TSTP Solution File: COM003_1 by E---3.2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.2.0
% Problem  : COM003_1 : TPTP v8.2.0. Released v5.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n017.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 : Mon Jun 24 04:53:10 EDT 2024

% Result   : Theorem 0.21s 0.52s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   27
% Syntax   : Number of formulae    :   77 (  13 unt;  22 typ;   0 def)
%            Number of atoms       :  337 (   0 equ)
%            Maximal formula atoms :   80 (   6 avg)
%            Number of connectives :  455 ( 173   ~; 198   |;  57   &)
%                                         (   0 <=>;  27  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :   18 (  12   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   14 (  14 usr;   6 con; 0-1 aty)
%            Number of variables   :  125 (   0 sgn 113   !;  12   ?; 125   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_sort1,type,
    output: $tType ).

tff(decl_sort2,type,
    algorithm: $tType ).

tff(decl_sort3,type,
    program: $tType ).

tff(decl_sort4,type,
    input: $tType ).

tff(decl_22,type,
    bad: output ).

tff(decl_23,type,
    good: output ).

tff(decl_24,type,
    decides: ( algorithm * program * input ) > $o ).

tff(decl_25,type,
    halts2: ( program * input ) > $o ).

tff(decl_26,type,
    halts3: ( program * program * input ) > $o ).

tff(decl_27,type,
    outputs: ( program * output ) > $o ).

tff(decl_28,type,
    algorithm_of: program > algorithm ).

tff(decl_29,type,
    as_input: program > input ).

tff(decl_30,type,
    esk1_0: algorithm ).

tff(decl_31,type,
    esk2_1: algorithm > program ).

tff(decl_32,type,
    esk3_1: algorithm > input ).

tff(decl_33,type,
    esk4_0: program ).

tff(decl_34,type,
    esk5_1: program > program ).

tff(decl_35,type,
    esk6_1: program > program ).

tff(decl_36,type,
    esk7_0: program ).

tff(decl_37,type,
    esk8_1: program > program ).

tff(decl_38,type,
    esk9_1: program > program ).

tff(decl_39,type,
    esk10_0: program ).

tff(prove_this,conjecture,
    ~ ? [X7: algorithm] :
      ! [X8: program,X9: input] : decides(X7,X8,X9),
    file('/export/starexec/sandbox2/tmp/tmp.USwuOyZ2yx/E---3.1_29931.p',prove_this) ).

tff(p2,axiom,
    ! [X4: program,X2: program,X3: input] :
      ( decides(algorithm_of(X4),X2,X3)
     => ! [X2: program,X3: input] :
          ( ( halts2(X2,X3)
           => ( halts3(X4,X2,X3)
              & outputs(X4,good) ) )
          & ( ~ halts2(X2,X3)
           => ( halts3(X4,X2,X3)
              & outputs(X4,bad) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.USwuOyZ2yx/E---3.1_29931.p',p2) ).

tff(p1,axiom,
    ( ? [X1: algorithm] :
      ! [X2: program,X3: input] : decides(X1,X2,X3)
   => ? [X4: program] :
      ! [X2: program,X3: input] : decides(algorithm_of(X4),X2,X3) ),
    file('/export/starexec/sandbox2/tmp/tmp.USwuOyZ2yx/E---3.1_29931.p',p1) ).

tff(p4,axiom,
    ( ? [X5: program] :
      ! [X2: program] :
        ( ( halts2(X2,as_input(X2))
         => ( halts2(X5,as_input(X2))
            & outputs(X5,good) ) )
        & ( ~ halts2(X2,as_input(X2))
         => ( halts2(X5,as_input(X2))
            & outputs(X5,bad) ) ) )
   => ? [X6: program] :
      ! [X2: program] :
        ( ( halts2(X2,as_input(X2))
         => ~ halts2(X6,as_input(X2)) )
        & ( ~ halts2(X2,as_input(X2))
         => ( halts2(X6,as_input(X2))
            & outputs(X6,bad) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.USwuOyZ2yx/E---3.1_29931.p',p4) ).

tff(p3,axiom,
    ( ? [X4: program] :
      ! [X2: program] :
        ( ( halts2(X2,as_input(X2))
         => ( halts3(X4,X2,as_input(X2))
            & outputs(X4,good) ) )
        & ( ~ halts2(X2,as_input(X2))
         => ( halts3(X4,X2,as_input(X2))
            & outputs(X4,bad) ) ) )
   => ? [X5: program] :
      ! [X2: program] :
        ( ( halts2(X2,as_input(X2))
         => ( halts2(X5,as_input(X2))
            & outputs(X5,good) ) )
        & ( ~ halts2(X2,as_input(X2))
         => ( halts2(X5,as_input(X2))
            & outputs(X5,bad) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.USwuOyZ2yx/E---3.1_29931.p',p3) ).

tff(c_0_5,negated_conjecture,
    ~ ~ ? [X7: algorithm] :
        ! [X8: program,X9: input] : decides(X7,X8,X9),
    inference(assume_negation,[status(cth)],[prove_this]) ).

tff(c_0_6,plain,
    ! [X4: program,X2: program,X3: input] :
      ( decides(algorithm_of(X4),X2,X3)
     => ! [X2: program,X3: input] :
          ( ( halts2(X2,X3)
           => ( halts3(X4,X2,X3)
              & outputs(X4,good) ) )
          & ( ~ halts2(X2,X3)
           => ( halts3(X4,X2,X3)
              & outputs(X4,bad) ) ) ) ),
    inference(fof_simplification,[status(thm)],[p2]) ).

tff(c_0_7,plain,
    ! [X13: algorithm,X17: program,X18: input] :
      ( ~ decides(X13,esk2_1(X13),esk3_1(X13))
      | decides(algorithm_of(esk4_0),X17,X18) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])])])]) ).

tff(c_0_8,negated_conjecture,
    ! [X11: program,X12: input] : decides(esk1_0,X11,X12),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

tff(c_0_9,plain,
    ( ? [X5: program] :
      ! [X2: program] :
        ( ( halts2(X2,as_input(X2))
         => ( halts2(X5,as_input(X2))
            & outputs(X5,good) ) )
        & ( ~ halts2(X2,as_input(X2))
         => ( halts2(X5,as_input(X2))
            & outputs(X5,bad) ) ) )
   => ? [X6: program] :
      ! [X2: program] :
        ( ( halts2(X2,as_input(X2))
         => ~ halts2(X6,as_input(X2)) )
        & ( ~ halts2(X2,as_input(X2))
         => ( halts2(X6,as_input(X2))
            & outputs(X6,bad) ) ) ) ),
    inference(fof_simplification,[status(thm)],[p4]) ).

tff(c_0_10,plain,
    ! [X19: program,X20: program,X21: input,X22: program,X23: input] :
      ( ( halts3(X19,X22,X23)
        | ~ halts2(X22,X23)
        | ~ decides(algorithm_of(X19),X20,X21) )
      & ( outputs(X19,good)
        | ~ halts2(X22,X23)
        | ~ decides(algorithm_of(X19),X20,X21) )
      & ( halts3(X19,X22,X23)
        | halts2(X22,X23)
        | ~ decides(algorithm_of(X19),X20,X21) )
      & ( outputs(X19,bad)
        | halts2(X22,X23)
        | ~ decides(algorithm_of(X19),X20,X21) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).

tcf(c_0_11,plain,
    ! [X3: input,X2: program,X1: algorithm] :
      ( decides(algorithm_of(esk4_0),X2,X3)
      | ~ decides(X1,esk2_1(X1),esk3_1(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

tcf(c_0_12,negated_conjecture,
    ! [X2: program,X3: input] : decides(esk1_0,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

tff(c_0_13,plain,
    ( ? [X4: program] :
      ! [X2: program] :
        ( ( halts2(X2,as_input(X2))
         => ( halts3(X4,X2,as_input(X2))
            & outputs(X4,good) ) )
        & ( ~ halts2(X2,as_input(X2))
         => ( halts3(X4,X2,as_input(X2))
            & outputs(X4,bad) ) ) )
   => ? [X5: program] :
      ! [X2: program] :
        ( ( halts2(X2,as_input(X2))
         => ( halts2(X5,as_input(X2))
            & outputs(X5,good) ) )
        & ( ~ halts2(X2,as_input(X2))
         => ( halts2(X5,as_input(X2))
            & outputs(X5,bad) ) ) ) ),
    inference(fof_simplification,[status(thm)],[p3]) ).

tff(c_0_14,plain,
    ! [X29: program,X33: program] :
      ( ( ~ halts2(X33,as_input(X33))
        | ~ halts2(esk10_0,as_input(X33))
        | ~ halts2(esk9_1(X29),as_input(esk9_1(X29)))
        | halts2(esk8_1(X29),as_input(esk8_1(X29))) )
      & ( halts2(esk10_0,as_input(X33))
        | halts2(X33,as_input(X33))
        | ~ halts2(esk9_1(X29),as_input(esk9_1(X29)))
        | halts2(esk8_1(X29),as_input(esk8_1(X29))) )
      & ( outputs(esk10_0,bad)
        | halts2(X33,as_input(X33))
        | ~ halts2(esk9_1(X29),as_input(esk9_1(X29)))
        | halts2(esk8_1(X29),as_input(esk8_1(X29))) )
      & ( ~ halts2(X33,as_input(X33))
        | ~ halts2(esk10_0,as_input(X33))
        | ~ halts2(X29,as_input(esk9_1(X29)))
        | ~ outputs(X29,bad)
        | halts2(esk8_1(X29),as_input(esk8_1(X29))) )
      & ( halts2(esk10_0,as_input(X33))
        | halts2(X33,as_input(X33))
        | ~ halts2(X29,as_input(esk9_1(X29)))
        | ~ outputs(X29,bad)
        | halts2(esk8_1(X29),as_input(esk8_1(X29))) )
      & ( outputs(esk10_0,bad)
        | halts2(X33,as_input(X33))
        | ~ halts2(X29,as_input(esk9_1(X29)))
        | ~ outputs(X29,bad)
        | halts2(esk8_1(X29),as_input(esk8_1(X29))) )
      & ( ~ halts2(X33,as_input(X33))
        | ~ halts2(esk10_0,as_input(X33))
        | ~ halts2(esk9_1(X29),as_input(esk9_1(X29)))
        | ~ halts2(X29,as_input(esk8_1(X29)))
        | ~ outputs(X29,good) )
      & ( halts2(esk10_0,as_input(X33))
        | halts2(X33,as_input(X33))
        | ~ halts2(esk9_1(X29),as_input(esk9_1(X29)))
        | ~ halts2(X29,as_input(esk8_1(X29)))
        | ~ outputs(X29,good) )
      & ( outputs(esk10_0,bad)
        | halts2(X33,as_input(X33))
        | ~ halts2(esk9_1(X29),as_input(esk9_1(X29)))
        | ~ halts2(X29,as_input(esk8_1(X29)))
        | ~ outputs(X29,good) )
      & ( ~ halts2(X33,as_input(X33))
        | ~ halts2(esk10_0,as_input(X33))
        | ~ halts2(X29,as_input(esk9_1(X29)))
        | ~ outputs(X29,bad)
        | ~ halts2(X29,as_input(esk8_1(X29)))
        | ~ outputs(X29,good) )
      & ( halts2(esk10_0,as_input(X33))
        | halts2(X33,as_input(X33))
        | ~ halts2(X29,as_input(esk9_1(X29)))
        | ~ outputs(X29,bad)
        | ~ halts2(X29,as_input(esk8_1(X29)))
        | ~ outputs(X29,good) )
      & ( outputs(esk10_0,bad)
        | halts2(X33,as_input(X33))
        | ~ halts2(X29,as_input(esk9_1(X29)))
        | ~ outputs(X29,bad)
        | ~ halts2(X29,as_input(esk8_1(X29)))
        | ~ outputs(X29,good) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])])])])]) ).

tcf(c_0_15,plain,
    ! [X2: program,X3: input,X4: program,X5: program,X9: input] :
      ( outputs(X2,bad)
      | halts2(X4,X3)
      | ~ decides(algorithm_of(X2),X5,X9) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

tcf(c_0_16,negated_conjecture,
    ! [X2: program,X3: input] : decides(algorithm_of(esk4_0),X2,X3),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

tcf(c_0_17,plain,
    ! [X2: program,X3: input,X4: program,X5: program,X9: input] :
      ( outputs(X2,good)
      | ~ halts2(X4,X3)
      | ~ decides(algorithm_of(X2),X5,X9) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

tff(c_0_18,plain,
    ! [X24: program,X28: program] :
      ( ( halts2(esk7_0,as_input(X28))
        | ~ halts2(X28,as_input(X28))
        | ~ halts2(esk6_1(X24),as_input(esk6_1(X24)))
        | halts2(esk5_1(X24),as_input(esk5_1(X24))) )
      & ( outputs(esk7_0,good)
        | ~ halts2(X28,as_input(X28))
        | ~ halts2(esk6_1(X24),as_input(esk6_1(X24)))
        | halts2(esk5_1(X24),as_input(esk5_1(X24))) )
      & ( halts2(esk7_0,as_input(X28))
        | halts2(X28,as_input(X28))
        | ~ halts2(esk6_1(X24),as_input(esk6_1(X24)))
        | halts2(esk5_1(X24),as_input(esk5_1(X24))) )
      & ( outputs(esk7_0,bad)
        | halts2(X28,as_input(X28))
        | ~ halts2(esk6_1(X24),as_input(esk6_1(X24)))
        | halts2(esk5_1(X24),as_input(esk5_1(X24))) )
      & ( halts2(esk7_0,as_input(X28))
        | ~ halts2(X28,as_input(X28))
        | ~ halts3(X24,esk6_1(X24),as_input(esk6_1(X24)))
        | ~ outputs(X24,bad)
        | halts2(esk5_1(X24),as_input(esk5_1(X24))) )
      & ( outputs(esk7_0,good)
        | ~ halts2(X28,as_input(X28))
        | ~ halts3(X24,esk6_1(X24),as_input(esk6_1(X24)))
        | ~ outputs(X24,bad)
        | halts2(esk5_1(X24),as_input(esk5_1(X24))) )
      & ( halts2(esk7_0,as_input(X28))
        | halts2(X28,as_input(X28))
        | ~ halts3(X24,esk6_1(X24),as_input(esk6_1(X24)))
        | ~ outputs(X24,bad)
        | halts2(esk5_1(X24),as_input(esk5_1(X24))) )
      & ( outputs(esk7_0,bad)
        | halts2(X28,as_input(X28))
        | ~ halts3(X24,esk6_1(X24),as_input(esk6_1(X24)))
        | ~ outputs(X24,bad)
        | halts2(esk5_1(X24),as_input(esk5_1(X24))) )
      & ( halts2(esk7_0,as_input(X28))
        | ~ halts2(X28,as_input(X28))
        | ~ halts2(esk6_1(X24),as_input(esk6_1(X24)))
        | ~ halts3(X24,esk5_1(X24),as_input(esk5_1(X24)))
        | ~ outputs(X24,good) )
      & ( outputs(esk7_0,good)
        | ~ halts2(X28,as_input(X28))
        | ~ halts2(esk6_1(X24),as_input(esk6_1(X24)))
        | ~ halts3(X24,esk5_1(X24),as_input(esk5_1(X24)))
        | ~ outputs(X24,good) )
      & ( halts2(esk7_0,as_input(X28))
        | halts2(X28,as_input(X28))
        | ~ halts2(esk6_1(X24),as_input(esk6_1(X24)))
        | ~ halts3(X24,esk5_1(X24),as_input(esk5_1(X24)))
        | ~ outputs(X24,good) )
      & ( outputs(esk7_0,bad)
        | halts2(X28,as_input(X28))
        | ~ halts2(esk6_1(X24),as_input(esk6_1(X24)))
        | ~ halts3(X24,esk5_1(X24),as_input(esk5_1(X24)))
        | ~ outputs(X24,good) )
      & ( halts2(esk7_0,as_input(X28))
        | ~ halts2(X28,as_input(X28))
        | ~ halts3(X24,esk6_1(X24),as_input(esk6_1(X24)))
        | ~ outputs(X24,bad)
        | ~ halts3(X24,esk5_1(X24),as_input(esk5_1(X24)))
        | ~ outputs(X24,good) )
      & ( outputs(esk7_0,good)
        | ~ halts2(X28,as_input(X28))
        | ~ halts3(X24,esk6_1(X24),as_input(esk6_1(X24)))
        | ~ outputs(X24,bad)
        | ~ halts3(X24,esk5_1(X24),as_input(esk5_1(X24)))
        | ~ outputs(X24,good) )
      & ( halts2(esk7_0,as_input(X28))
        | halts2(X28,as_input(X28))
        | ~ halts3(X24,esk6_1(X24),as_input(esk6_1(X24)))
        | ~ outputs(X24,bad)
        | ~ halts3(X24,esk5_1(X24),as_input(esk5_1(X24)))
        | ~ outputs(X24,good) )
      & ( outputs(esk7_0,bad)
        | halts2(X28,as_input(X28))
        | ~ halts3(X24,esk6_1(X24),as_input(esk6_1(X24)))
        | ~ outputs(X24,bad)
        | ~ halts3(X24,esk5_1(X24),as_input(esk5_1(X24)))
        | ~ outputs(X24,good) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])])])])]) ).

tcf(c_0_19,plain,
    ! [X2: program,X3: input,X4: program,X5: program,X9: input] :
      ( halts3(X2,X4,X3)
      | halts2(X4,X3)
      | ~ decides(algorithm_of(X2),X5,X9) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

tcf(c_0_20,plain,
    ! [X2: program,X3: input,X4: program,X5: program,X9: input] :
      ( halts3(X2,X4,X3)
      | ~ halts2(X4,X3)
      | ~ decides(algorithm_of(X2),X5,X9) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

tcf(c_0_21,plain,
    ! [X2: program,X4: program] :
      ( ~ halts2(X2,as_input(X2))
      | ~ halts2(esk10_0,as_input(X2))
      | ~ halts2(esk9_1(X4),as_input(esk9_1(X4)))
      | ~ halts2(X4,as_input(esk8_1(X4)))
      | ~ outputs(X4,good) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

tcf(c_0_22,negated_conjecture,
    ! [X2: program,X3: input] :
      ( outputs(esk4_0,bad)
      | halts2(X2,X3) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

tcf(c_0_23,negated_conjecture,
    ! [X2: program,X3: input] :
      ( outputs(esk4_0,good)
      | ~ halts2(X2,X3) ),
    inference(spm,[status(thm)],[c_0_17,c_0_16]) ).

tcf(c_0_24,plain,
    ! [X2: program,X4: program] :
      ( halts2(esk7_0,as_input(X2))
      | halts2(esk5_1(X4),as_input(esk5_1(X4)))
      | ~ halts2(X2,as_input(X2))
      | ~ halts3(X4,esk6_1(X4),as_input(esk6_1(X4)))
      | ~ outputs(X4,bad) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

tcf(c_0_25,plain,
    ! [X2: program,X4: program] :
      ( halts2(esk7_0,as_input(X2))
      | halts2(X2,as_input(X2))
      | halts2(esk5_1(X4),as_input(esk5_1(X4)))
      | ~ halts3(X4,esk6_1(X4),as_input(esk6_1(X4)))
      | ~ outputs(X4,bad) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

tcf(c_0_26,plain,
    ! [X2: program,X3: input,X4: program,X5: program,X9: input] :
      ( halts3(X2,X4,X3)
      | ~ decides(algorithm_of(X2),X5,X9) ),
    inference(csr,[status(thm)],[c_0_19,c_0_20]) ).

tcf(c_0_27,negated_conjecture,
    ! [X2: program] :
      ( outputs(esk4_0,bad)
      | ~ outputs(X2,good) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_22]),c_0_22]),c_0_22]) ).

tcf(c_0_28,negated_conjecture,
    ( outputs(esk4_0,bad)
    | outputs(esk4_0,good) ),
    inference(spm,[status(thm)],[c_0_23,c_0_22]) ).

tcf(c_0_29,plain,
    ! [X4: program,X2: program] :
      ( halts2(esk5_1(X2),as_input(esk5_1(X2)))
      | halts2(esk7_0,as_input(X4))
      | ~ outputs(X2,bad)
      | ~ halts3(X2,esk6_1(X2),as_input(esk6_1(X2))) ),
    inference(csr,[status(thm)],[c_0_24,c_0_25]) ).

tcf(c_0_30,negated_conjecture,
    ! [X2: program,X3: input] : halts3(esk4_0,X2,X3),
    inference(spm,[status(thm)],[c_0_26,c_0_16]) ).

tcf(c_0_31,negated_conjecture,
    outputs(esk4_0,bad),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

tcf(c_0_32,negated_conjecture,
    ! [X2: program] :
      ( halts2(esk5_1(esk4_0),as_input(esk5_1(esk4_0)))
      | halts2(esk7_0,as_input(X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).

tcf(c_0_33,plain,
    ! [X2: program,X4: program] :
      ( outputs(esk7_0,good)
      | ~ halts2(X2,as_input(X2))
      | ~ halts3(X4,esk6_1(X4),as_input(esk6_1(X4)))
      | ~ outputs(X4,bad)
      | ~ halts3(X4,esk5_1(X4),as_input(esk5_1(X4)))
      | ~ outputs(X4,good) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

tcf(c_0_34,negated_conjecture,
    outputs(esk4_0,good),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_32]),c_0_23]) ).

tcf(c_0_35,plain,
    ! [X2: program,X4: program] :
      ( outputs(esk7_0,bad)
      | halts2(X2,as_input(X2))
      | ~ halts3(X4,esk6_1(X4),as_input(esk6_1(X4)))
      | ~ outputs(X4,bad)
      | ~ halts3(X4,esk5_1(X4),as_input(esk5_1(X4)))
      | ~ outputs(X4,good) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

tcf(c_0_36,plain,
    ! [X2: program,X4: program] :
      ( halts2(esk7_0,as_input(X2))
      | halts2(X2,as_input(X2))
      | ~ halts3(X4,esk6_1(X4),as_input(esk6_1(X4)))
      | ~ outputs(X4,bad)
      | ~ halts3(X4,esk5_1(X4),as_input(esk5_1(X4)))
      | ~ outputs(X4,good) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

tcf(c_0_37,plain,
    ! [X2: program,X4: program] :
      ( halts2(esk7_0,as_input(X2))
      | ~ halts2(X2,as_input(X2))
      | ~ halts3(X4,esk6_1(X4),as_input(esk6_1(X4)))
      | ~ outputs(X4,bad)
      | ~ halts3(X4,esk5_1(X4),as_input(esk5_1(X4)))
      | ~ outputs(X4,good) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

tcf(c_0_38,negated_conjecture,
    ! [X2: program] :
      ( outputs(esk7_0,good)
      | ~ halts2(X2,as_input(X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_30]),c_0_31]),c_0_34]),c_0_30])]) ).

tcf(c_0_39,negated_conjecture,
    ! [X2: program] :
      ( outputs(esk7_0,bad)
      | halts2(X2,as_input(X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_30]),c_0_31]),c_0_34]),c_0_30])]) ).

tcf(c_0_40,plain,
    ! [X2: program,X4: program] :
      ( halts2(esk7_0,as_input(X2))
      | ~ outputs(X4,bad)
      | ~ outputs(X4,good)
      | ~ halts3(X4,esk5_1(X4),as_input(esk5_1(X4)))
      | ~ halts3(X4,esk6_1(X4),as_input(esk6_1(X4))) ),
    inference(csr,[status(thm)],[c_0_36,c_0_37]) ).

tcf(c_0_41,negated_conjecture,
    ! [X2: program] :
      ( outputs(esk7_0,good)
      | halts2(esk7_0,as_input(X2)) ),
    inference(spm,[status(thm)],[c_0_38,c_0_32]) ).

tcf(c_0_42,negated_conjecture,
    ! [X2: program,X4: program] :
      ( outputs(esk7_0,bad)
      | ~ outputs(X2,good)
      | ~ halts2(X2,as_input(esk8_1(X2)))
      | ~ halts2(esk10_0,as_input(X4)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_39]),c_0_39]) ).

tcf(c_0_43,negated_conjecture,
    ! [X2: program] : halts2(esk7_0,as_input(X2)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_30]),c_0_31]),c_0_34]),c_0_30])]) ).

tcf(c_0_44,negated_conjecture,
    outputs(esk7_0,good),
    inference(spm,[status(thm)],[c_0_38,c_0_41]) ).

tcf(c_0_45,plain,
    ! [X2: program,X4: program] :
      ( halts2(esk10_0,as_input(X2))
      | halts2(X2,as_input(X2))
      | ~ halts2(X4,as_input(esk9_1(X4)))
      | ~ outputs(X4,bad)
      | ~ halts2(X4,as_input(esk8_1(X4)))
      | ~ outputs(X4,good) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

tcf(c_0_46,negated_conjecture,
    ! [X2: program] :
      ( outputs(esk7_0,bad)
      | ~ halts2(esk10_0,as_input(X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).

tcf(c_0_47,plain,
    ! [X2: program,X4: program] :
      ( ~ halts2(X2,as_input(X2))
      | ~ halts2(esk10_0,as_input(X2))
      | ~ halts2(X4,as_input(esk9_1(X4)))
      | ~ outputs(X4,bad)
      | ~ halts2(X4,as_input(esk8_1(X4)))
      | ~ outputs(X4,good) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

tcf(c_0_48,negated_conjecture,
    ! [X2: program] :
      ( halts2(esk10_0,as_input(X2))
      | halts2(X2,as_input(X2))
      | ~ outputs(esk7_0,bad) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_43]),c_0_44]),c_0_43])]) ).

tcf(c_0_49,negated_conjecture,
    outputs(esk7_0,bad),
    inference(spm,[status(thm)],[c_0_46,c_0_39]) ).

tcf(c_0_50,negated_conjecture,
    ! [X2: program] :
      ( ~ outputs(esk7_0,bad)
      | ~ halts2(esk10_0,as_input(X2))
      | ~ halts2(X2,as_input(X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_43]),c_0_44]),c_0_43])]) ).

tcf(c_0_51,negated_conjecture,
    ! [X2: program] :
      ( halts2(esk10_0,as_input(X2))
      | halts2(X2,as_input(X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]) ).

tcf(c_0_52,negated_conjecture,
    ! [X2: program] :
      ( ~ halts2(esk10_0,as_input(X2))
      | ~ halts2(X2,as_input(X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_49])]) ).

tcf(c_0_53,negated_conjecture,
    halts2(esk10_0,as_input(esk10_0)),
    inference(ef,[status(thm)],[c_0_51]) ).

cnf(c_0_54,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_53])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : COM003_1 : TPTP v8.2.0. Released v5.0.0.
% 0.10/0.12  % Command    : run_E %s %d THM
% 0.12/0.34  % Computer : n017.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Fri Jun 21 00:14:54 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.21/0.50  Running first-order theorem proving
% 0.21/0.50  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.USwuOyZ2yx/E---3.1_29931.p
% 0.21/0.52  # Version: 3.2.0
% 0.21/0.52  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.52  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.52  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.52  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.52  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.52  # Starting sh5l with 300s (1) cores
% 0.21/0.52  # new_bool_3 with pid 30077 completed with status 0
% 0.21/0.52  # Result found by new_bool_3
% 0.21/0.52  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.52  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.52  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.52  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.52  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.52  # Search class: FGHNF-FFMF11-SFFFFFNN
% 0.21/0.52  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.52  # Starting G-E--_208_C47_F1_SE_CS_SP_PS_S0Y with 181s (1) cores
% 0.21/0.52  # G-E--_208_C47_F1_SE_CS_SP_PS_S0Y with pid 30082 completed with status 0
% 0.21/0.52  # Result found by G-E--_208_C47_F1_SE_CS_SP_PS_S0Y
% 0.21/0.52  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.52  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.52  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.52  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.52  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.52  # Search class: FGHNF-FFMF11-SFFFFFNN
% 0.21/0.52  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.52  # Starting G-E--_208_C47_F1_SE_CS_SP_PS_S0Y with 181s (1) cores
% 0.21/0.52  # Preprocessing time       : 0.002 s
% 0.21/0.52  # Presaturation interreduction done
% 0.21/0.52  
% 0.21/0.52  # Proof found!
% 0.21/0.52  # SZS status Theorem
% 0.21/0.52  # SZS output start CNFRefutation
% See solution above
% 0.21/0.52  # Parsed axioms                        : 17
% 0.21/0.52  # Removed by relevancy pruning/SinE    : 12
% 0.21/0.52  # Initial clauses                      : 34
% 0.21/0.52  # Removed in clause preprocessing      : 0
% 0.21/0.52  # Initial clauses in saturation        : 34
% 0.21/0.52  # Processed clauses                    : 93
% 0.21/0.52  # ...of these trivial                  : 1
% 0.21/0.52  # ...subsumed                          : 1
% 0.21/0.52  # ...remaining for further processing  : 91
% 0.21/0.52  # Other redundant clauses eliminated   : 0
% 0.21/0.52  # Clauses deleted for lack of memory   : 0
% 0.21/0.52  # Backward-subsumed                    : 27
% 0.21/0.52  # Backward-rewritten                   : 20
% 0.21/0.52  # Generated clauses                    : 61
% 0.21/0.52  # ...of the previous two non-redundant : 58
% 0.21/0.52  # ...aggressively subsumed             : 0
% 0.21/0.52  # Contextual simplify-reflections      : 13
% 0.21/0.52  # Paramodulations                      : 57
% 0.21/0.52  # Factorizations                       : 4
% 0.21/0.52  # NegExts                              : 0
% 0.21/0.52  # Equation resolutions                 : 0
% 0.21/0.52  # Disequality decompositions           : 0
% 0.21/0.52  # Total rewrite steps                  : 41
% 0.21/0.52  # ...of those cached                   : 30
% 0.21/0.52  # Propositional unsat checks           : 0
% 0.21/0.52  #    Propositional check models        : 0
% 0.21/0.52  #    Propositional check unsatisfiable : 0
% 0.21/0.52  #    Propositional clauses             : 0
% 0.21/0.52  #    Propositional clauses after purity: 0
% 0.21/0.52  #    Propositional unsat core size     : 0
% 0.21/0.52  #    Propositional preprocessing time  : 0.000
% 0.21/0.52  #    Propositional encoding time       : 0.000
% 0.21/0.52  #    Propositional solver time         : 0.000
% 0.21/0.52  #    Success case prop preproc time    : 0.000
% 0.21/0.52  #    Success case prop encoding time   : 0.000
% 0.21/0.52  #    Success case prop solver time     : 0.000
% 0.21/0.52  # Current number of processed clauses  : 15
% 0.21/0.52  #    Positive orientable unit clauses  : 10
% 0.21/0.52  #    Positive unorientable unit clauses: 0
% 0.21/0.52  #    Negative unit clauses             : 0
% 0.21/0.52  #    Non-unit-clauses                  : 5
% 0.21/0.52  # Current number of unprocessed clauses: 14
% 0.21/0.52  # ...number of literals in the above   : 64
% 0.21/0.52  # Current number of archived formulas  : 0
% 0.21/0.52  # Current number of archived clauses   : 76
% 0.21/0.52  # Clause-clause subsumption calls (NU) : 1029
% 0.21/0.52  # Rec. Clause-clause subsumption calls : 276
% 0.21/0.52  # Non-unit clause-clause subsumptions  : 39
% 0.21/0.52  # Unit Clause-clause subsumption calls : 38
% 0.21/0.52  # Rewrite failures with RHS unbound    : 0
% 0.21/0.52  # BW rewrite match attempts            : 8
% 0.21/0.52  # BW rewrite match successes           : 8
% 0.21/0.52  # Condensation attempts                : 0
% 0.21/0.52  # Condensation successes               : 0
% 0.21/0.52  # Termbank termtop insertions          : 5205
% 0.21/0.52  # Search garbage collected termcells   : 375
% 0.21/0.52  
% 0.21/0.52  # -------------------------------------------------
% 0.21/0.52  # User time                : 0.013 s
% 0.21/0.52  # System time              : 0.003 s
% 0.21/0.52  # Total time               : 0.016 s
% 0.21/0.52  # Maximum resident set size: 1736 pages
% 0.21/0.52  
% 0.21/0.52  # -------------------------------------------------
% 0.21/0.52  # User time                : 0.016 s
% 0.21/0.52  # System time              : 0.004 s
% 0.21/0.52  # Total time               : 0.019 s
% 0.21/0.52  # Maximum resident set size: 1716 pages
% 0.21/0.52  % E---3.1 exiting
% 0.21/0.52  % E exiting
%------------------------------------------------------------------------------