%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP166-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n017.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 : Thu Aug 31 00:17:23 EDT 2023

% Result   : Unsatisfiable 0.19s 0.60s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   20 (  13 unt;   7 typ;   0 def)
%            Number of atoms       :   13 (  12 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   14 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    identity: $i ).

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

tff(decl_24,type,
    inverse: $i > $i ).

tff(decl_25,type,
    greatest_lower_bound: ( $i * $i ) > $i ).

tff(decl_26,type,
    least_upper_bound: ( $i * $i ) > $i ).

tff(decl_27,type,
    a: $i ).

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

cnf(monotony_lub2,axiom,
    multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).

cnf(left_identity,axiom,
    multiply(identity,X1) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).

cnf(symmetry_of_lub,axiom,
    least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).

cnf(lat3a_2,hypothesis,
    least_upper_bound(b,identity) = b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lat3a_2) ).

cnf(prove_lat3a,negated_conjecture,
    least_upper_bound(a,multiply(b,a)) != multiply(b,a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lat3a) ).

cnf(c_0_5,axiom,
    multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
    monotony_lub2 ).

cnf(c_0_6,axiom,
    multiply(identity,X1) = X1,
    left_identity ).

cnf(c_0_7,axiom,
    least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
    symmetry_of_lub ).

cnf(c_0_8,hypothesis,
    least_upper_bound(b,identity) = b,
    lat3a_2 ).

cnf(c_0_9,negated_conjecture,
    least_upper_bound(a,multiply(b,a)) != multiply(b,a),
    prove_lat3a ).

cnf(c_0_10,plain,
    least_upper_bound(X1,multiply(X2,X1)) = multiply(least_upper_bound(X2,identity),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_7]) ).

cnf(c_0_11,hypothesis,
    least_upper_bound(identity,b) = b,
    inference(rw,[status(thm)],[c_0_8,c_0_7]) ).

cnf(c_0_12,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_7]),c_0_11])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : GRP166-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.11/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n017.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Mon Aug 28 23:32:58 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.60  % Version  : CSE_E---1.5
% 0.19/0.60  % Problem  : theBenchmark.p
% 0.19/0.60  % Proof found
% 0.19/0.60  % SZS status Theorem for theBenchmark.p
% 0.19/0.60  % SZS output start Proof
% See solution above
% 0.19/0.60  % Total time : 0.025000 s
% 0.19/0.60  % SZS output end Proof
% 0.19/0.60  % Total time : 0.028000 s
%------------------------------------------------------------------------------