_inverse: $i > $i ).

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

tff(decl_31,type,
    a: $i ).

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

cnf(transitivity_of_equality,axiom,
    ( equalish(X1,X2)
    | ~ equalish(X1,X3)
    | ~ equalish(X3,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).

cnf(existence_of_identity_addition,axiom,
    ( equalish(add(additive_identity,X1),X1)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_identity_addition) ).

cnf(compatibility_of_equality_and_addition,axiom,
    ( equalish(add(X1,X2),add(X3,X2))
    | ~ defined(X2)
    | ~ equalish(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_addition) ).

cnf(symmetry_of_equality,axiom,
    ( equalish(X1,X2)
    | ~ equalish(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).

cnf(existence_of_inverse_addition,axiom,
    ( equalish(add(X1,additive_inverse(X1)),additive_identity)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_addition) ).

cnf(commutativity_addition,axiom,
    ( equalish(add(X1,X2),add(X2,X1))
    | ~ defined(X1)
    | ~ defined(X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',commutativity_addition) ).

cnf(add_not_equal_to_a_3,negated_conjecture,
    ~ equalish(add(a,add(b,additive_inverse(b))),a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_not_equal_to_a_3) ).

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

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

cnf(well_definedness_of_addition,axiom,
    ( defined(add(X1,X2))
    | ~ defined(X1)
    | ~ defined(X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_addition) ).

cnf(well_definedness_of_additive_inverse,axiom,
    ( defined(additive_inverse(X1))
    | ~ defined(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_inverse) ).

cnf(c_0_11,axiom,
    ( equalish(X1,X2)
    | ~ equalish(X1,X3)
    | ~ equalish(X3,X2) ),
    transitivity_of_equality ).

cnf(c_0_12,axiom,
    ( equalish(add(additive_identity,X1),X1)
    | ~ defined(X1) ),
    existence_of_identity_addition ).

cnf(c_0_13,plain,
    ( equalish(X1,X2)
    | ~ defined(X2)
    | ~ equalish(X1,add(additive_identity,X2)) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_14,axiom,
    ( equalish(add(X1,X2),add(X3,X2))
    | ~ defined(X2)
    | ~ equalish(X1,X3) ),
    compatibility_of_equality_and_addition ).

cnf(c_0_15,plain,
    ( equalish(add(X1,X2),X2)
    | ~ defined(X2)
    | ~ equalish(X1,additive_identity) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_16,axiom,
    ( equalish(X1,X2)
    | ~ equalish(X2,X1) ),
    symmetry_of_equality ).

cnf(c_0_17,axiom,
    ( equalish(add(X1,additive_inverse(X1)),additive_identity)
    | ~ defined(X1) ),
    existence_of_inverse_addition ).

cnf(c_0_18,plain,
    ( equalish(X1,X2)
    | ~ defined(X2)
    | ~ equalish(X1,add(X3,X2))
    | ~ equalish(X3,additive_identity) ),
    inference(spm,[status(thm)],[c_0_11,c_0_15]) ).

cnf(c_0_19,axiom,
    ( equalish(add(X1,X2),add(X2,X1))
    | ~ defined(X1)
    | ~ defined(X2) ),
    commutativity_addition ).

cnf(c_0_20,plain,
    ( equalish(additive_identity,add(X1,additive_inverse(X1)))
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_21,plain,
    ( equalish(X1,additive_identity)
    | ~ defined(X2)
    | ~ equalish(X1,add(X2,additive_inverse(X2))) ),
    inference(spm,[status(thm)],[c_0_11,c_0_17]) ).

cnf(c_0_22,negated_conjecture,
    ~ equalish(add(a,add(b,additive_inverse(b))),a),
    add_not_equal_to_a_3 ).

cnf(c_0_23,plain,
    ( equalish(add(X1,X2),X1)
    | ~ defined(X1)
    | ~ defined(X2)
    | ~ equalish(X2,additive_identity) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_24,hypothesis,
    defined(a),
    a_is_defined ).

cnf(c_0_25,plain,
    ( equalish(X1,add(X2,additive_inverse(X2)))
    | ~ defined(X2)
    | ~ equalish(X1,additive_identity) ),
    inference(spm,[status(thm)],[c_0_11,c_0_20]) ).

cnf(c_0_26,plain,
    ( equalish(additive_identity,additive_identity)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_21,c_0_20]) ).

cnf(c_0_27,hypothesis,
    defined(b),
    b_is_defined ).

cnf(c_0_28,negated_conjecture,
    ( ~ defined(add(b,additive_inverse(b)))
    | ~ equalish(add(b,additive_inverse(b)),additive_identity) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).

cnf(c_0_29,plain,
    ( equalish(add(X1,additive_inverse(X1)),X2)
    | ~ defined(X1)
    | ~ equalish(X2,additive_identity) ),
    inference(spm,[status(thm)],[c_0_16,c_0_25]) ).

cnf(c_0_30,hypothesis,
    equalish(additive_identity,additive_identity),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_31,negated_conjecture,
    ~ defined(add(b,additive_inverse(b))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_27]),c_0_30])]) ).

cnf(c_0_32,axiom,
    ( defined(add(X1,X2))
    | ~ defined(X1)
    | ~ defined(X2) ),
    well_definedness_of_addition ).

cnf(c_0_33,negated_conjecture,
    ~ defined(additive_inverse(b)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_27])]) ).

cnf(c_0_34,axiom,
    ( defined(additive_inverse(X1))
    | ~ defined(X1) ),
    well_definedness_of_additive_inverse ).

cnf(c_0_35,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_27])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : FLD003-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n002.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 01:06:49 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 1.53/1.67  % Version  : CSE_E---1.5
% 1.53/1.67  % Problem  : theBenchmark.p
% 1.53/1.67  % Proof found
% 1.53/1.67  % SZS status Theorem for theBenchmark.p
% 1.53/1.67  % SZS output start Proof
% See solution above
% 1.53/1.68  % Total time : 1.099000 s
% 1.53/1.68  % SZS output end Proof
% 1.53/1.68  % Total time : 1.102000 s
%------------------------------------------------------------------------------