%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP573-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n025.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 00:21:39 EDT 2023

% Result   : Unsatisfiable 0.18s 0.57s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   21 (  16 unt;   5 typ;   0 def)
%            Number of atoms       :   16 (  15 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    4 (   4   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    5 (   3   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   16 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    double_divide: ( $i * $i ) > $i ).

tff(decl_23,type,
    identity: $i ).

tff(decl_24,type,
    multiply: ( $i * $i ) > $i ).

tff(decl_25,type,
    inverse: $i > $i ).

tff(decl_26,type,
    a1: $i ).

cnf(identity,axiom,
    identity = double_divide(X1,inverse(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).

cnf(inverse,axiom,
    inverse(X1) = double_divide(X1,identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).

cnf(single_axiom,axiom,
    double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),double_divide(X3,identity))),double_divide(identity,identity)) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).

cnf(prove_these_axioms_1,negated_conjecture,
    multiply(inverse(a1),a1) != identity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_1) ).

cnf(multiply,axiom,
    multiply(X1,X2) = double_divide(double_divide(X2,X1),identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).

cnf(c_0_5,axiom,
    identity = double_divide(X1,inverse(X1)),
    identity ).

cnf(c_0_6,axiom,
    inverse(X1) = double_divide(X1,identity),
    inverse ).

cnf(c_0_7,axiom,
    double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),double_divide(X3,identity))),double_divide(identity,identity)) = X2,
    single_axiom ).

cnf(c_0_8,plain,
    identity = double_divide(X1,double_divide(X1,identity)),
    inference(rw,[status(thm)],[c_0_5,c_0_6]) ).

cnf(c_0_9,negated_conjecture,
    multiply(inverse(a1),a1) != identity,
    prove_these_axioms_1 ).

cnf(c_0_10,axiom,
    multiply(X1,X2) = double_divide(double_divide(X2,X1),identity),
    multiply ).

cnf(c_0_11,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(X1,identity))),double_divide(identity,identity)) = X1,
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_12,negated_conjecture,
    double_divide(double_divide(a1,double_divide(a1,identity)),identity) != identity,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_6]),c_0_10]) ).

cnf(c_0_13,plain,
    double_divide(double_divide(identity,identity),double_divide(identity,identity)) = identity,
    inference(spm,[status(thm)],[c_0_11,c_0_8]) ).

cnf(c_0_14,negated_conjecture,
    double_divide(identity,identity) != identity,
    inference(rw,[status(thm)],[c_0_12,c_0_8]) ).

cnf(c_0_15,plain,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_13]),c_0_8]),c_0_13]),c_0_14]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : GRP573-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33  % Computer : n025.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Mon Aug 28 23:41:40 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.18/0.55  start to proof: theBenchmark
% 0.18/0.57  % Version  : CSE_E---1.5
% 0.18/0.57  % Problem  : theBenchmark.p
% 0.18/0.57  % Proof found
% 0.18/0.57  % SZS status Theorem for theBenchmark.p
% 0.18/0.57  % SZS output start Proof
% See solution above
% 0.18/0.57  % Total time : 0.003000 s
% 0.18/0.57  % SZS output end Proof
% 0.18/0.57  % Total time : 0.005000 s
%------------------------------------------------------------------------------