%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP188-2 : 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 : 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 : Thu Aug 31 00:17:38 EDT 2023

% Result   : Unsatisfiable 0.19s 0.58s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   21 (  14 unt;   7 typ;   0 def)
%            Number of atoms       :   14 (  13 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    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   20 (   5 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,
    b: $i ).

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

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

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(prove_p38a,negated_conjecture,
    least_upper_bound(b,least_upper_bound(a,b)) != least_upper_bound(a,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p38a) ).

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(c_0_5,axiom,
    least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
    lub_absorbtion ).

cnf(c_0_6,axiom,
    greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
    symmetry_of_glb ).

cnf(c_0_7,negated_conjecture,
    least_upper_bound(b,least_upper_bound(a,b)) != least_upper_bound(a,b),
    prove_p38a ).

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

cnf(c_0_9,plain,
    least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
    inference(spm,[status(thm)],[c_0_5,c_0_6]) ).

cnf(c_0_10,axiom,
    greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
    glb_absorbtion ).

cnf(c_0_11,negated_conjecture,
    least_upper_bound(b,least_upper_bound(b,a)) != least_upper_bound(b,a),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8]),c_0_8]) ).

cnf(c_0_12,plain,
    least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_8]) ).

cnf(c_0_13,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : GRP188-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n011.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Aug 28 19:47:26 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.19/0.58  % Version  : CSE_E---1.5
% 0.19/0.58  % Problem  : theBenchmark.p
% 0.19/0.58  % Proof found
% 0.19/0.58  % SZS status Theorem for theBenchmark.p
% 0.19/0.58  % SZS output start Proof
% See solution above
% 0.19/0.58  % Total time : 0.004000 s
% 0.19/0.58  % SZS output end Proof
% 0.19/0.58  % Total time : 0.007000 s
%------------------------------------------------------------------------------