%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SYN056+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n005.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 01:49:21 EDT 2023

% Result   : Theorem 0.21s 0.61s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   34 (   5 unt;   8 typ;   0 def)
%            Number of atoms       :   79 (   0 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :   89 (  36   ~;  37   |;   7   &)
%                                         (   4 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-1 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :   28 (   4 sgn;  12   !;   2   ?;   0   :)

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

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

tff(decl_24,type,
    big_r: $i > $o ).

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

tff(decl_26,type,
    esk1_0: $i ).

tff(decl_27,type,
    esk2_0: $i ).

tff(decl_28,type,
    esk3_0: $i ).

tff(decl_29,type,
    esk4_0: $i ).

fof(pel26,conjecture,
    ( ! [X1] :
        ( big_p(X1)
       => big_r(X1) )
  <=> ! [X2] :
        ( big_q(X2)
       => big_s(X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel26) ).

fof(pel26_1,axiom,
    ( ? [X1] : big_p(X1)
  <=> ? [X2] : big_q(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel26_1) ).

fof(pel26_2,axiom,
    ! [X1,X2] :
      ( ( big_p(X1)
        & big_q(X2) )
     => ( big_r(X1)
      <=> big_s(X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel26_2) ).

fof(c_0_3,negated_conjecture,
    ~ ( ! [X1] :
          ( big_p(X1)
         => big_r(X1) )
    <=> ! [X2] :
          ( big_q(X2)
         => big_s(X2) ) ),
    inference(assume_negation,[status(cth)],[pel26]) ).

fof(c_0_4,plain,
    ! [X3,X5] :
      ( ( ~ big_p(X3)
        | big_q(esk1_0) )
      & ( ~ big_q(X5)
        | big_p(esk2_0) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pel26_1])])])]) ).

fof(c_0_5,negated_conjecture,
    ! [X11,X12] :
      ( ( big_q(esk4_0)
        | big_p(esk3_0) )
      & ( ~ big_s(esk4_0)
        | big_p(esk3_0) )
      & ( big_q(esk4_0)
        | ~ big_r(esk3_0) )
      & ( ~ big_s(esk4_0)
        | ~ big_r(esk3_0) )
      & ( ~ big_p(X11)
        | big_r(X11)
        | ~ big_q(X12)
        | big_s(X12) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])])]) ).

fof(c_0_6,plain,
    ! [X7,X8] :
      ( ( ~ big_r(X7)
        | big_s(X8)
        | ~ big_p(X7)
        | ~ big_q(X8) )
      & ( ~ big_s(X8)
        | big_r(X7)
        | ~ big_p(X7)
        | ~ big_q(X8) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pel26_2])])]) ).

cnf(c_0_7,plain,
    ( big_p(esk2_0)
    | ~ big_q(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,negated_conjecture,
    ( big_q(esk4_0)
    | big_p(esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    ( big_r(X2)
    | ~ big_s(X1)
    | ~ big_p(X2)
    | ~ big_q(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    ( big_r(X1)
    | big_s(X2)
    | ~ big_p(X1)
    | ~ big_q(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_11,plain,
    ( big_q(esk1_0)
    | ~ big_p(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_12,negated_conjecture,
    ( big_p(esk3_0)
    | big_p(esk2_0) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_13,plain,
    ( big_r(X1)
    | ~ big_q(X2)
    | ~ big_p(X1) ),
    inference(csr,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,negated_conjecture,
    big_q(esk1_0),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_11]) ).

cnf(c_0_15,plain,
    ( big_s(X2)
    | ~ big_r(X1)
    | ~ big_p(X1)
    | ~ big_q(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_16,negated_conjecture,
    ( ~ big_s(esk4_0)
    | ~ big_r(esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_17,negated_conjecture,
    ( big_r(X1)
    | ~ big_p(X1) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_18,negated_conjecture,
    ( big_p(esk3_0)
    | ~ big_s(esk4_0) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_19,plain,
    ( big_s(X1)
    | ~ big_q(X1)
    | ~ big_p(X2) ),
    inference(csr,[status(thm)],[c_0_15,c_0_13]) ).

cnf(c_0_20,negated_conjecture,
    big_p(esk2_0),
    inference(spm,[status(thm)],[c_0_7,c_0_14]) ).

cnf(c_0_21,negated_conjecture,
    ( big_q(esk4_0)
    | ~ big_r(esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_22,negated_conjecture,
    ~ big_s(esk4_0),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).

cnf(c_0_23,negated_conjecture,
    ( big_s(X1)
    | ~ big_q(X1) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_24,negated_conjecture,
    big_q(esk4_0),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_17]),c_0_8]) ).

cnf(c_0_25,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : SYN056+1 : TPTP v8.1.2. Released v2.0.0.
% 0.14/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.15/0.35  % Computer : n005.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Sat Aug 26 19:15:38 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 0.21/0.60  start to proof: theBenchmark
% 0.21/0.61  % Version  : CSE_E---1.5
% 0.21/0.61  % Problem  : theBenchmark.p
% 0.21/0.61  % Proof found
% 0.21/0.61  % SZS status Theorem for theBenchmark.p
% 0.21/0.61  % SZS output start Proof
% See solution above
% 0.21/0.61  % Total time : 0.006000 s
% 0.21/0.61  % SZS output end Proof
% 0.21/0.61  % Total time : 0.008000 s
%------------------------------------------------------------------------------