TSTP Solution File: FLD067-1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : FLD067-1 : 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 : n028.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 15.32s 15.36s
% Output   : CNFRefutation 15.32s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   55 (  16 unt;  11 typ;   0 def)
%            Number of atoms       :   85 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   85 (  44   ~;  41   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Maximal term depth    :    3 (   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   :   50 (   0 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(existence_of_identity_addition,axiom,
    ( equalish(add(additive_identity,X1),X1)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_identity_addition) ).

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

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

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

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

cnf(less_or_equal_3,negated_conjecture,
    less_or_equal(a,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_3) ).

cnf(well_definedness_of_additive_identity,axiom,
    defined(additive_identity),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_identity) ).

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

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

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

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

cnf(not_less_or_equal_4,negated_conjecture,
    ~ less_or_equal(additive_identity,add(b,additive_inverse(a))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_4) ).

cnf(c_0_13,axiom,
    ( equalish(add(additive_identity,X1),X1)
    | ~ defined(X1) ),
    existence_of_identity_addition ).

cnf(c_0_14,hypothesis,
    defined(a),
    a_is_defined ).

cnf(c_0_15,axiom,
    ( equalish(X1,X2)
    | ~ equalish(X1,X3)
    | ~ equalish(X3,X2) ),
    transitivity_of_equality ).

cnf(c_0_16,hypothesis,
    equalish(add(additive_identity,a),a),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_17,axiom,
    ( defined(add(X1,X2))
    | ~ defined(X1)
    | ~ defined(X2) ),
    well_definedness_of_addition ).

cnf(c_0_18,axiom,
    ( less_or_equal(X1,X2)
    | ~ less_or_equal(X3,X2)
    | ~ equalish(X3,X1) ),
    compatibility_of_equality_and_order_relation ).

cnf(c_0_19,negated_conjecture,
    less_or_equal(a,b),
    less_or_equal_3 ).

cnf(c_0_20,hypothesis,
    ( equalish(X1,a)
    | ~ equalish(X1,add(additive_identity,a)) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_21,plain,
    ( equalish(add(additive_identity,add(X1,X2)),add(X1,X2))
    | ~ defined(X2)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_13,c_0_17]) ).

cnf(c_0_22,axiom,
    defined(additive_identity),
    well_definedness_of_additive_identity ).

cnf(c_0_23,negated_conjecture,
    ( less_or_equal(X1,b)
    | ~ equalish(a,X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_24,axiom,
    ( equalish(X1,X2)
    | ~ equalish(X2,X1) ),
    symmetry_of_equality ).

cnf(c_0_25,hypothesis,
    equalish(add(additive_identity,add(additive_identity,a)),a),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_14]),c_0_22])]) ).

cnf(c_0_26,negated_conjecture,
    ( less_or_equal(X1,b)
    | ~ equalish(a,X2)
    | ~ equalish(X2,X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_23]) ).

cnf(c_0_27,hypothesis,
    equalish(a,add(additive_identity,add(additive_identity,a))),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_28,axiom,
    ( equalish(add(X1,additive_inverse(X1)),additive_identity)
    | ~ defined(X1) ),
    existence_of_inverse_addition ).

cnf(c_0_29,negated_conjecture,
    ( less_or_equal(X1,b)
    | ~ equalish(add(additive_identity,add(additive_identity,a)),X1) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_30,hypothesis,
    equalish(add(a,additive_inverse(a)),additive_identity),
    inference(spm,[status(thm)],[c_0_28,c_0_14]) ).

cnf(c_0_31,axiom,
    ( equalish(add(X1,X2),add(X3,X2))
    | ~ defined(X2)
    | ~ equalish(X1,X3) ),
    compatibility_of_equality_and_addition ).

cnf(c_0_32,axiom,
    ( less_or_equal(add(X1,X2),add(X3,X2))
    | ~ defined(X2)
    | ~ less_or_equal(X1,X3) ),
    compatibility_of_order_relation_and_addition ).

cnf(c_0_33,negated_conjecture,
    less_or_equal(add(additive_identity,a),b),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_21]),c_0_14]),c_0_22])]) ).

cnf(c_0_34,hypothesis,
    ( equalish(X1,additive_identity)
    | ~ equalish(X1,add(a,additive_inverse(a))) ),
    inference(spm,[status(thm)],[c_0_15,c_0_30]) ).

cnf(c_0_35,hypothesis,
    ( equalish(add(add(additive_identity,a),X1),add(a,X1))
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_31,c_0_16]) ).

cnf(c_0_36,negated_conjecture,
    ( less_or_equal(add(add(additive_identity,a),X1),add(b,X1))
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_37,hypothesis,
    ( equalish(add(add(additive_identity,a),additive_inverse(a)),additive_identity)
    | ~ defined(additive_inverse(a)) ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_38,axiom,
    ( defined(additive_inverse(X1))
    | ~ defined(X1) ),
    well_definedness_of_additive_inverse ).

cnf(c_0_39,negated_conjecture,
    ( less_or_equal(X1,add(b,X2))
    | ~ defined(X2)
    | ~ equalish(add(add(additive_identity,a),X2),X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_36]) ).

cnf(c_0_40,hypothesis,
    equalish(add(add(additive_identity,a),additive_inverse(a)),additive_identity),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_14])]) ).

cnf(c_0_41,negated_conjecture,
    ~ less_or_equal(additive_identity,add(b,additive_inverse(a))),
    not_less_or_equal_4 ).

cnf(c_0_42,hypothesis,
    ~ defined(additive_inverse(a)),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).

cnf(c_0_43,hypothesis,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_38]),c_0_14])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : FLD067-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34  % Computer : n028.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Mon Aug 28 00:56:39 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.55  start to proof: theBenchmark
% 15.32/15.36  % Version  : CSE_E---1.5
% 15.32/15.36  % Problem  : theBenchmark.p
% 15.32/15.36  % Proof found
% 15.32/15.36  % SZS status Theorem for theBenchmark.p
% 15.32/15.36  % SZS output start Proof
% See solution above
% 15.32/15.37  % Total time : 14.803000 s
% 15.32/15.37  % SZS output end Proof
% 15.32/15.37  % Total time : 14.807000 s
%------------------------------------------------------------------------------