TSTP Solution File: FLD007-1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : FLD007-1 : 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 : n011.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 22:27:13 EDT 2023

% Result   : Unsatisfiable 279.61s 280.13s
% Output   : CNFRefutation 279.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   54 (   5 unt;  10 typ;   0 def)
%            Number of atoms       :  116 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  146 (  74   ~;  72   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   4 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    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   77 (   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 ).

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

cnf(additive_inverse_not_equal_to_a_2,negated_conjecture,
    ~ equalish(additive_inverse(additive_inverse(a)),a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_not_equal_to_a_2) ).

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

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

cnf(c_0_14,axiom,
    ( equalish(add(X1,additive_inverse(X1)),additive_identity)
    | ~ defined(X1) ),
    existence_of_inverse_addition ).

cnf(c_0_15,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_16,plain,
    ( equalish(add(add(X1,additive_inverse(X1)),X2),add(additive_identity,X2))
    | ~ defined(X2)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_17,plain,
    ( equalish(add(add(X1,additive_inverse(X1)),X2),X2)
    | ~ defined(X2)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_18,plain,
    ( equalish(X1,X2)
    | ~ defined(X2)
    | ~ defined(X3)
    | ~ equalish(X1,add(add(X3,additive_inverse(X3)),X2)) ),
    inference(spm,[status(thm)],[c_0_11,c_0_17]) ).

cnf(c_0_19,axiom,
    ( equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3))
    | ~ defined(X1)
    | ~ defined(X2)
    | ~ defined(X3) ),
    associativity_addition ).

cnf(c_0_20,axiom,
    ( defined(additive_inverse(X1))
    | ~ defined(X1) ),
    well_definedness_of_additive_inverse ).

cnf(c_0_21,axiom,
    ( equalish(add(X1,X2),add(X2,X1))
    | ~ defined(X1)
    | ~ defined(X2) ),
    commutativity_addition ).

cnf(c_0_22,plain,
    ( equalish(add(X1,add(additive_inverse(X1),X2)),X2)
    | ~ defined(X2)
    | ~ defined(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).

cnf(c_0_23,plain,
    ( equalish(X1,add(X2,X3))
    | ~ defined(X2)
    | ~ defined(X3)
    | ~ equalish(X1,add(X3,X2)) ),
    inference(spm,[status(thm)],[c_0_11,c_0_21]) ).

cnf(c_0_24,plain,
    ( equalish(add(add(X1,X2),X3),add(add(X2,X1),X3))
    | ~ defined(X3)
    | ~ defined(X2)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_13,c_0_21]) ).

cnf(c_0_25,axiom,
    ( defined(add(X1,X2))
    | ~ defined(X1)
    | ~ defined(X2) ),
    well_definedness_of_addition ).

cnf(c_0_26,plain,
    ( equalish(X1,additive_identity)
    | ~ defined(X2)
    | ~ equalish(X1,add(X2,additive_inverse(X2))) ),
    inference(spm,[status(thm)],[c_0_11,c_0_14]) ).

cnf(c_0_27,plain,
    ( equalish(X1,X2)
    | ~ defined(X2)
    | ~ defined(X3)
    | ~ equalish(X1,add(X3,add(additive_inverse(X3),X2))) ),
    inference(spm,[status(thm)],[c_0_11,c_0_22]) ).

cnf(c_0_28,plain,
    ( equalish(add(add(X1,X2),X3),add(X3,add(X2,X1)))
    | ~ defined(X3)
    | ~ defined(X2)
    | ~ defined(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).

cnf(c_0_29,axiom,
    ( equalish(X1,X2)
    | ~ equalish(X2,X1) ),
    symmetry_of_equality ).

cnf(c_0_30,plain,
    ( equalish(add(additive_inverse(X1),X1),additive_identity)
    | ~ defined(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_21]),c_0_20]) ).

cnf(c_0_31,plain,
    ( equalish(add(add(X1,additive_inverse(X2)),X2),X1)
    | ~ defined(X1)
    | ~ defined(X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_20]) ).

cnf(c_0_32,plain,
    ( equalish(additive_identity,add(additive_inverse(X1),X1))
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_33,plain,
    ( equalish(X1,X2)
    | ~ defined(X2)
    | ~ defined(X3)
    | ~ equalish(X1,add(add(X2,additive_inverse(X3)),X3)) ),
    inference(spm,[status(thm)],[c_0_11,c_0_31]) ).

cnf(c_0_34,plain,
    ( equalish(add(additive_identity,X1),add(add(additive_inverse(X2),X2),X1))
    | ~ defined(X1)
    | ~ defined(X2) ),
    inference(spm,[status(thm)],[c_0_13,c_0_32]) ).

cnf(c_0_35,plain,
    ( equalish(add(additive_identity,X1),additive_inverse(additive_inverse(X1)))
    | ~ defined(additive_inverse(additive_inverse(X1)))
    | ~ defined(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_20]) ).

cnf(c_0_36,plain,
    ( equalish(add(additive_identity,X1),additive_inverse(additive_inverse(X1)))
    | ~ defined(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_20]),c_0_20]) ).

cnf(c_0_37,plain,
    ( equalish(X1,additive_inverse(additive_inverse(X2)))
    | ~ defined(X2)
    | ~ equalish(X1,add(additive_identity,X2)) ),
    inference(spm,[status(thm)],[c_0_11,c_0_36]) ).

cnf(c_0_38,plain,
    ( equalish(X1,add(additive_identity,X1))
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_29,c_0_12]) ).

cnf(c_0_39,plain,
    ( equalish(X1,additive_inverse(additive_inverse(X1)))
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_40,negated_conjecture,
    ~ equalish(additive_inverse(additive_inverse(a)),a),
    additive_inverse_not_equal_to_a_2 ).

cnf(c_0_41,plain,
    ( equalish(additive_inverse(additive_inverse(X1)),X1)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_29,c_0_39]) ).

cnf(c_0_42,hypothesis,
    defined(a),
    a_is_defined ).

cnf(c_0_43,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : FLD007-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.10/0.34  % Computer : n011.cluster.edu
% 0.10/0.34  % Model    : x86_64 x86_64
% 0.10/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34  % Memory   : 8042.1875MB
% 0.10/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.34  % CPULimit   : 300
% 0.10/0.34  % WCLimit    : 300
% 0.10/0.34  % DateTime   : Mon Aug 28 00:23:25 EDT 2023
% 0.10/0.34  % CPUTime  : 
% 0.16/0.55  start to proof: theBenchmark
% 279.61/280.13  % Version  : CSE_E---1.5
% 279.61/280.13  % Problem  : theBenchmark.p
% 279.61/280.13  % Proof found
% 279.61/280.13  % SZS status Theorem for theBenchmark.p
% 279.61/280.13  % SZS output start Proof
% See solution above
% 279.61/280.14  % Total time : 279.052000 s
% 279.61/280.14  % SZS output end Proof
% 279.61/280.14  % Total time : 279.068000 s
%------------------------------------------------------------------------------