TSTP Solution File: FLD070-2 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : FLD070-2 : 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 : n009.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 22:27:50 EDT 2023

% Result   : Unsatisfiable 0.54s 0.60s
% Output   : CNFRefutation 0.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   27
% Syntax   : Number of formulae    :   55 (  20 unt;  12 typ;   0 def)
%            Number of atoms       :   81 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   76 (  38   ~;  38   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    2 (   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    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :   46 (   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 ).

tff(decl_33,type,
    c: $i ).

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(add_equals_c_4,negated_conjecture,
    equalish(add(a,b),c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_equals_c_4) ).

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

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

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

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

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

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

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

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(less_or_equal_6,negated_conjecture,
    less_or_equal(additive_identity,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_6) ).

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(less_or_equal_5,negated_conjecture,
    less_or_equal(additive_identity,a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_5) ).

cnf(not_less_or_equal_7,negated_conjecture,
    ~ less_or_equal(additive_identity,c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_7) ).

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

cnf(c_0_16,negated_conjecture,
    equalish(add(a,b),c),
    add_equals_c_4 ).

cnf(c_0_17,negated_conjecture,
    ( equalish(X1,c)
    | ~ equalish(X1,add(a,b)) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_18,axiom,
    ( equalish(add(X1,X2),add(X2,X1))
    | ~ defined(X1)
    | ~ defined(X2) ),
    commutativity_addition ).

cnf(c_0_19,hypothesis,
    defined(a),
    a_is_defined ).

cnf(c_0_20,hypothesis,
    defined(b),
    b_is_defined ).

cnf(c_0_21,axiom,
    ( equalish(X1,X2)
    | ~ equalish(X2,X1) ),
    symmetry_of_equality ).

cnf(c_0_22,negated_conjecture,
    equalish(add(b,a),c),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]) ).

cnf(c_0_23,axiom,
    ( less_or_equal(X1,X2)
    | ~ less_or_equal(X3,X2)
    | ~ equalish(X3,X1) ),
    compatibility_of_equality_and_order_relation ).

cnf(c_0_24,negated_conjecture,
    equalish(c,add(b,a)),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_25,axiom,
    ( less_or_equal(X1,X2)
    | less_or_equal(X2,X1)
    | ~ defined(X1)
    | ~ defined(X2) ),
    totality_of_order_relation ).

cnf(c_0_26,negated_conjecture,
    ( less_or_equal(add(b,a),X1)
    | ~ less_or_equal(c,X1) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_27,plain,
    ( less_or_equal(X1,X1)
    | ~ defined(X1) ),
    inference(ef,[status(thm)],[c_0_25]) ).

cnf(c_0_28,hypothesis,
    defined(c),
    c_is_defined ).

cnf(c_0_29,axiom,
    ( less_or_equal(X1,X2)
    | ~ less_or_equal(X1,X3)
    | ~ less_or_equal(X3,X2) ),
    transitivity_of_order_relation ).

cnf(c_0_30,negated_conjecture,
    less_or_equal(add(b,a),c),
    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,
    ( 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_32,negated_conjecture,
    less_or_equal(additive_identity,b),
    less_or_equal_6 ).

cnf(c_0_33,axiom,
    ( equalish(add(additive_identity,X1),X1)
    | ~ defined(X1) ),
    existence_of_identity_addition ).

cnf(c_0_34,negated_conjecture,
    ( less_or_equal(X1,c)
    | ~ less_or_equal(X1,add(b,a)) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_35,negated_conjecture,
    ( less_or_equal(add(additive_identity,X1),add(b,X1))
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_36,plain,
    ( less_or_equal(X1,X2)
    | ~ less_or_equal(add(additive_identity,X1),X2)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_23,c_0_33]) ).

cnf(c_0_37,negated_conjecture,
    less_or_equal(add(additive_identity,a),c),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_19])]) ).

cnf(c_0_38,negated_conjecture,
    less_or_equal(a,c),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_19])]) ).

cnf(c_0_39,negated_conjecture,
    ( less_or_equal(X1,c)
    | ~ less_or_equal(X1,a) ),
    inference(spm,[status(thm)],[c_0_29,c_0_38]) ).

cnf(c_0_40,negated_conjecture,
    less_or_equal(additive_identity,a),
    less_or_equal_5 ).

cnf(c_0_41,negated_conjecture,
    ~ less_or_equal(additive_identity,c),
    not_less_or_equal_7 ).

cnf(c_0_42,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : FLD070-2 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.11/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34  % Computer : n009.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   : Sun Aug 27 23:41:05 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.54/0.60  % Version  : CSE_E---1.5
% 0.54/0.60  % Problem  : theBenchmark.p
% 0.54/0.60  % Proof found
% 0.54/0.60  % SZS status Theorem for theBenchmark.p
% 0.54/0.60  % SZS output start Proof
% See solution above
% 0.54/0.61  % Total time : 0.024000 s
% 0.54/0.61  % SZS output end Proof
% 0.54/0.61  % Total time : 0.028000 s
%------------------------------------------------------------------------------