%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET822-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n021.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 14:35:42 EDT 2023

% Result   : Unsatisfiable 0.21s 0.60s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   25 (  10 unt;   8 typ;   0 def)
%            Number of atoms       :   26 (   4 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   20 (  11   ~;   9   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (   5   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-3 aty)
%            Number of variables   :   32 (   7 sgn;   0   !;   0   ?;   0   :)

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

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

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

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

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

tff(decl_27,type,
    v_P: $i > $o ).

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

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

cnf(cls_conjecture_1,negated_conjecture,
    ( c_in(v_x(X1,X2),X2,tc_IntDef_Oint)
    | ~ c_in(v_f(X1),X2,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

cnf(cls_Set_OinsertCI_1,axiom,
    c_in(X1,c_insert(X1,X2,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).

cnf(cls_Set_OinsertE_0,axiom,
    ( c_in(X1,X3,X4)
    | X1 = X2
    | ~ c_in(X1,c_insert(X2,X3,X4),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).

cnf(cls_Set_OemptyE_0,axiom,
    ~ c_in(X1,c_emptyset,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).

cnf(cls_conjecture_2,negated_conjecture,
    ( ~ c_in(v_f(X1),X2,tc_IntDef_Oint)
    | ~ v_P(v_x(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

cnf(cls_conjecture_0,negated_conjecture,
    v_P(v_f(v_b)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

cnf(c_0_6,negated_conjecture,
    ( c_in(v_x(X1,X2),X2,tc_IntDef_Oint)
    | ~ c_in(v_f(X1),X2,tc_IntDef_Oint) ),
    cls_conjecture_1 ).

cnf(c_0_7,axiom,
    c_in(X1,c_insert(X1,X2,X3),X3),
    cls_Set_OinsertCI_1 ).

cnf(c_0_8,axiom,
    ( c_in(X1,X3,X4)
    | X1 = X2
    | ~ c_in(X1,c_insert(X2,X3,X4),X4) ),
    cls_Set_OinsertE_0 ).

cnf(c_0_9,negated_conjecture,
    c_in(v_x(X1,c_insert(v_f(X1),X2,tc_IntDef_Oint)),c_insert(v_f(X1),X2,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_10,axiom,
    ~ c_in(X1,c_emptyset,X2),
    cls_Set_OemptyE_0 ).

cnf(c_0_11,negated_conjecture,
    ( v_x(X1,c_insert(v_f(X1),X2,tc_IntDef_Oint)) = v_f(X1)
    | c_in(v_x(X1,c_insert(v_f(X1),X2,tc_IntDef_Oint)),X2,tc_IntDef_Oint) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_12,negated_conjecture,
    ( ~ c_in(v_f(X1),X2,tc_IntDef_Oint)
    | ~ v_P(v_x(X1,X2)) ),
    cls_conjecture_2 ).

cnf(c_0_13,negated_conjecture,
    v_x(X1,c_insert(v_f(X1),c_emptyset,tc_IntDef_Oint)) = v_f(X1),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_14,negated_conjecture,
    v_P(v_f(v_b)),
    cls_conjecture_0 ).

cnf(c_0_15,negated_conjecture,
    ~ v_P(v_f(X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_7])]) ).

cnf(c_0_16,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[c_0_14,c_0_15]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET822-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n021.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sat Aug 26 16:37:42 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.59  start to proof: theBenchmark
% 0.21/0.60  % Version  : CSE_E---1.5
% 0.21/0.60  % Problem  : theBenchmark.p
% 0.21/0.60  % Proof found
% 0.21/0.60  % SZS status Theorem for theBenchmark.p
% 0.21/0.60  % SZS output start Proof
% See solution above
% 0.21/0.60  % Total time : 0.004000 s
% 0.21/0.60  % SZS output end Proof
% 0.21/0.60  % Total time : 0.007000 s
%------------------------------------------------------------------------------