%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP148-1 : 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 : n003.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 00:17:17 EDT 2023

% Result   : Unsatisfiable 0.52s 0.67s
% Output   : CNFRefutation 0.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   29 (  21 unt;   8 typ;   0 def)
%            Number of atoms       :   21 (  20 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    3 (   3   ~;   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    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   22 (   3 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,
    c: $i ).

tff(decl_29,type,
    b: $i ).

cnf(ax_lub1c_2,hypothesis,
    least_upper_bound(b,c) = c,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_lub1c_2) ).

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

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

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

cnf(ax_lub1c_1,hypothesis,
    least_upper_bound(a,c) = c,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_lub1c_1) ).

cnf(prove_ax_lub1c,negated_conjecture,
    greatest_lower_bound(least_upper_bound(a,b),c) != least_upper_bound(a,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ax_lub1c) ).

cnf(c_0_7,hypothesis,
    least_upper_bound(b,c) = c,
    ax_lub1c_2 ).

cnf(c_0_8,axiom,
    least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
    symmetry_of_lub ).

cnf(c_0_9,axiom,
    greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
    glb_absorbtion ).

cnf(c_0_10,axiom,
    least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3),
    associativity_of_lub ).

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

cnf(c_0_12,plain,
    greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
    inference(spm,[status(thm)],[c_0_9,c_0_8]) ).

cnf(c_0_13,hypothesis,
    least_upper_bound(c,least_upper_bound(b,X1)) = least_upper_bound(c,X1),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_14,axiom,
    greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
    symmetry_of_glb ).

cnf(c_0_15,hypothesis,
    least_upper_bound(a,c) = c,
    ax_lub1c_1 ).

cnf(c_0_16,negated_conjecture,
    greatest_lower_bound(least_upper_bound(a,b),c) != least_upper_bound(a,b),
    prove_ax_lub1c ).

cnf(c_0_17,hypothesis,
    greatest_lower_bound(least_upper_bound(c,X1),least_upper_bound(b,X1)) = least_upper_bound(b,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).

cnf(c_0_18,hypothesis,
    least_upper_bound(c,a) = c,
    inference(rw,[status(thm)],[c_0_15,c_0_8]) ).

cnf(c_0_19,negated_conjecture,
    greatest_lower_bound(c,least_upper_bound(a,b)) != least_upper_bound(a,b),
    inference(rw,[status(thm)],[c_0_16,c_0_14]) ).

cnf(c_0_20,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_8]),c_0_8]),c_0_19]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : GRP148-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.03/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n003.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Mon Aug 28 20:03:10 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.18/0.58  start to proof: theBenchmark
% 0.52/0.66  % Version  : CSE_E---1.5
% 0.52/0.66  % Problem  : theBenchmark.p
% 0.52/0.66  % Proof found
% 0.52/0.67  % SZS status Theorem for theBenchmark.p
% 0.52/0.67  % SZS output start Proof
% See solution above
% 0.52/0.67  % Total time : 0.075000 s
% 0.52/0.67  % SZS output end Proof
% 0.52/0.67  % Total time : 0.078000 s
%------------------------------------------------------------------------------