%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : COL074-3 : TPTP v8.1.2. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n014.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 18:22:28 EDT 2023

% Result   : Unsatisfiable 0.19s 0.58s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   28 (  14 unt;  11 typ;   0 def)
%            Number of atoms       :   20 (  19 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    5 (   2   ~;   3   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   8 con; 0-2 aty)
%            Number of variables   :   11 (   3 sgn;   0   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    projection1: $i ).

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

tff(decl_26,type,
    projection2: $i ).

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

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

tff(decl_29,type,
    n: ( $i * $i ) > $i ).

tff(decl_30,type,
    k_projection1: $i ).

tff(decl_31,type,
    k_projection2: $i ).

tff(decl_32,type,
    s: $i ).

cnf(self_referential,axiom,
    s = apply(eq,pair(apply(k,s),apply(k,projection2))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',self_referential) ).

cnf(k_projection2,axiom,
    apply(k,projection2) = k_projection2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_projection2) ).

cnf(extensionality1,axiom,
    ( X1 = X2
    | apply(eq,pair(X1,X2)) = projection2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality1) ).

cnf(k_definition,negated_conjecture,
    apply(apply(k,X1),X2) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_definition) ).

cnf(equality,axiom,
    apply(eq,pair(X1,X1)) = projection1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality) ).

cnf(different_projections,axiom,
    projection1 != projection2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',different_projections) ).

cnf(c_0_6,axiom,
    s = apply(eq,pair(apply(k,s),apply(k,projection2))),
    self_referential ).

cnf(c_0_7,axiom,
    apply(k,projection2) = k_projection2,
    k_projection2 ).

cnf(c_0_8,axiom,
    ( X1 = X2
    | apply(eq,pair(X1,X2)) = projection2 ),
    extensionality1 ).

cnf(c_0_9,plain,
    apply(eq,pair(apply(k,s),k_projection2)) = s,
    inference(rw,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_10,negated_conjecture,
    apply(apply(k,X1),X2) = X1,
    k_definition ).

cnf(c_0_11,plain,
    ( apply(k,s) = k_projection2
    | s = projection2 ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_12,negated_conjecture,
    apply(k_projection2,X1) = projection2,
    inference(spm,[status(thm)],[c_0_10,c_0_7]) ).

cnf(c_0_13,negated_conjecture,
    s = projection2,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]) ).

cnf(c_0_14,axiom,
    apply(eq,pair(X1,X1)) = projection1,
    equality ).

cnf(c_0_15,axiom,
    projection1 != projection2,
    different_projections ).

cnf(c_0_16,plain,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_13]),c_0_7]),c_0_14]),c_0_13]),c_0_15]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : COL074-3 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n014.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   : Sun Aug 27 04:08:17 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
% 0.19/0.59  % Total time : 0.005000 s
% 0.19/0.59  % SZS output end Proof
% 0.19/0.59  % Total time : 0.008000 s
%------------------------------------------------------------------------------