%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LCL843-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n027.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 06:59:56 EDT 2023

% Result   : Unsatisfiable 0.20s 0.58s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   27 (   5 unt;  22 typ;   0 def)
%            Number of atoms       :    5 (   0 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    2 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   28 (  19   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :   11 (  10 usr;   1 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   3 con; 0-3 aty)
%            Number of variables   :    2 (   2 sgn;   0   !;   0   ?;   0   :)

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

tff(decl_23,type,
    c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).

tff(decl_24,type,
    c_HOL_Ozero__class_Ozero: $i > $i ).

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

tff(decl_26,type,
    class_Ring__and__Field_Osemiring__1: $i > $o ).

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

tff(decl_28,type,
    class_Nat_Osemiring__char__0: $i > $o ).

tff(decl_29,type,
    class_Orderings_Opreorder: $i > $o ).

tff(decl_30,type,
    class_Orderings_Olinorder: $i > $o ).

tff(decl_31,type,
    class_Orderings_Oorder: $i > $o ).

tff(decl_32,type,
    class_Ring__and__Field_Oordered__idom: $i > $o ).

tff(decl_33,type,
    c_Lambda_OdB_OAbs: $i > $i ).

tff(decl_34,type,
    c_Lambda_Obeta: ( $i * $i ) > $o ).

tff(decl_35,type,
    c_Lambda_Osko__Lambda__Xbeta__cases__2__1: ( $i * $i ) > $i ).

tff(decl_36,type,
    c_Lambda_Olift: ( $i * $i ) > $i ).

tff(decl_37,type,
    c_Lambda_OdB_OVar: $i > $i ).

tff(decl_38,type,
    c_Lambda_Osubst: ( $i * $i * $i ) > $i ).

tff(decl_39,type,
    c_Lambda_OdB_OApp: ( $i * $i ) > $i ).

tff(decl_40,type,
    v_x______: $i ).

tff(decl_41,type,
    v_env______: $i > $i ).

tff(decl_42,type,
    v_Ta______: $i ).

tff(decl_43,type,
    c_InductTermi_OIT: $i > $o ).

cnf(cls_conjecture_0,negated_conjecture,
    ~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_x______)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

cnf(cls_Var__IT_0,axiom,
    c_InductTermi_OIT(c_Lambda_OdB_OVar(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__IT_0) ).

cnf(c_0_2,negated_conjecture,
    ~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_x______)),
    cls_conjecture_0 ).

cnf(c_0_3,axiom,
    c_InductTermi_OIT(c_Lambda_OdB_OVar(X1)),
    cls_Var__IT_0 ).

cnf(c_0_4,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_2,c_0_3])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : LCL843-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n027.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri Aug 25 05:31:33 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.20/0.58  % Version  : CSE_E---1.5
% 0.20/0.58  % Problem  : theBenchmark.p
% 0.20/0.58  % Proof found
% 0.20/0.58  % SZS status Theorem for theBenchmark.p
% 0.20/0.58  % SZS output start Proof
% See solution above
% 0.20/0.58  % Total time : 0.004000 s
% 0.20/0.58  % SZS output end Proof
% 0.20/0.58  % Total time : 0.008000 s
%------------------------------------------------------------------------------