↑ Up

E---3.5.1.THM-CRf.s

View TPTP
Problem
Process solution in
SystemOnTSTP
Download .tgz
%------------------------------------------------------------------------------
% File     : E---3.5.1
% Problem  : SYN551+2 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM

% Computer : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 24 03:25:35 PM UTC 2026

% Result   : Theorem 0.15s 0.46s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   56
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   70 (   6 unt;   0 def)
%            Number of atoms       :  275 ( 274 equ)
%            Maximal formula atoms :   32 (   3 avg)
%            Number of connectives :  251 (  46   ~; 192   |;   7   &)
%                                         (   6 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-1 aty)
%            Number of variables   :   90 (   0 sgn   8   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(prove_this_cute_thing,conjecture,
    ( ? [X1] :
      ! [X2] :
        ( X2 = f(g(X2))
      <=> X1 = X2 )
  <=> ? [X1] :
      ! [X2] :
        ( X2 = g(f(X2))
      <=> X1 = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_cute_thing) ).

fof(c_0_1,negated_conjecture,
    ~ ( ? [X1] :
        ! [X2] :
          ( X2 = f(g(X2))
        <=> X1 = X2 )
    <=> ? [X1] :
        ! [X2] :
          ( X2 = g(f(X2))
        <=> X1 = X2 ) ),
    inference(assume_negation,[status(cth)],[prove_this_cute_thing]) ).

fof(c_0_2,negated_conjecture,
    ! [X3,X5,X8,X10] :
      ( ( X8 = f(g(X8))
        | esk3_0 != X8
        | X10 = g(f(X10))
        | esk4_0 != X10 )
      & ( X8 = f(g(X8))
        | esk3_0 != X8
        | esk4_0 = X10
        | X10 != g(f(X10)) )
      & ( esk3_0 = X8
        | X8 != f(g(X8))
        | X10 = g(f(X10))
        | esk4_0 != X10 )
      & ( esk3_0 = X8
        | X8 != f(g(X8))
        | esk4_0 = X10
        | X10 != g(f(X10)) )
      & ( X3 = esk1_1(X3)
        | esk1_1(X3) = f(g(esk1_1(X3)))
        | X5 = esk2_1(X5)
        | esk2_1(X5) = g(f(esk2_1(X5))) )
      & ( X3 = esk1_1(X3)
        | esk1_1(X3) = f(g(esk1_1(X3)))
        | X5 != esk2_1(X5)
        | esk2_1(X5) != g(f(esk2_1(X5))) )
      & ( X3 != esk1_1(X3)
        | esk1_1(X3) != f(g(esk1_1(X3)))
        | X5 = esk2_1(X5)
        | esk2_1(X5) = g(f(esk2_1(X5))) )
      & ( X3 != esk1_1(X3)
        | esk1_1(X3) != f(g(esk1_1(X3)))
        | X5 != esk2_1(X5)
        | esk2_1(X5) != g(f(esk2_1(X5))) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])])])])]) ).

cnf(c_0_3,negated_conjecture,
    ( X2 != f(g(X2))
    | esk4_0 != X1
    | esk3_0 = X2
    | X1 = g(f(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_4,negated_conjecture,
    ( f(g(X1)) != X1
    | esk3_0 = X1
    | g(f(esk4_0)) = esk4_0 ),
    inference(er,[status(thm)],[c_0_3]) ).

cnf(c_0_5,negated_conjecture,
    ( X2 = esk1_1(X2)
    | esk1_1(X2) = f(g(esk1_1(X2)))
    | X1 = esk2_1(X1)
    | esk2_1(X1) = g(f(esk2_1(X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_6,negated_conjecture,
    ( esk2_1(X1) = X1
    | esk1_1(X2) = X2
    | esk1_1(X2) = esk3_0
    | g(f(esk4_0)) = esk4_0
    | g(f(esk2_1(X1))) = esk2_1(X1) ),
    inference(spm,[status(thm)],[c_0_4,c_0_5]) ).

cnf(c_0_7,negated_conjecture,
    ( esk2_1(X1) = X1
    | esk1_1(esk3_0) = esk3_0
    | g(f(esk4_0)) = esk4_0
    | g(f(esk2_1(X1))) = esk2_1(X1) ),
    inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_6])]) ).

cnf(c_0_8,negated_conjecture,
    ( esk2_1(X1) = X1
    | esk1_1(esk3_0) = esk3_0
    | f(esk2_1(X1)) = esk3_0
    | g(f(esk4_0)) = esk4_0 ),
    inference(spm,[status(thm)],[c_0_4,c_0_7]) ).

cnf(c_0_9,negated_conjecture,
    ( esk2_1(X1) = X1
    | esk1_1(esk3_0) = esk3_0
    | esk2_1(X1) = g(esk3_0)
    | g(f(esk4_0)) = esk4_0 ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_10,negated_conjecture,
    ( X1 != esk2_1(X1)
    | esk2_1(X1) != g(f(esk2_1(X1)))
    | X2 = esk1_1(X2)
    | esk1_1(X2) = f(g(esk1_1(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_11,negated_conjecture,
    ( esk1_1(esk3_0) = esk3_0
    | g(f(esk4_0)) = esk4_0
    | esk2_1(g(esk3_0)) = g(esk3_0) ),
    inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_9])]) ).

cnf(c_0_12,negated_conjecture,
    ( g(f(g(esk3_0))) != g(esk3_0)
    | esk1_1(X1) = X1
    | esk1_1(esk3_0) = esk3_0
    | g(f(esk4_0)) = esk4_0
    | f(g(esk1_1(X1))) = esk1_1(X1) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_13,negated_conjecture,
    ( esk3_0 != X2
    | esk4_0 != X1
    | X2 = f(g(X2))
    | X1 = g(f(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_14,negated_conjecture,
    ( g(f(g(esk3_0))) != g(esk3_0)
    | esk1_1(X1) = X1
    | esk1_1(X1) = esk3_0
    | esk1_1(esk3_0) = esk3_0
    | g(f(esk4_0)) = esk4_0 ),
    inference(spm,[status(thm)],[c_0_4,c_0_12]) ).

cnf(c_0_15,negated_conjecture,
    ( g(f(esk4_0)) = esk4_0
    | f(g(esk3_0)) = esk3_0 ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_13])]) ).

cnf(c_0_16,negated_conjecture,
    ( esk1_1(X1) = X1
    | esk1_1(X1) = esk3_0
    | esk1_1(esk3_0) = esk3_0
    | g(f(esk4_0)) = esk4_0 ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_17,negated_conjecture,
    ( X2 != esk1_1(X2)
    | esk1_1(X2) != f(g(esk1_1(X2)))
    | X1 = esk2_1(X1)
    | esk2_1(X1) = g(f(esk2_1(X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_18,negated_conjecture,
    ( esk1_1(esk3_0) = esk3_0
    | g(f(esk4_0)) = esk4_0 ),
    inference(ef,[status(thm)],[c_0_16]) ).

cnf(c_0_19,negated_conjecture,
    ( esk2_1(X1) = X1
    | g(f(esk4_0)) = esk4_0
    | g(f(esk2_1(X1))) = esk2_1(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_15]) ).

cnf(c_0_20,negated_conjecture,
    ( esk2_1(X1) = X1
    | f(esk2_1(X1)) = esk3_0
    | g(f(esk4_0)) = esk4_0 ),
    inference(spm,[status(thm)],[c_0_4,c_0_19]) ).

cnf(c_0_21,negated_conjecture,
    ( X2 != esk1_1(X2)
    | esk1_1(X2) != f(g(esk1_1(X2)))
    | X1 != esk2_1(X1)
    | esk2_1(X1) != g(f(esk2_1(X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_22,negated_conjecture,
    ( esk2_1(X1) = X1
    | esk2_1(X1) = g(esk3_0)
    | g(f(esk4_0)) = esk4_0 ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_23,negated_conjecture,
    ( esk2_1(X1) != X1
    | g(f(esk2_1(X1))) != esk2_1(X1)
    | g(f(esk4_0)) = esk4_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_18]),c_0_15]) ).

cnf(c_0_24,negated_conjecture,
    ( g(f(esk4_0)) = esk4_0
    | esk2_1(g(esk3_0)) = g(esk3_0) ),
    inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_22])]) ).

cnf(c_0_25,negated_conjecture,
    ( g(f(g(esk3_0))) != g(esk3_0)
    | g(f(esk4_0)) = esk4_0 ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_26,negated_conjecture,
    ( X2 != f(g(X2))
    | X1 != g(f(X1))
    | esk3_0 = X2
    | esk4_0 = X1 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_27,negated_conjecture,
    g(f(esk4_0)) = esk4_0,
    inference(spm,[status(thm)],[c_0_25,c_0_15]) ).

cnf(c_0_28,negated_conjecture,
    ( g(f(X1)) != X1
    | esk4_0 = X1
    | f(esk4_0) = esk3_0 ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_29,negated_conjecture,
    ( esk2_1(X2) = X2
    | esk1_1(X1) = X1
    | esk2_1(X2) = esk4_0
    | f(esk4_0) = esk3_0
    | f(g(esk1_1(X1))) = esk1_1(X1) ),
    inference(spm,[status(thm)],[c_0_28,c_0_5]) ).

cnf(c_0_30,negated_conjecture,
    ( esk1_1(X1) = X1
    | f(esk4_0) = esk3_0
    | esk2_1(esk4_0) = esk4_0
    | f(g(esk1_1(X1))) = esk1_1(X1) ),
    inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_29])]) ).

cnf(c_0_31,negated_conjecture,
    ( esk1_1(X1) = X1
    | f(esk4_0) = esk3_0
    | esk2_1(esk4_0) = esk4_0
    | g(esk1_1(X1)) = esk4_0 ),
    inference(spm,[status(thm)],[c_0_28,c_0_30]) ).

cnf(c_0_32,negated_conjecture,
    ( esk1_1(X1) = X1
    | esk2_1(esk4_0) = esk4_0
    | f(esk4_0) = esk3_0
    | esk1_1(X1) = f(esk4_0) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_33,negated_conjecture,
    ( f(esk4_0) = esk3_0
    | esk2_1(esk4_0) = esk4_0
    | esk1_1(f(esk4_0)) = f(esk4_0) ),
    inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_32])]) ).

cnf(c_0_34,negated_conjecture,
    ( esk2_1(X1) = X1
    | esk2_1(esk4_0) = esk4_0
    | f(esk4_0) = esk3_0
    | g(f(esk2_1(X1))) = esk2_1(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_33]),c_0_27])]) ).

cnf(c_0_35,negated_conjecture,
    ( esk2_1(X1) = X1
    | esk2_1(X1) = esk4_0
    | f(esk4_0) = esk3_0
    | esk2_1(esk4_0) = esk4_0 ),
    inference(spm,[status(thm)],[c_0_28,c_0_34]) ).

cnf(c_0_36,negated_conjecture,
    ( f(esk4_0) = esk3_0
    | esk2_1(esk4_0) = esk4_0 ),
    inference(ef,[status(thm)],[c_0_35]) ).

cnf(c_0_37,negated_conjecture,
    ( esk1_1(X1) = X1
    | f(esk4_0) = esk3_0
    | f(g(esk1_1(X1))) = esk1_1(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_36]),c_0_27])]) ).

cnf(c_0_38,negated_conjecture,
    ( esk1_1(X1) = X1
    | f(esk4_0) = esk3_0
    | g(esk1_1(X1)) = esk4_0 ),
    inference(spm,[status(thm)],[c_0_28,c_0_37]) ).

cnf(c_0_39,negated_conjecture,
    ( g(f(X3)) != X3
    | esk4_0 = X3
    | esk2_1(X1) = X1
    | esk1_1(X2) = X2
    | esk1_1(X2) = esk3_0
    | g(f(esk2_1(X1))) = esk2_1(X1) ),
    inference(spm,[status(thm)],[c_0_26,c_0_5]) ).

cnf(c_0_40,negated_conjecture,
    ( esk1_1(X1) = X1
    | f(esk4_0) = esk3_0
    | esk1_1(X1) = f(esk4_0) ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_41,negated_conjecture,
    ( esk1_1(X4) = X4
    | esk2_1(X2) = X2
    | esk2_1(X1) = X1
    | esk1_1(X3) = X3
    | esk1_1(X4) = esk3_0
    | g(esk1_1(X3)) = esk4_0
    | g(f(esk2_1(X2))) = esk2_1(X2)
    | g(f(esk2_1(X1))) = esk2_1(X1) ),
    inference(spm,[status(thm)],[c_0_39,c_0_5]) ).

cnf(c_0_42,negated_conjecture,
    ( f(esk4_0) = esk3_0
    | esk1_1(f(esk4_0)) = f(esk4_0) ),
    inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_40])]) ).

cnf(c_0_43,negated_conjecture,
    ( esk1_1(X2) = X2
    | esk2_1(X1) = X1
    | esk1_1(X3) = X3
    | esk1_1(X3) = esk3_0
    | g(esk1_1(X2)) = esk4_0
    | g(f(esk2_1(X1))) = esk2_1(X1) ),
    inference(ef,[status(thm)],[c_0_41]) ).

cnf(c_0_44,negated_conjecture,
    ( esk2_1(X1) != X1
    | g(f(esk2_1(X1))) != esk2_1(X1)
    | f(esk4_0) = esk3_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_42]),c_0_27])]) ).

cnf(c_0_45,negated_conjecture,
    ( esk2_1(X1) = X1
    | esk1_1(X2) = X2
    | esk1_1(esk3_0) = esk3_0
    | g(esk1_1(X2)) = esk4_0
    | g(f(esk2_1(X1))) = esk2_1(X1) ),
    inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_43])]) ).

cnf(c_0_46,negated_conjecture,
    f(esk4_0) = esk3_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_36]),c_0_27])]) ).

cnf(c_0_47,negated_conjecture,
    ( esk2_1(X2) = X2
    | esk1_1(X3) = X3
    | esk2_1(X1) = X1
    | esk1_1(X3) = esk3_0
    | esk1_1(esk3_0) = esk3_0
    | g(f(esk2_1(X2))) = esk2_1(X2)
    | g(f(esk2_1(X1))) = esk2_1(X1) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_45]),c_0_46]) ).

cnf(c_0_48,negated_conjecture,
    ( esk2_1(X1) = X1
    | esk1_1(X2) = X2
    | esk1_1(X2) = esk3_0
    | esk1_1(esk3_0) = esk3_0
    | g(f(esk2_1(X1))) = esk2_1(X1) ),
    inference(ef,[status(thm)],[c_0_47]) ).

cnf(c_0_49,negated_conjecture,
    ( esk2_1(X1) = X1
    | esk1_1(esk3_0) = esk3_0
    | g(f(esk2_1(X1))) = esk2_1(X1) ),
    inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_48])]) ).

cnf(c_0_50,negated_conjecture,
    ( g(f(X2)) != X2
    | esk4_0 = X2
    | esk2_1(X1) = X1
    | esk1_1(esk3_0) = esk3_0
    | f(esk2_1(X1)) = esk3_0 ),
    inference(spm,[status(thm)],[c_0_26,c_0_49]) ).

cnf(c_0_51,negated_conjecture,
    ( esk2_1(X1) = X1
    | esk2_1(X2) = X2
    | esk2_1(X2) = esk4_0
    | esk1_1(esk3_0) = esk3_0
    | f(esk2_1(X1)) = esk3_0 ),
    inference(spm,[status(thm)],[c_0_50,c_0_49]) ).

cnf(c_0_52,negated_conjecture,
    ( esk2_1(X1) = X1
    | esk1_1(esk3_0) = esk3_0
    | esk2_1(esk4_0) = esk4_0
    | f(esk2_1(X1)) = esk3_0 ),
    inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_51])]) ).

cnf(c_0_53,negated_conjecture,
    g(esk3_0) = esk4_0,
    inference(rw,[status(thm)],[c_0_27,c_0_46]) ).

cnf(c_0_54,negated_conjecture,
    ( esk2_1(X1) = X1
    | esk2_1(X1) = esk4_0
    | esk1_1(esk3_0) = esk3_0
    | esk2_1(esk4_0) = esk4_0 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_52]),c_0_53]) ).

cnf(c_0_55,negated_conjecture,
    ( esk2_1(esk4_0) = esk4_0
    | esk1_1(esk3_0) = esk3_0 ),
    inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_54])]) ).

cnf(c_0_56,negated_conjecture,
    ( esk2_1(X1) = X1
    | esk2_1(esk4_0) = esk4_0
    | g(f(esk2_1(X1))) = esk2_1(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_55]),c_0_53]),c_0_46])]) ).

cnf(c_0_57,negated_conjecture,
    ( g(f(X2)) != X2
    | esk4_0 = X2
    | esk2_1(X1) = X1
    | esk2_1(esk4_0) = esk4_0
    | f(esk2_1(X1)) = esk3_0 ),
    inference(spm,[status(thm)],[c_0_26,c_0_56]) ).

cnf(c_0_58,negated_conjecture,
    ( esk2_1(X1) = X1
    | esk2_1(X2) = X2
    | esk2_1(X2) = esk4_0
    | esk2_1(esk4_0) = esk4_0
    | f(esk2_1(X1)) = esk3_0 ),
    inference(spm,[status(thm)],[c_0_57,c_0_56]) ).

cnf(c_0_59,negated_conjecture,
    ( esk2_1(X1) = X1
    | esk2_1(esk4_0) = esk4_0
    | f(esk2_1(X1)) = esk3_0 ),
    inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_58])]) ).

cnf(c_0_60,negated_conjecture,
    ( esk2_1(X1) = X1
    | esk2_1(X1) = esk4_0
    | esk2_1(esk4_0) = esk4_0 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_59]),c_0_53]) ).

cnf(c_0_61,negated_conjecture,
    esk2_1(esk4_0) = esk4_0,
    inference(ef,[status(thm)],[c_0_60]) ).

cnf(c_0_62,negated_conjecture,
    ( esk1_1(X1) = X1
    | f(g(esk1_1(X1))) = esk1_1(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_61]),c_0_46]),c_0_53])]) ).

cnf(c_0_63,negated_conjecture,
    ( g(f(X2)) != X2
    | esk4_0 = X2
    | esk1_1(X1) = X1
    | esk1_1(X1) = esk3_0 ),
    inference(spm,[status(thm)],[c_0_26,c_0_62]) ).

cnf(c_0_64,negated_conjecture,
    ( esk1_1(X2) = X2
    | esk1_1(X1) = X1
    | esk1_1(X2) = esk3_0
    | g(esk1_1(X1)) = esk4_0 ),
    inference(spm,[status(thm)],[c_0_63,c_0_62]) ).

cnf(c_0_65,negated_conjecture,
    ( esk1_1(X1) = X1
    | esk1_1(esk3_0) = esk3_0
    | g(esk1_1(X1)) = esk4_0 ),
    inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_64])]) ).

cnf(c_0_66,negated_conjecture,
    ( esk1_1(X1) = X1
    | esk1_1(X1) = esk3_0
    | esk1_1(esk3_0) = esk3_0 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_65]),c_0_46]) ).

cnf(c_0_67,negated_conjecture,
    esk1_1(esk3_0) = esk3_0,
    inference(ef,[status(thm)],[c_0_66]) ).

cnf(c_0_68,negated_conjecture,
    ( esk2_1(X1) != X1
    | g(f(esk2_1(X1))) != esk2_1(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_67]),c_0_53]),c_0_46])]) ).

cnf(c_0_69,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_61]),c_0_46]),c_0_53])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SYN551+2 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.05  % Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37  % Computer : n017.cluster.edu
% 0.10/0.37  % Model    : x86_64 x86_64
% 0.10/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37  % Memory   : 8046.5625MB
% 0.10/0.37  % OS       : Linux 6.8.0-71-generic
% 0.10/0.37  % CPULimit : 300
% 0.10/0.37  % WCLimit  : 300
% 0.10/0.37  % DateTime : Mon Sep 21 11:03:43 UTC 2026
% 0.10/0.38  % CPUTime  : 
% 0.10/0.38  Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42  Running first-order theorem proving
% 0.15/0.42  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/benchmark/theBenchmark.p
% 0.15/0.46  % Version: 3.5.1
% 0.15/0.46  % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/0.46  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.46  % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/0.46  % Starting new_bool_3 with 300s (1) cores
% 0.15/0.46  % Starting new_bool_1 with 300s (1) cores
% 0.15/0.46  % Starting sh5l with 300s (1) cores
% 0.15/0.46  % new_bool_3 with pid 2174021 completed with status 0
% 0.15/0.46  % Result found by new_bool_3
% 0.15/0.46  % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/0.46  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.46  % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/0.46  % Starting new_bool_3 with 300s (1) cores
% 0.15/0.46  % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.46  % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.46  % Search class: FGHPF-FFSF11-MFFFFFNN
% 0.15/0.46  % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.46  % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.46  % SubtermCWHack with pid 2174029 completed with status 0
% 0.15/0.46  % Result found by SubtermCWHack
% 0.15/0.46  % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/0.46  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.46  % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/0.46  % Starting new_bool_3 with 300s (1) cores
% 0.15/0.46  % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.46  % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.46  % Search class: FGHPF-FFSF11-MFFFFFNN
% 0.15/0.46  % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.46  % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.46  % Preprocessing time       : 0.001 s
% 0.15/0.46  
% 0.15/0.46  % Proof found!
% 0.15/0.46  % SZS status Theorem
% 0.15/0.46  % SZS output start CNFRefutation
% See solution above
% 0.15/0.46  % Parsed axioms                        : 1
% 0.15/0.46  % Removed by relevancy pruning/SinE    : 0
% 0.15/0.46  % Initial clauses                      : 8
% 0.15/0.46  % Removed in clause preprocessing      : 0
% 0.15/0.46  % Initial clauses in saturation        : 8
% 0.15/0.46  % Processed clauses                    : 151
% 0.15/0.46  % ...of these trivial                  : 3
% 0.15/0.46  % ...subsumed                          : 54
% 0.15/0.46  % ...remaining for further processing  : 94
% 0.15/0.46  % Other redundant clauses eliminated   : 135
% 0.15/0.46  % Clauses deleted for lack of memory   : 0
% 0.15/0.46  % Backward-subsumed                    : 45
% 0.15/0.46  % Backward-rewritten                   : 34
% 0.15/0.46  % Generated clauses                    : 1058
% 0.15/0.46  % ...of the previous two non-redundant : 641
% 0.15/0.46  % ...aggressively subsumed             : 0
% 0.15/0.46  % Contextual simplify-reflections      : 2
% 0.15/0.46  % Paramodulations                      : 834
% 0.15/0.46  % Factorizations                       : 90
% 0.15/0.46  % NegExts                              : 0
% 0.15/0.46  % Equation resolutions                 : 135
% 0.15/0.46  % Disequality decompositions           : 0
% 0.15/0.46  % Total rewrite steps                  : 471
% 0.15/0.46  % ...of those cached                   : 466
% 0.15/0.46  % Propositional unsat checks           : 0
% 0.15/0.46  %    Propositional check models        : 0
% 0.15/0.46  %    Propositional check unsatisfiable : 0
% 0.15/0.46  %    Propositional clauses             : 0
% 0.15/0.46  %    Propositional clauses after purity: 0
% 0.15/0.46  %    Propositional unsat core size     : 0
% 0.15/0.46  %    Propositional preprocessing time  : 0.000
% 0.15/0.46  %    Propositional encoding time       : 0.000
% 0.15/0.46  %    Propositional solver time         : 0.000
% 0.15/0.46  %    Success case prop preproc time    : 0.000
% 0.15/0.46  %    Success case prop encoding time   : 0.000
% 0.15/0.46  %    Success case prop solver time     : 0.000
% 0.15/0.46  % Current number of processed clauses  : 12
% 0.15/0.46  %    Positive orientable unit clauses  : 4
% 0.15/0.46  %    Positive unorientable unit clauses: 0
% 0.15/0.46  %    Negative unit clauses             : 0
% 0.15/0.46  %    Non-unit-clauses                  : 8
% 0.15/0.46  % Current number of unprocessed clauses: 177
% 0.15/0.46  % ...number of literals in the above   : 1411
% 0.15/0.46  % Current number of archived formulas  : 0
% 0.15/0.46  % Current number of archived clauses   : 79
% 0.15/0.46  % Clause-clause subsumption calls (NU) : 296
% 0.15/0.46  % Rec. Clause-clause subsumption calls : 135
% 0.15/0.46  % Non-unit clause-clause subsumptions  : 99
% 0.15/0.46  % Unit Clause-clause subsumption calls : 18
% 0.15/0.46  % Rewrite failures with RHS unbound    : 0
% 0.15/0.46  % BW rewrite match attempts            : 5
% 0.15/0.46  % BW rewrite match successes           : 5
% 0.15/0.46  % Condensation attempts                : 0
% 0.15/0.46  % Condensation successes               : 0
% 0.15/0.46  % Termbank termtop insertions          : 22505
% 0.15/0.46  % Search garbage collected termcells   : 228
% 0.15/0.46  
% 0.15/0.46  % -------------------------------------------------
% 0.15/0.46  % User time                : 0.021 s
% 0.15/0.46  % System time              : 0.005 s
% 0.15/0.46  % Total time               : 0.026 s
% 0.15/0.46  % Maximum resident set size: 3628 pages
% 0.15/0.46  
% 0.15/0.46  % -------------------------------------------------
% 0.15/0.46  % User time                : 0.022 s
% 0.15/0.46  % System time              : 0.009 s
% 0.15/0.46  % Total time               : 0.031 s
% 0.15/0.46  % Maximum resident set size: 4608 pages
% 0.15/0.46  % E exiting
%------------------------------------------------------------------------------