%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : DAT041_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n013.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 May  3 02:14:16 EDT 2024

% Result   : Theorem 0.43s 1.15s
% Output   : CNFRefutation 0.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   13 (   6 unt;   0 typ;   0 def)
%            Number of atoms       :   40 (   8 equ)
%            Maximal formula atoms :    4 (   3 avg)
%            Number of connectives :   22 (  13   ~;   6   |;   1   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :   18 (  18 fml;   0 var)
%            Number arithmetic     :    7 (   0 atm;   0 fun;   0 num;   7 var)
%            Number of types       :    1 (   0 usr;   1 ari)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   2 prp; 0-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   24 (   3 sgn  14   !;   0   ?;  14   :)

% Comments : 
%------------------------------------------------------------------------------
tff(f2,axiom,
    ! [X1: $int,X2: collection] : in(X1,add(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).

tff(f11,axiom,
    ! [X19: $int,X20: collection] :
      ( ~ in(X19,X20)
    <=> ( count(remove(X19,X20)) = count(X20) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).

tff(f30,plain,
    ! [X0: $int,X1: collection] : in(X0,add(X0,X1)),
    inference(rectify,[],[f2]) ).

tff(f39,plain,
    ! [X0: $int,X1: collection] :
      ( ~ in(X0,X1)
    <=> ( count(X1) = count(remove(X0,X1)) ) ),
    inference(rectify,[],[f11]) ).

tff(f51,plain,
    ! [X0: $int,X1: collection] :
      ( ( ~ in(X0,X1)
        | ( count(X1) != count(remove(X0,X1)) ) )
      & ( ( count(X1) = count(remove(X0,X1)) )
        | in(X0,X1) ) ),
    inference(nnf_transformation,[],[f39]) ).

tff(f53,plain,
    ! [X0: $int,X1: collection] : in(X0,add(X0,X1)),
    inference(cnf_transformation,[],[f30]) ).

tff(f71,plain,
    ! [X0: $int,X1: collection] :
      ( ~ in(X0,X1)
      | ( count(X1) != count(remove(X0,X1)) ) ),
    inference(cnf_transformation,[],[f51]) ).

cnf(c_62,negated_conjecture,
    in(X0_3,add(X0_3,X0_13)),
    inference(cnf_transformation,[],[f53]) ).

cnf(c_79,negated_conjecture,
    ( count(remove(X0_3,X0_13)) != count(X0_13)
    | ~ in(X0_3,X0_13) ),
    inference(cnf_transformation,[],[f71]) ).

cnf(c_120,plain,
    ( ~ in(X0_3,X0_13)
    | count(remove(X0_3,X0_13)) != count(X0_13) ),
    inference(prop_impl_just,[status(thm)],[c_79]) ).

cnf(c_121,plain,
    ( count(remove(X0_3,X0_13)) != count(X0_13)
    | ~ in(X0_3,X0_13) ),
    inference(renaming,[status(thm)],[c_120]) ).

cnf(c_341,plain,
    ~ in(X0_3,X0_13),
    inference(global_subsumption_just,[status(thm)],[c_121]) ).

cnf(c_420,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[c_62,c_341]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : DAT041_1 : TPTP v8.1.2. Released v5.0.0.
% 0.10/0.12  % Command  : run_iprover %s %d THM
% 0.12/0.33  % Computer : n013.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu May  2 18:38:19 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.17/0.45  Running TFA theorem proving
% 0.17/0.45  Running: /export/starexec/sandbox2/solver/bin/run_problem --no_cores 8 --schedule casc_29_tfa --heuristic_context casc_unsat /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.43/1.15  % SZS status Started for theBenchmark.p
% 0.43/1.15  % SZS status Theorem for theBenchmark.p
% 0.43/1.15  
% 0.43/1.15  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.43/1.15  
% 0.43/1.15  ------  iProver source info
% 0.43/1.15  
% 0.43/1.15  git: date: 2024-05-02 19:28:25 +0000
% 0.43/1.15  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.43/1.15  git: non_committed_changes: false
% 0.43/1.15  
% 0.43/1.15  ------ Parsing...
% 0.43/1.15  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.43/1.15  
% 0.43/1.15  ------ Preprocessing... sup_sim: 7  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 0.43/1.15  
% 0.43/1.15  % SZS status Theorem for theBenchmark.p
% 0.43/1.15  
% 0.43/1.15  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.43/1.15  
% 0.43/1.15  
%------------------------------------------------------------------------------