%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SYN075-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n004.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 : Fri Sep  1 01:49:57 EDT 2023

% Result   : Unsatisfiable 0.20s 0.62s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   27 (   4 unt;   6 typ;   0 def)
%            Number of atoms       :   48 (  29 equ)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   52 (  25   ~;  27   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   4   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   35 (   3 sgn;   0   !;   0   ?;   0   :)

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

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

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

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

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

tff(decl_27,type,
    h: ( $i * $i ) > $i ).

cnf(clause_4,negated_conjecture,
    ( f(X2) = X2
    | ~ big_f(X1,f(X2))
    | X1 != g(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).

cnf(clause_6,negated_conjecture,
    ( big_f(X1,f(X2))
    | f(X2) = X2
    | X1 != g(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).

cnf(clause_9,negated_conjecture,
    ( big_f(h(X1,X2),f(X1))
    | h(X1,X2) = X2
    | f(X1) != X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).

cnf(clause_10,negated_conjecture,
    ( f(X1) != X1
    | h(X1,X2) != X2
    | ~ big_f(h(X1,X2),f(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10) ).

cnf(clause_1,axiom,
    ( X1 = a
    | ~ big_f(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).

cnf(clause_3,axiom,
    ( big_f(X1,X2)
    | X1 != a
    | X2 != b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).

cnf(c_0_6,negated_conjecture,
    ( f(X2) = X2
    | ~ big_f(X1,f(X2))
    | X1 != g(X2) ),
    clause_4 ).

cnf(c_0_7,negated_conjecture,
    ( big_f(X1,f(X2))
    | f(X2) = X2
    | X1 != g(X2) ),
    clause_6 ).

cnf(c_0_8,negated_conjecture,
    ( f(X1) = X1
    | ~ big_f(g(X1),f(X1)) ),
    inference(er,[status(thm)],[c_0_6]) ).

cnf(c_0_9,negated_conjecture,
    ( big_f(h(X1,X2),f(X1))
    | h(X1,X2) = X2
    | f(X1) != X1 ),
    clause_9 ).

cnf(c_0_10,negated_conjecture,
    f(X1) = X1,
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_7]),c_0_8]) ).

cnf(c_0_11,negated_conjecture,
    ( f(X1) != X1
    | h(X1,X2) != X2
    | ~ big_f(h(X1,X2),f(X1)) ),
    clause_10 ).

cnf(c_0_12,axiom,
    ( X1 = a
    | ~ big_f(X1,X2) ),
    clause_1 ).

cnf(c_0_13,negated_conjecture,
    ( h(X1,X2) = X2
    | big_f(h(X1,X2),X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_10])]) ).

cnf(c_0_14,negated_conjecture,
    ( h(X1,X2) != X2
    | ~ big_f(h(X1,X2),X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_10]),c_0_10])]) ).

cnf(c_0_15,negated_conjecture,
    ( h(X1,X2) = a
    | h(X1,X2) = X2 ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_16,axiom,
    ( big_f(X1,X2)
    | X1 != a
    | X2 != b ),
    clause_3 ).

cnf(c_0_17,negated_conjecture,
    ( h(X1,X2) = a
    | ~ big_f(X2,X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_18,plain,
    big_f(a,b),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_16])]) ).

cnf(c_0_19,negated_conjecture,
    ~ big_f(a,X1),
    inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_17])]) ).

cnf(c_0_20,plain,
    $false,
    inference(sr,[status(thm)],[c_0_18,c_0_19]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SYN075-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n004.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   : Sat Aug 26 20:39:08 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.60  start to proof: theBenchmark
% 0.20/0.62  % Version  : CSE_E---1.5
% 0.20/0.62  % Problem  : theBenchmark.p
% 0.20/0.62  % Proof found
% 0.20/0.62  % SZS status Theorem for theBenchmark.p
% 0.20/0.62  % SZS output start Proof
% See solution above
% 0.20/0.62  % Total time : 0.003000 s
% 0.20/0.62  % SZS output end Proof
% 0.20/0.62  % Total time : 0.004000 s
%------------------------------------------------------------------------------