%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : FLD019-1 : 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 22:27:20 EDT 2023

% Result   : Unsatisfiable 0.17s 0.65s
% Output   : CNFRefutation 0.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   50 (  14 unt;  10 typ;   0 def)
%            Number of atoms       :   73 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   70 (  37   ~;  33   |;   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    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   37 (   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(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_equals_additive_identity_2,negated_conjecture,
    equalish(additive_inverse(a),additive_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_equals_additive_identity_2) ).

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

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(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(a_not_equal_to_additive_identity_3,negated_conjecture,
    ~ equalish(a,additive_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_equal_to_additive_identity_3) ).

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_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_10,axiom,
    ( equalish(X1,X2)
    | ~ equalish(X2,X1) ),
    symmetry_of_equality ).

cnf(c_0_11,negated_conjecture,
    equalish(additive_inverse(a),additive_identity),
    additive_inverse_equals_additive_identity_2 ).

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

cnf(c_0_13,hypothesis,
    defined(a),
    a_is_defined ).

cnf(c_0_14,axiom,
    ( equalish(X1,X2)
    | ~ equalish(X1,X3)
    | ~ equalish(X3,X2) ),
    transitivity_of_equality ).

cnf(c_0_15,negated_conjecture,
    equalish(additive_identity,additive_inverse(a)),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_16,hypothesis,
    equalish(add(additive_identity,a),a),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_17,negated_conjecture,
    ( equalish(X1,additive_inverse(a))
    | ~ equalish(X1,additive_identity) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_18,hypothesis,
    ( equalish(X1,a)
    | ~ equalish(X1,add(additive_identity,a)) ),
    inference(spm,[status(thm)],[c_0_14,c_0_16]) ).

cnf(c_0_19,negated_conjecture,
    ( equalish(additive_inverse(a),X1)
    | ~ equalish(X1,additive_identity) ),
    inference(spm,[status(thm)],[c_0_10,c_0_17]) ).

cnf(c_0_20,axiom,
    ( equalish(add(X1,X2),add(X3,X2))
    | ~ defined(X2)
    | ~ equalish(X1,X3) ),
    compatibility_of_equality_and_addition ).

cnf(c_0_21,axiom,
    ( equalish(add(X1,additive_inverse(X1)),additive_identity)
    | ~ defined(X1) ),
    existence_of_inverse_addition ).

cnf(c_0_22,hypothesis,
    equalish(a,add(additive_identity,a)),
    inference(spm,[status(thm)],[c_0_10,c_0_16]) ).

cnf(c_0_23,negated_conjecture,
    ( equalish(additive_inverse(a),a)
    | ~ equalish(add(additive_identity,a),additive_identity) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_24,negated_conjecture,
    ( equalish(add(additive_inverse(a),X1),add(additive_identity,X1))
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_20,c_0_11]) ).

cnf(c_0_25,hypothesis,
    equalish(add(a,additive_inverse(a)),additive_identity),
    inference(spm,[status(thm)],[c_0_21,c_0_13]) ).

cnf(c_0_26,hypothesis,
    ( equalish(X1,add(additive_identity,a))
    | ~ equalish(X1,a) ),
    inference(spm,[status(thm)],[c_0_14,c_0_22]) ).

cnf(c_0_27,negated_conjecture,
    ( equalish(X1,additive_identity)
    | ~ equalish(X1,additive_inverse(a)) ),
    inference(spm,[status(thm)],[c_0_14,c_0_11]) ).

cnf(c_0_28,negated_conjecture,
    ( equalish(a,additive_inverse(a))
    | ~ equalish(add(additive_identity,a),additive_identity) ),
    inference(spm,[status(thm)],[c_0_10,c_0_23]) ).

cnf(c_0_29,negated_conjecture,
    ~ equalish(a,additive_identity),
    a_not_equal_to_additive_identity_3 ).

cnf(c_0_30,hypothesis,
    equalish(add(additive_inverse(a),a),a),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_24]),c_0_13])]) ).

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

cnf(c_0_32,axiom,
    ( defined(additive_inverse(X1))
    | ~ defined(X1) ),
    well_definedness_of_additive_inverse ).

cnf(c_0_33,hypothesis,
    ( equalish(X1,additive_identity)
    | ~ equalish(X1,add(a,additive_inverse(a))) ),
    inference(spm,[status(thm)],[c_0_14,c_0_25]) ).

cnf(c_0_34,hypothesis,
    ( equalish(add(additive_identity,a),X1)
    | ~ equalish(X1,a) ),
    inference(spm,[status(thm)],[c_0_10,c_0_26]) ).

cnf(c_0_35,negated_conjecture,
    ~ equalish(add(additive_identity,a),additive_identity),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).

cnf(c_0_36,hypothesis,
    ( equalish(X1,a)
    | ~ equalish(X1,add(additive_inverse(a),a)) ),
    inference(spm,[status(thm)],[c_0_14,c_0_30]) ).

cnf(c_0_37,plain,
    ( equalish(add(X1,additive_inverse(X2)),add(additive_inverse(X2),X1))
    | ~ defined(X1)
    | ~ defined(X2) ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_38,hypothesis,
    ~ equalish(add(a,additive_inverse(a)),a),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).

cnf(c_0_39,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_13])]),c_0_38]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem    : FLD019-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.06/0.11  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.32  % Computer : n002.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Mon Aug 28 00:11:49 EDT 2023
% 0.11/0.32  % CPUTime  : 
% 0.17/0.55  start to proof: theBenchmark
% 0.17/0.65  % Version  : CSE_E---1.5
% 0.17/0.65  % Problem  : theBenchmark.p
% 0.17/0.65  % Proof found
% 0.17/0.65  % SZS status Theorem for theBenchmark.p
% 0.17/0.65  % SZS output start Proof
% See solution above
% 0.56/0.65  % Total time : 0.093000 s
% 0.56/0.66  % SZS output end Proof
% 0.56/0.66  % Total time : 0.095000 s
%------------------------------------------------------------------------------