%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : COL049-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n008.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 18:22:17 EDT 2023

% Result   : Unsatisfiable 0.19s 0.60s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   19 (  14 unt;   5 typ;   0 def)
%            Number of atoms       :   14 (  13 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    :    9 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   2   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   24 (   0 sgn;   0   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    w: $i ).

tff(decl_25,type,
    m: $i ).

tff(decl_26,type,
    f: $i > $i ).

cnf(w_definition,axiom,
    apply(apply(w,X1),X2) = apply(apply(X1,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_definition) ).

cnf(b_definition,axiom,
    apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).

cnf(prove_strong_fixed_point,negated_conjecture,
    apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_strong_fixed_point) ).

cnf(m_definition,axiom,
    apply(m,X1) = apply(X1,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_definition) ).

cnf(c_0_4,axiom,
    apply(apply(w,X1),X2) = apply(apply(X1,X2),X2),
    w_definition ).

cnf(c_0_5,axiom,
    apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
    b_definition ).

cnf(c_0_6,negated_conjecture,
    apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1))),
    prove_strong_fixed_point ).

cnf(c_0_7,plain,
    apply(apply(w,apply(b,X1)),X2) = apply(X1,apply(X2,X2)),
    inference(spm,[status(thm)],[c_0_4,c_0_5]) ).

cnf(c_0_8,axiom,
    apply(m,X1) = apply(X1,X1),
    m_definition ).

cnf(c_0_9,negated_conjecture,
    apply(f(apply(apply(b,X1),X2)),apply(X1,apply(X2,f(apply(apply(b,X1),X2))))) != apply(X1,apply(X2,f(apply(apply(b,X1),X2)))),
    inference(spm,[status(thm)],[c_0_6,c_0_5]) ).

cnf(c_0_10,plain,
    apply(apply(w,apply(b,X1)),X2) = apply(X1,apply(m,X2)),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,negated_conjecture,
    apply(f(apply(apply(b,X1),apply(apply(b,X2),X3))),apply(X1,apply(X2,apply(X3,f(apply(apply(b,X1),apply(apply(b,X2),X3))))))) != apply(X1,apply(X2,apply(X3,f(apply(apply(b,X1),apply(apply(b,X2),X3)))))),
    inference(spm,[status(thm)],[c_0_9,c_0_5]) ).

cnf(c_0_12,plain,
    apply(X1,apply(m,apply(w,apply(b,X1)))) = apply(m,apply(w,apply(b,X1))),
    inference(spm,[status(thm)],[c_0_8,c_0_10]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : COL049-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.16/0.33  % Computer : n008.cluster.edu
% 0.16/0.33  % Model    : x86_64 x86_64
% 0.16/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33  % Memory   : 8042.1875MB
% 0.16/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33  % CPULimit   : 300
% 0.16/0.33  % WCLimit    : 300
% 0.16/0.33  % DateTime   : Sun Aug 27 05:01:17 EDT 2023
% 0.16/0.33  % CPUTime  : 
% 0.19/0.54  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 : 0.044000 s
% 0.19/0.60  % SZS output end Proof
% 0.19/0.60  % Total time : 0.047000 s
%------------------------------------------------------------------------------