TSTP Solution File: ALG023+1 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : ALG023+1 : TPTP v8.2.0. Released v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% 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 : Mon May 20 18:06:31 EDT 2024

% Result   : Unsatisfiable 1.41s 0.73s
% Output   : CNFRefutation 1.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :   13
% Syntax   : Number of formulae    :  121 (  34 unt;   0 def)
%            Number of atoms       :  878 ( 782 equ)
%            Maximal formula atoms :  256 (   7 avg)
%            Number of connectives : 1046 ( 289   ~; 399   |; 356   &)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   68 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   2 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn   0   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(ax9,axiom,
    ( op(e0,e0) != op(e1,e0)
    & op(e0,e0) != op(e2,e0)
    & op(e0,e0) != op(e3,e0)
    & op(e1,e0) != op(e2,e0)
    & op(e1,e0) != op(e3,e0)
    & op(e2,e0) != op(e3,e0)
    & op(e0,e1) != op(e1,e1)
    & op(e0,e1) != op(e2,e1)
    & op(e0,e1) != op(e3,e1)
    & op(e1,e1) != op(e2,e1)
    & op(e1,e1) != op(e3,e1)
    & op(e2,e1) != op(e3,e1)
    & op(e0,e2) != op(e1,e2)
    & op(e0,e2) != op(e2,e2)
    & op(e0,e2) != op(e3,e2)
    & op(e1,e2) != op(e2,e2)
    & op(e1,e2) != op(e3,e2)
    & op(e2,e2) != op(e3,e2)
    & op(e0,e3) != op(e1,e3)
    & op(e0,e3) != op(e2,e3)
    & op(e0,e3) != op(e3,e3)
    & op(e1,e3) != op(e2,e3)
    & op(e1,e3) != op(e3,e3)
    & op(e2,e3) != op(e3,e3)
    & op(e0,e0) != op(e0,e1)
    & op(e0,e0) != op(e0,e2)
    & op(e0,e0) != op(e0,e3)
    & op(e0,e1) != op(e0,e2)
    & op(e0,e1) != op(e0,e3)
    & op(e0,e2) != op(e0,e3)
    & op(e1,e0) != op(e1,e1)
    & op(e1,e0) != op(e1,e2)
    & op(e1,e0) != op(e1,e3)
    & op(e1,e1) != op(e1,e2)
    & op(e1,e1) != op(e1,e3)
    & op(e1,e2) != op(e1,e3)
    & op(e2,e0) != op(e2,e1)
    & op(e2,e0) != op(e2,e2)
    & op(e2,e0) != op(e2,e3)
    & op(e2,e1) != op(e2,e2)
    & op(e2,e1) != op(e2,e3)
    & op(e2,e2) != op(e2,e3)
    & op(e3,e0) != op(e3,e1)
    & op(e3,e0) != op(e3,e2)
    & op(e3,e0) != op(e3,e3)
    & op(e3,e1) != op(e3,e2)
    & op(e3,e1) != op(e3,e3)
    & op(e3,e2) != op(e3,e3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax9) ).

fof(ax11,axiom,
    ( ( op(e0,e0) = e0
      & op(e1,e1) = e0
      & op(e2,e2) = e0
      & op(e3,e3) = e0 )
    | ( op(e0,e0) = e1
      & op(e1,e1) = e1
      & op(e2,e2) = e1
      & op(e3,e3) = e1 )
    | ( op(e0,e0) = e2
      & op(e1,e1) = e2
      & op(e2,e2) = e2
      & op(e3,e3) = e2 )
    | ( op(e0,e0) = e3
      & op(e1,e1) = e3
      & op(e2,e2) = e3
      & op(e3,e3) = e3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11) ).

fof(ax34,axiom,
    ~ ( e3 = op(e1,e1)
      & e2 = op(e0,e1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax34) ).

fof(ax1,axiom,
    ( ( op(e0,e0) = e0
      | op(e0,e0) = e1
      | op(e0,e0) = e2
      | op(e0,e0) = e3 )
    & ( op(e0,e1) = e0
      | op(e0,e1) = e1
      | op(e0,e1) = e2
      | op(e0,e1) = e3 )
    & ( op(e0,e2) = e0
      | op(e0,e2) = e1
      | op(e0,e2) = e2
      | op(e0,e2) = e3 )
    & ( op(e0,e3) = e0
      | op(e0,e3) = e1
      | op(e0,e3) = e2
      | op(e0,e3) = e3 )
    & ( op(e1,e0) = e0
      | op(e1,e0) = e1
      | op(e1,e0) = e2
      | op(e1,e0) = e3 )
    & ( op(e1,e1) = e0
      | op(e1,e1) = e1
      | op(e1,e1) = e2
      | op(e1,e1) = e3 )
    & ( op(e1,e2) = e0
      | op(e1,e2) = e1
      | op(e1,e2) = e2
      | op(e1,e2) = e3 )
    & ( op(e1,e3) = e0
      | op(e1,e3) = e1
      | op(e1,e3) = e2
      | op(e1,e3) = e3 )
    & ( op(e2,e0) = e0
      | op(e2,e0) = e1
      | op(e2,e0) = e2
      | op(e2,e0) = e3 )
    & ( op(e2,e1) = e0
      | op(e2,e1) = e1
      | op(e2,e1) = e2
      | op(e2,e1) = e3 )
    & ( op(e2,e2) = e0
      | op(e2,e2) = e1
      | op(e2,e2) = e2
      | op(e2,e2) = e3 )
    & ( op(e2,e3) = e0
      | op(e2,e3) = e1
      | op(e2,e3) = e2
      | op(e2,e3) = e3 )
    & ( op(e3,e0) = e0
      | op(e3,e0) = e1
      | op(e3,e0) = e2
      | op(e3,e0) = e3 )
    & ( op(e3,e1) = e0
      | op(e3,e1) = e1
      | op(e3,e1) = e2
      | op(e3,e1) = e3 )
    & ( op(e3,e2) = e0
      | op(e3,e2) = e1
      | op(e3,e2) = e2
      | op(e3,e2) = e3 )
    & ( op(e3,e3) = e0
      | op(e3,e3) = e1
      | op(e3,e3) = e2
      | op(e3,e3) = e3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).

fof(ax2,axiom,
    ( op(op(e0,e0),e0) = op(e0,op(e0,e0))
    & op(op(e0,e0),e1) = op(e0,op(e0,e1))
    & op(op(e0,e0),e2) = op(e0,op(e0,e2))
    & op(op(e0,e0),e3) = op(e0,op(e0,e3))
    & op(op(e0,e1),e0) = op(e0,op(e1,e0))
    & op(op(e0,e1),e1) = op(e0,op(e1,e1))
    & op(op(e0,e1),e2) = op(e0,op(e1,e2))
    & op(op(e0,e1),e3) = op(e0,op(e1,e3))
    & op(op(e0,e2),e0) = op(e0,op(e2,e0))
    & op(op(e0,e2),e1) = op(e0,op(e2,e1))
    & op(op(e0,e2),e2) = op(e0,op(e2,e2))
    & op(op(e0,e2),e3) = op(e0,op(e2,e3))
    & op(op(e0,e3),e0) = op(e0,op(e3,e0))
    & op(op(e0,e3),e1) = op(e0,op(e3,e1))
    & op(op(e0,e3),e2) = op(e0,op(e3,e2))
    & op(op(e0,e3),e3) = op(e0,op(e3,e3))
    & op(op(e1,e0),e0) = op(e1,op(e0,e0))
    & op(op(e1,e0),e1) = op(e1,op(e0,e1))
    & op(op(e1,e0),e2) = op(e1,op(e0,e2))
    & op(op(e1,e0),e3) = op(e1,op(e0,e3))
    & op(op(e1,e1),e0) = op(e1,op(e1,e0))
    & op(op(e1,e1),e1) = op(e1,op(e1,e1))
    & op(op(e1,e1),e2) = op(e1,op(e1,e2))
    & op(op(e1,e1),e3) = op(e1,op(e1,e3))
    & op(op(e1,e2),e0) = op(e1,op(e2,e0))
    & op(op(e1,e2),e1) = op(e1,op(e2,e1))
    & op(op(e1,e2),e2) = op(e1,op(e2,e2))
    & op(op(e1,e2),e3) = op(e1,op(e2,e3))
    & op(op(e1,e3),e0) = op(e1,op(e3,e0))
    & op(op(e1,e3),e1) = op(e1,op(e3,e1))
    & op(op(e1,e3),e2) = op(e1,op(e3,e2))
    & op(op(e1,e3),e3) = op(e1,op(e3,e3))
    & op(op(e2,e0),e0) = op(e2,op(e0,e0))
    & op(op(e2,e0),e1) = op(e2,op(e0,e1))
    & op(op(e2,e0),e2) = op(e2,op(e0,e2))
    & op(op(e2,e0),e3) = op(e2,op(e0,e3))
    & op(op(e2,e1),e0) = op(e2,op(e1,e0))
    & op(op(e2,e1),e1) = op(e2,op(e1,e1))
    & op(op(e2,e1),e2) = op(e2,op(e1,e2))
    & op(op(e2,e1),e3) = op(e2,op(e1,e3))
    & op(op(e2,e2),e0) = op(e2,op(e2,e0))
    & op(op(e2,e2),e1) = op(e2,op(e2,e1))
    & op(op(e2,e2),e2) = op(e2,op(e2,e2))
    & op(op(e2,e2),e3) = op(e2,op(e2,e3))
    & op(op(e2,e3),e0) = op(e2,op(e3,e0))
    & op(op(e2,e3),e1) = op(e2,op(e3,e1))
    & op(op(e2,e3),e2) = op(e2,op(e3,e2))
    & op(op(e2,e3),e3) = op(e2,op(e3,e3))
    & op(op(e3,e0),e0) = op(e3,op(e0,e0))
    & op(op(e3,e0),e1) = op(e3,op(e0,e1))
    & op(op(e3,e0),e2) = op(e3,op(e0,e2))
    & op(op(e3,e0),e3) = op(e3,op(e0,e3))
    & op(op(e3,e1),e0) = op(e3,op(e1,e0))
    & op(op(e3,e1),e1) = op(e3,op(e1,e1))
    & op(op(e3,e1),e2) = op(e3,op(e1,e2))
    & op(op(e3,e1),e3) = op(e3,op(e1,e3))
    & op(op(e3,e2),e0) = op(e3,op(e2,e0))
    & op(op(e3,e2),e1) = op(e3,op(e2,e1))
    & op(op(e3,e2),e2) = op(e3,op(e2,e2))
    & op(op(e3,e2),e3) = op(e3,op(e2,e3))
    & op(op(e3,e3),e0) = op(e3,op(e3,e0))
    & op(op(e3,e3),e1) = op(e3,op(e3,e1))
    & op(op(e3,e3),e2) = op(e3,op(e3,e2))
    & op(op(e3,e3),e3) = op(e3,op(e3,e3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).

fof(ax5,axiom,
    inv(unit) = unit,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).

fof(ax3,axiom,
    ( op(unit,e0) = e0
    & op(e0,unit) = e0
    & op(unit,e1) = e1
    & op(e1,unit) = e1
    & op(unit,e2) = e2
    & op(e2,unit) = e2
    & op(unit,e3) = e3
    & op(e3,unit) = e3
    & ( unit = e0
      | unit = e1
      | unit = e2
      | unit = e3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).

fof(ax4,axiom,
    ( op(e0,inv(e0)) = unit
    & op(inv(e0),e0) = unit
    & op(e1,inv(e1)) = unit
    & op(inv(e1),e1) = unit
    & op(e2,inv(e2)) = unit
    & op(inv(e2),e2) = unit
    & op(e3,inv(e3)) = unit
    & op(inv(e3),e3) = unit
    & ( inv(e0) = e0
      | inv(e0) = e1
      | inv(e0) = e2
      | inv(e0) = e3 )
    & ( inv(e1) = e0
      | inv(e1) = e1
      | inv(e1) = e2
      | inv(e1) = e3 )
    & ( inv(e2) = e0
      | inv(e2) = e1
      | inv(e2) = e2
      | inv(e2) = e3 )
    & ( inv(e3) = e0
      | inv(e3) = e1
      | inv(e3) = e2
      | inv(e3) = e3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).

fof(ax28,axiom,
    ~ ( e2 = op(e1,e1)
      & e3 = op(e0,e1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).

fof(ax10,axiom,
    ( e0 != e1
    & e0 != e2
    & e0 != e3
    & e1 != e2
    & e1 != e3
    & e2 != e3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10) ).

fof(ax21,axiom,
    ~ ( e1 = op(e0,e0)
      & e2 = op(e3,e0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).

fof(ax17,axiom,
    ~ ( e0 = op(e1,e1)
      & e3 = op(e2,e1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).

fof(c_0_12,plain,
    ( epred1_0
  <=> ( ( op(e0,e0) = e0
        & op(e1,e1) = e0
        & op(e2,e2) = e0
        & op(e3,e3) = e0 )
      | ( op(e0,e0) = e1
        & op(e1,e1) = e1
        & op(e2,e2) = e1
        & op(e3,e3) = e1 )
      | ( op(e0,e0) = e2
        & op(e1,e1) = e2
        & op(e2,e2) = e2
        & op(e3,e3) = e2 ) ) ),
    introduced(definition) ).

fof(c_0_13,plain,
    ( op(e0,e0) != op(e1,e0)
    & op(e0,e0) != op(e2,e0)
    & op(e0,e0) != op(e3,e0)
    & op(e1,e0) != op(e2,e0)
    & op(e1,e0) != op(e3,e0)
    & op(e2,e0) != op(e3,e0)
    & op(e0,e1) != op(e1,e1)
    & op(e0,e1) != op(e2,e1)
    & op(e0,e1) != op(e3,e1)
    & op(e1,e1) != op(e2,e1)
    & op(e1,e1) != op(e3,e1)
    & op(e2,e1) != op(e3,e1)
    & op(e0,e2) != op(e1,e2)
    & op(e0,e2) != op(e2,e2)
    & op(e0,e2) != op(e3,e2)
    & op(e1,e2) != op(e2,e2)
    & op(e1,e2) != op(e3,e2)
    & op(e2,e2) != op(e3,e2)
    & op(e0,e3) != op(e1,e3)
    & op(e0,e3) != op(e2,e3)
    & op(e0,e3) != op(e3,e3)
    & op(e1,e3) != op(e2,e3)
    & op(e1,e3) != op(e3,e3)
    & op(e2,e3) != op(e3,e3)
    & op(e0,e0) != op(e0,e1)
    & op(e0,e0) != op(e0,e2)
    & op(e0,e0) != op(e0,e3)
    & op(e0,e1) != op(e0,e2)
    & op(e0,e1) != op(e0,e3)
    & op(e0,e2) != op(e0,e3)
    & op(e1,e0) != op(e1,e1)
    & op(e1,e0) != op(e1,e2)
    & op(e1,e0) != op(e1,e3)
    & op(e1,e1) != op(e1,e2)
    & op(e1,e1) != op(e1,e3)
    & op(e1,e2) != op(e1,e3)
    & op(e2,e0) != op(e2,e1)
    & op(e2,e0) != op(e2,e2)
    & op(e2,e0) != op(e2,e3)
    & op(e2,e1) != op(e2,e2)
    & op(e2,e1) != op(e2,e3)
    & op(e2,e2) != op(e2,e3)
    & op(e3,e0) != op(e3,e1)
    & op(e3,e0) != op(e3,e2)
    & op(e3,e0) != op(e3,e3)
    & op(e3,e1) != op(e3,e2)
    & op(e3,e1) != op(e3,e3)
    & op(e3,e2) != op(e3,e3) ),
    inference(fof_simplification,[status(thm)],[ax9]) ).

fof(c_0_14,axiom,
    ( epred1_0
    | ( op(e0,e0) = e3
      & op(e1,e1) = e3
      & op(e2,e2) = e3
      & op(e3,e3) = e3 ) ),
    inference(apply_def,[status(thm)],[ax11,c_0_12]) ).

fof(c_0_15,plain,
    ( op(e0,e0) != op(e1,e0)
    & op(e0,e0) != op(e2,e0)
    & op(e0,e0) != op(e3,e0)
    & op(e1,e0) != op(e2,e0)
    & op(e1,e0) != op(e3,e0)
    & op(e2,e0) != op(e3,e0)
    & op(e0,e1) != op(e1,e1)
    & op(e0,e1) != op(e2,e1)
    & op(e0,e1) != op(e3,e1)
    & op(e1,e1) != op(e2,e1)
    & op(e1,e1) != op(e3,e1)
    & op(e2,e1) != op(e3,e1)
    & op(e0,e2) != op(e1,e2)
    & op(e0,e2) != op(e2,e2)
    & op(e0,e2) != op(e3,e2)
    & op(e1,e2) != op(e2,e2)
    & op(e1,e2) != op(e3,e2)
    & op(e2,e2) != op(e3,e2)
    & op(e0,e3) != op(e1,e3)
    & op(e0,e3) != op(e2,e3)
    & op(e0,e3) != op(e3,e3)
    & op(e1,e3) != op(e2,e3)
    & op(e1,e3) != op(e3,e3)
    & op(e2,e3) != op(e3,e3)
    & op(e0,e0) != op(e0,e1)
    & op(e0,e0) != op(e0,e2)
    & op(e0,e0) != op(e0,e3)
    & op(e0,e1) != op(e0,e2)
    & op(e0,e1) != op(e0,e3)
    & op(e0,e2) != op(e0,e3)
    & op(e1,e0) != op(e1,e1)
    & op(e1,e0) != op(e1,e2)
    & op(e1,e0) != op(e1,e3)
    & op(e1,e1) != op(e1,e2)
    & op(e1,e1) != op(e1,e3)
    & op(e1,e2) != op(e1,e3)
    & op(e2,e0) != op(e2,e1)
    & op(e2,e0) != op(e2,e2)
    & op(e2,e0) != op(e2,e3)
    & op(e2,e1) != op(e2,e2)
    & op(e2,e1) != op(e2,e3)
    & op(e2,e2) != op(e2,e3)
    & op(e3,e0) != op(e3,e1)
    & op(e3,e0) != op(e3,e2)
    & op(e3,e0) != op(e3,e3)
    & op(e3,e1) != op(e3,e2)
    & op(e3,e1) != op(e3,e3)
    & op(e3,e2) != op(e3,e3) ),
    inference(fof_nnf,[status(thm)],[c_0_13]) ).

fof(c_0_16,plain,
    ( ( op(e0,e0) = e3
      | epred1_0 )
    & ( op(e1,e1) = e3
      | epred1_0 )
    & ( op(e2,e2) = e3
      | epred1_0 )
    & ( op(e3,e3) = e3
      | epred1_0 ) ),
    inference(distribute,[status(thm)],[c_0_14]) ).

cnf(c_0_17,plain,
    op(e0,e1) != op(e1,e1),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_18,plain,
    ( op(e1,e1) = e3
    | epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_19,plain,
    ( e3 != op(e1,e1)
    | e2 != op(e0,e1) ),
    inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[ax34])]) ).

cnf(c_0_20,plain,
    ( epred1_0
    | op(e0,e1) != e3 ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_21,plain,
    ( op(e0,e1) = e0
    | op(e0,e1) = e1
    | op(e0,e1) = e2
    | op(e0,e1) = e3 ),
    inference(split_conjunct,[status(thm)],[ax1]) ).

cnf(c_0_22,plain,
    op(op(e0,e0),e1) = op(e0,op(e0,e1)),
    inference(split_conjunct,[status(thm)],[ax2]) ).

cnf(c_0_23,plain,
    ( op(e0,e0) = e3
    | epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_24,plain,
    ( e3 != op(e1,e1)
    | e2 != op(e0,e1) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_25,plain,
    ( op(e0,e1) = e2
    | op(e0,e1) = e1
    | op(e0,e1) = e0
    | epred1_0 ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

fof(c_0_26,plain,
    ( epred1_0
   => ( ( op(e0,e0) = e0
        & op(e1,e1) = e0
        & op(e2,e2) = e0
        & op(e3,e3) = e0 )
      | ( op(e0,e0) = e1
        & op(e1,e1) = e1
        & op(e2,e2) = e1
        & op(e3,e3) = e1 )
      | ( op(e0,e0) = e2
        & op(e1,e1) = e2
        & op(e2,e2) = e2
        & op(e3,e3) = e2 ) ) ),
    inference(split_equiv,[status(thm)],[c_0_12]) ).

cnf(c_0_27,plain,
    ( op(e0,op(e0,e1)) = op(e3,e1)
    | epred1_0 ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_28,plain,
    ( op(e0,e1) = e0
    | op(e0,e1) = e1
    | epred1_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_18]) ).

cnf(c_0_29,plain,
    op(e0,e1) != op(e3,e1),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_30,plain,
    ( ( op(e0,e0) = e2
      | op(e0,e0) = e1
      | op(e0,e0) = e0
      | ~ epred1_0 )
    & ( op(e1,e1) = e2
      | op(e0,e0) = e1
      | op(e0,e0) = e0
      | ~ epred1_0 )
    & ( op(e2,e2) = e2
      | op(e0,e0) = e1
      | op(e0,e0) = e0
      | ~ epred1_0 )
    & ( op(e3,e3) = e2
      | op(e0,e0) = e1
      | op(e0,e0) = e0
      | ~ epred1_0 )
    & ( op(e0,e0) = e2
      | op(e1,e1) = e1
      | op(e0,e0) = e0
      | ~ epred1_0 )
    & ( op(e1,e1) = e2
      | op(e1,e1) = e1
      | op(e0,e0) = e0
      | ~ epred1_0 )
    & ( op(e2,e2) = e2
      | op(e1,e1) = e1
      | op(e0,e0) = e0
      | ~ epred1_0 )
    & ( op(e3,e3) = e2
      | op(e1,e1) = e1
      | op(e0,e0) = e0
      | ~ epred1_0 )
    & ( op(e0,e0) = e2
      | op(e2,e2) = e1
      | op(e0,e0) = e0
      | ~ epred1_0 )
    & ( op(e1,e1) = e2
      | op(e2,e2) = e1
      | op(e0,e0) = e0
      | ~ epred1_0 )
    & ( op(e2,e2) = e2
      | op(e2,e2) = e1
      | op(e0,e0) = e0
      | ~ epred1_0 )
    & ( op(e3,e3) = e2
      | op(e2,e2) = e1
      | op(e0,e0) = e0
      | ~ epred1_0 )
    & ( op(e0,e0) = e2
      | op(e3,e3) = e1
      | op(e0,e0) = e0
      | ~ epred1_0 )
    & ( op(e1,e1) = e2
      | op(e3,e3) = e1
      | op(e0,e0) = e0
      | ~ epred1_0 )
    & ( op(e2,e2) = e2
      | op(e3,e3) = e1
      | op(e0,e0) = e0
      | ~ epred1_0 )
    & ( op(e3,e3) = e2
      | op(e3,e3) = e1
      | op(e0,e0) = e0
      | ~ epred1_0 )
    & ( op(e0,e0) = e2
      | op(e0,e0) = e1
      | op(e1,e1) = e0
      | ~ epred1_0 )
    & ( op(e1,e1) = e2
      | op(e0,e0) = e1
      | op(e1,e1) = e0
      | ~ epred1_0 )
    & ( op(e2,e2) = e2
      | op(e0,e0) = e1
      | op(e1,e1) = e0
      | ~ epred1_0 )
    & ( op(e3,e3) = e2
      | op(e0,e0) = e1
      | op(e1,e1) = e0
      | ~ epred1_0 )
    & ( op(e0,e0) = e2
      | op(e1,e1) = e1
      | op(e1,e1) = e0
      | ~ epred1_0 )
    & ( op(e1,e1) = e2
      | op(e1,e1) = e1
      | op(e1,e1) = e0
      | ~ epred1_0 )
    & ( op(e2,e2) = e2
      | op(e1,e1) = e1
      | op(e1,e1) = e0
      | ~ epred1_0 )
    & ( op(e3,e3) = e2
      | op(e1,e1) = e1
      | op(e1,e1) = e0
      | ~ epred1_0 )
    & ( op(e0,e0) = e2
      | op(e2,e2) = e1
      | op(e1,e1) = e0
      | ~ epred1_0 )
    & ( op(e1,e1) = e2
      | op(e2,e2) = e1
      | op(e1,e1) = e0
      | ~ epred1_0 )
    & ( op(e2,e2) = e2
      | op(e2,e2) = e1
      | op(e1,e1) = e0
      | ~ epred1_0 )
    & ( op(e3,e3) = e2
      | op(e2,e2) = e1
      | op(e1,e1) = e0
      | ~ epred1_0 )
    & ( op(e0,e0) = e2
      | op(e3,e3) = e1
      | op(e1,e1) = e0
      | ~ epred1_0 )
    & ( op(e1,e1) = e2
      | op(e3,e3) = e1
      | op(e1,e1) = e0
      | ~ epred1_0 )
    & ( op(e2,e2) = e2
      | op(e3,e3) = e1
      | op(e1,e1) = e0
      | ~ epred1_0 )
    & ( op(e3,e3) = e2
      | op(e3,e3) = e1
      | op(e1,e1) = e0
      | ~ epred1_0 )
    & ( op(e0,e0) = e2
      | op(e0,e0) = e1
      | op(e2,e2) = e0
      | ~ epred1_0 )
    & ( op(e1,e1) = e2
      | op(e0,e0) = e1
      | op(e2,e2) = e0
      | ~ epred1_0 )
    & ( op(e2,e2) = e2
      | op(e0,e0) = e1
      | op(e2,e2) = e0
      | ~ epred1_0 )
    & ( op(e3,e3) = e2
      | op(e0,e0) = e1
      | op(e2,e2) = e0
      | ~ epred1_0 )
    & ( op(e0,e0) = e2
      | op(e1,e1) = e1
      | op(e2,e2) = e0
      | ~ epred1_0 )
    & ( op(e1,e1) = e2
      | op(e1,e1) = e1
      | op(e2,e2) = e0
      | ~ epred1_0 )
    & ( op(e2,e2) = e2
      | op(e1,e1) = e1
      | op(e2,e2) = e0
      | ~ epred1_0 )
    & ( op(e3,e3) = e2
      | op(e1,e1) = e1
      | op(e2,e2) = e0
      | ~ epred1_0 )
    & ( op(e0,e0) = e2
      | op(e2,e2) = e1
      | op(e2,e2) = e0
      | ~ epred1_0 )
    & ( op(e1,e1) = e2
      | op(e2,e2) = e1
      | op(e2,e2) = e0
      | ~ epred1_0 )
    & ( op(e2,e2) = e2
      | op(e2,e2) = e1
      | op(e2,e2) = e0
      | ~ epred1_0 )
    & ( op(e3,e3) = e2
      | op(e2,e2) = e1
      | op(e2,e2) = e0
      | ~ epred1_0 )
    & ( op(e0,e0) = e2
      | op(e3,e3) = e1
      | op(e2,e2) = e0
      | ~ epred1_0 )
    & ( op(e1,e1) = e2
      | op(e3,e3) = e1
      | op(e2,e2) = e0
      | ~ epred1_0 )
    & ( op(e2,e2) = e2
      | op(e3,e3) = e1
      | op(e2,e2) = e0
      | ~ epred1_0 )
    & ( op(e3,e3) = e2
      | op(e3,e3) = e1
      | op(e2,e2) = e0
      | ~ epred1_0 )
    & ( op(e0,e0) = e2
      | op(e0,e0) = e1
      | op(e3,e3) = e0
      | ~ epred1_0 )
    & ( op(e1,e1) = e2
      | op(e0,e0) = e1
      | op(e3,e3) = e0
      | ~ epred1_0 )
    & ( op(e2,e2) = e2
      | op(e0,e0) = e1
      | op(e3,e3) = e0
      | ~ epred1_0 )
    & ( op(e3,e3) = e2
      | op(e0,e0) = e1
      | op(e3,e3) = e0
      | ~ epred1_0 )
    & ( op(e0,e0) = e2
      | op(e1,e1) = e1
      | op(e3,e3) = e0
      | ~ epred1_0 )
    & ( op(e1,e1) = e2
      | op(e1,e1) = e1
      | op(e3,e3) = e0
      | ~ epred1_0 )
    & ( op(e2,e2) = e2
      | op(e1,e1) = e1
      | op(e3,e3) = e0
      | ~ epred1_0 )
    & ( op(e3,e3) = e2
      | op(e1,e1) = e1
      | op(e3,e3) = e0
      | ~ epred1_0 )
    & ( op(e0,e0) = e2
      | op(e2,e2) = e1
      | op(e3,e3) = e0
      | ~ epred1_0 )
    & ( op(e1,e1) = e2
      | op(e2,e2) = e1
      | op(e3,e3) = e0
      | ~ epred1_0 )
    & ( op(e2,e2) = e2
      | op(e2,e2) = e1
      | op(e3,e3) = e0
      | ~ epred1_0 )
    & ( op(e3,e3) = e2
      | op(e2,e2) = e1
      | op(e3,e3) = e0
      | ~ epred1_0 )
    & ( op(e0,e0) = e2
      | op(e3,e3) = e1
      | op(e3,e3) = e0
      | ~ epred1_0 )
    & ( op(e1,e1) = e2
      | op(e3,e3) = e1
      | op(e3,e3) = e0
      | ~ epred1_0 )
    & ( op(e2,e2) = e2
      | op(e3,e3) = e1
      | op(e3,e3) = e0
      | ~ epred1_0 )
    & ( op(e3,e3) = e2
      | op(e3,e3) = e1
      | op(e3,e3) = e0
      | ~ epred1_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])]) ).

cnf(c_0_31,plain,
    op(e3,e1) != op(e3,e3),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_32,plain,
    ( op(e3,e3) = e3
    | epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_33,plain,
    ( op(e0,e1) = e0
    | epred1_0 ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).

cnf(c_0_34,plain,
    op(e3,e2) != op(e3,e3),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_35,plain,
    ( op(e3,e3) = e2
    | op(e3,e3) = e1
    | op(e3,e3) = e0
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_36,plain,
    ( epred1_0
    | op(e3,e1) != e3 ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_37,plain,
    ( op(e3,e1) = op(e0,e0)
    | epred1_0 ),
    inference(spm,[status(thm)],[c_0_27,c_0_33]) ).

cnf(c_0_38,plain,
    inv(unit) = unit,
    inference(split_conjunct,[status(thm)],[ax5]) ).

cnf(c_0_39,plain,
    ( unit = e0
    | unit = e1
    | unit = e2
    | unit = e3 ),
    inference(split_conjunct,[status(thm)],[ax3]) ).

cnf(c_0_40,plain,
    ( op(e3,e3) = e1
    | op(e3,e3) = e0
    | op(e3,e2) != e2
    | ~ epred1_0 ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_41,plain,
    epred1_0,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_23]) ).

cnf(c_0_42,plain,
    op(unit,e2) = e2,
    inference(split_conjunct,[status(thm)],[ax3]) ).

cnf(c_0_43,plain,
    op(e3,inv(e3)) = unit,
    inference(split_conjunct,[status(thm)],[ax4]) ).

cnf(c_0_44,plain,
    ( inv(e3) = e3
    | unit = e2
    | unit = e1
    | unit = e0 ),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_45,plain,
    ( op(e3,e3) = e0
    | op(e3,e3) = e1
    | op(e3,e2) != e2 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]) ).

cnf(c_0_46,plain,
    ( op(e3,e2) = e2
    | unit = e2
    | unit = e1
    | unit = e0 ),
    inference(spm,[status(thm)],[c_0_42,c_0_39]) ).

cnf(c_0_47,plain,
    ( op(e3,e3) = unit
    | unit = e0
    | unit = e1
    | unit = e2 ),
    inference(spm,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_48,plain,
    ( op(e3,e3) = e1
    | op(e3,e3) = e0
    | unit = e0
    | unit = e1
    | unit = e2 ),
    inference(spm,[status(thm)],[c_0_45,c_0_46]) ).

fof(c_0_49,plain,
    ( e2 != op(e1,e1)
    | e3 != op(e0,e1) ),
    inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).

cnf(c_0_50,plain,
    ( op(e1,e1) = e2
    | op(e0,e0) = e1
    | op(e0,e0) = e0
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_51,plain,
    ( op(e3,e3) = e0
    | unit = e2
    | unit = e0
    | unit = e1 ),
    inference(spm,[status(thm)],[c_0_47,c_0_48]) ).

cnf(c_0_52,plain,
    ( op(e0,e0) = e2
    | op(e0,e0) = e1
    | op(e0,e0) = e0
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_53,plain,
    ( e2 != op(e1,e1)
    | e3 != op(e0,e1) ),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

cnf(c_0_54,plain,
    ( op(e0,e0) = e1
    | op(e0,e0) = e0
    | op(e0,e1) != e2
    | ~ epred1_0 ),
    inference(spm,[status(thm)],[c_0_17,c_0_50]) ).

fof(c_0_55,plain,
    ( e0 != e1
    & e0 != e2
    & e0 != e3
    & e1 != e2
    & e1 != e3
    & e2 != e3 ),
    inference(fof_simplification,[status(thm)],[ax10]) ).

cnf(c_0_56,plain,
    op(e0,unit) = e0,
    inference(split_conjunct,[status(thm)],[ax3]) ).

cnf(c_0_57,plain,
    ( unit = e2
    | unit = e1
    | unit = e0 ),
    inference(spm,[status(thm)],[c_0_47,c_0_51]) ).

cnf(c_0_58,plain,
    ( op(e0,op(e0,e1)) = op(e2,e1)
    | op(e0,e0) = e1
    | op(e0,e0) = e0
    | ~ epred1_0 ),
    inference(spm,[status(thm)],[c_0_22,c_0_52]) ).

cnf(c_0_59,plain,
    ( op(e0,e0) = e1
    | op(e0,e0) = e0
    | op(e0,e1) != e3 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_50]),c_0_20]) ).

cnf(c_0_60,plain,
    ( op(e0,e0) = e0
    | op(e0,e0) = e1
    | op(e0,e1) != e2 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_41])]) ).

cnf(c_0_61,plain,
    ( op(e0,e0) = e2
    | op(e2,e2) = e1
    | op(e2,e2) = e0
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_62,plain,
    op(e2,unit) = e2,
    inference(split_conjunct,[status(thm)],[ax3]) ).

fof(c_0_63,plain,
    ( e0 != e1
    & e0 != e2
    & e0 != e3
    & e1 != e2
    & e1 != e3
    & e2 != e3 ),
    inference(fof_nnf,[status(thm)],[c_0_55]) ).

cnf(c_0_64,plain,
    op(e0,e1) != op(e0,e2),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_65,plain,
    ( op(e0,e2) = e0
    | unit = e0
    | unit = e1 ),
    inference(spm,[status(thm)],[c_0_56,c_0_57]) ).

cnf(c_0_66,plain,
    ( op(e0,op(e0,e1)) = op(e2,e1)
    | op(e0,e0) = e0
    | op(e0,e0) = e1 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_41])]) ).

cnf(c_0_67,plain,
    ( op(e0,e1) = e1
    | op(e0,e1) = e0
    | op(e0,e0) = e0
    | op(e0,e0) = e1 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_21]),c_0_60]) ).

cnf(c_0_68,plain,
    op(e0,e1) != op(e2,e1),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_69,plain,
    op(e0,e0) != op(e0,e2),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_70,plain,
    ( op(e2,e2) = e1
    | op(e2,e2) = e0
    | op(e0,e0) = e2 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_41])]) ).

cnf(c_0_71,plain,
    ( op(e2,e2) = e2
    | unit = e0
    | unit = e1 ),
    inference(spm,[status(thm)],[c_0_62,c_0_57]) ).

cnf(c_0_72,plain,
    e1 != e2,
    inference(split_conjunct,[status(thm)],[c_0_63]) ).

cnf(c_0_73,plain,
    e0 != e2,
    inference(split_conjunct,[status(thm)],[c_0_63]) ).

cnf(c_0_74,plain,
    ( unit = e1
    | unit = e0
    | op(e0,e1) != e0 ),
    inference(spm,[status(thm)],[c_0_64,c_0_65]) ).

cnf(c_0_75,plain,
    ( op(e0,e1) = e0
    | op(e0,e0) = e1
    | op(e0,e0) = e0 ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]) ).

cnf(c_0_76,plain,
    ( unit = e1
    | unit = e0
    | op(e0,e0) != e0 ),
    inference(spm,[status(thm)],[c_0_69,c_0_65]) ).

cnf(c_0_77,plain,
    ( op(e0,e0) = e2
    | unit = e1
    | unit = e0 ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]),c_0_73]) ).

cnf(c_0_78,plain,
    ( op(e0,e0) = e1
    | unit = e0
    | unit = e1 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]) ).

cnf(c_0_79,plain,
    ( op(e1,e1) = e2
    | op(e0,e0) = e1
    | op(e1,e1) = e0
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_80,plain,
    op(e1,unit) = e1,
    inference(split_conjunct,[status(thm)],[ax3]) ).

cnf(c_0_81,plain,
    ( unit = e0
    | unit = e1 ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_72]) ).

cnf(c_0_82,plain,
    op(e3,unit) = e3,
    inference(split_conjunct,[status(thm)],[ax3]) ).

fof(c_0_83,plain,
    ( e1 != op(e0,e0)
    | e2 != op(e3,e0) ),
    inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])]) ).

cnf(c_0_84,plain,
    ( op(e1,e1) = e2
    | op(e1,e1) = e0
    | op(e0,e0) = e1 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_41])]) ).

cnf(c_0_85,plain,
    ( op(e1,e1) = e1
    | unit = e0 ),
    inference(spm,[status(thm)],[c_0_80,c_0_81]) ).

cnf(c_0_86,plain,
    e0 != e1,
    inference(split_conjunct,[status(thm)],[c_0_63]) ).

cnf(c_0_87,plain,
    op(e3,e0) != op(e3,e1),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_88,plain,
    ( op(e3,e1) = e3
    | unit = e0 ),
    inference(spm,[status(thm)],[c_0_82,c_0_81]) ).

cnf(c_0_89,plain,
    ( e1 != op(e0,e0)
    | e2 != op(e3,e0) ),
    inference(split_conjunct,[status(thm)],[c_0_83]) ).

cnf(c_0_90,plain,
    ( op(e0,e0) = e1
    | unit = e0 ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_72]),c_0_86]) ).

cnf(c_0_91,plain,
    ( unit = e0
    | op(e3,e0) != e3 ),
    inference(spm,[status(thm)],[c_0_87,c_0_88]) ).

cnf(c_0_92,plain,
    ( op(e3,e0) = e0
    | op(e3,e0) = e1
    | op(e3,e0) = e2
    | op(e3,e0) = e3 ),
    inference(split_conjunct,[status(thm)],[ax1]) ).

cnf(c_0_93,plain,
    ( unit = e0
    | op(e3,e0) != e2 ),
    inference(spm,[status(thm)],[c_0_89,c_0_90]) ).

cnf(c_0_94,plain,
    op(e0,e0) != op(e3,e0),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_95,plain,
    ( op(e3,e0) = e1
    | op(e3,e0) = e0
    | unit = e0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]) ).

cnf(c_0_96,plain,
    op(unit,e0) = e0,
    inference(split_conjunct,[status(thm)],[ax3]) ).

fof(c_0_97,plain,
    ( e0 != op(e1,e1)
    | e3 != op(e2,e1) ),
    inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[ax17])]) ).

cnf(c_0_98,plain,
    op(e2,e1) != op(e2,e2),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_99,plain,
    ( op(e2,e2) = e3
    | epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_100,plain,
    ( op(e0,e0) = e2
    | op(e0,e0) = e1
    | op(e2,e2) = e0
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_101,plain,
    op(e1,e0) != op(e3,e0),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_102,plain,
    ( op(e3,e0) = e0
    | unit = e0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_90]) ).

cnf(c_0_103,plain,
    ( op(e1,e0) = e0
    | unit = e0 ),
    inference(spm,[status(thm)],[c_0_96,c_0_81]) ).

cnf(c_0_104,plain,
    ( e0 != op(e1,e1)
    | e3 != op(e2,e1) ),
    inference(split_conjunct,[status(thm)],[c_0_97]) ).

cnf(c_0_105,plain,
    ( op(e0,e0) = e2
    | op(e0,e0) = e1
    | op(e1,e1) = e0
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_106,plain,
    ( epred1_0
    | op(e2,e1) != e3 ),
    inference(spm,[status(thm)],[c_0_98,c_0_99]) ).

cnf(c_0_107,plain,
    ( op(e0,e0) = e2
    | op(e0,e0) = e1
    | op(e2,e1) != e0
    | ~ epred1_0 ),
    inference(spm,[status(thm)],[c_0_98,c_0_100]) ).

cnf(c_0_108,plain,
    unit = e0,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_103]) ).

cnf(c_0_109,plain,
    op(unit,e1) = e1,
    inference(split_conjunct,[status(thm)],[ax3]) ).

cnf(c_0_110,plain,
    ( op(e0,e0) = e2
    | op(e0,e0) = e1
    | op(e2,e1) != e3 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_106]) ).

cnf(c_0_111,plain,
    ( op(e2,e1) = e0
    | op(e2,e1) = e1
    | op(e2,e1) = e2
    | op(e2,e1) = e3 ),
    inference(split_conjunct,[status(thm)],[ax1]) ).

cnf(c_0_112,plain,
    ( op(e0,e0) = e1
    | op(e0,e0) = e2
    | op(e2,e1) != e0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_41])]) ).

cnf(c_0_113,plain,
    op(e2,e0) != op(e2,e1),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_114,plain,
    op(e2,e0) = e2,
    inference(rw,[status(thm)],[c_0_62,c_0_108]) ).

cnf(c_0_115,plain,
    op(e0,e1) = e1,
    inference(rw,[status(thm)],[c_0_109,c_0_108]) ).

cnf(c_0_116,plain,
    ( op(e2,e1) = e2
    | op(e2,e1) = e1
    | op(e0,e0) = e1
    | op(e0,e0) = e2 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112]) ).

cnf(c_0_117,plain,
    op(e0,e0) = e0,
    inference(rw,[status(thm)],[c_0_96,c_0_108]) ).

cnf(c_0_118,plain,
    op(e2,e1) != e2,
    inference(rw,[status(thm)],[c_0_113,c_0_114]) ).

cnf(c_0_119,plain,
    op(e2,e1) != e1,
    inference(rw,[status(thm)],[c_0_68,c_0_115]) ).

cnf(c_0_120,plain,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_117]),c_0_117]),c_0_86]),c_0_73]),c_0_118]),c_0_119]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : ALG023+1 : TPTP v8.2.0. Released v2.7.0.
% 0.13/0.14  % Command    : run_E %s %d THM
% 0.13/0.35  % Computer : n005.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   : Sat May 18 23:07:08 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.20/0.48  Running first-order model finding
% 0.20/0.48  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.41/0.73  # Version: 3.1.0
% 1.41/0.73  # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.41/0.73  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.41/0.73  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.41/0.73  # Starting new_bool_3 with 300s (1) cores
% 1.41/0.73  # Starting new_bool_1 with 300s (1) cores
% 1.41/0.73  # Starting sh5l with 300s (1) cores
% 1.41/0.73  # new_bool_1 with pid 31644 completed with status 8
% 1.41/0.73  # new_bool_3 with pid 31643 completed with status 8
% 1.41/0.73  # sh5l with pid 31645 completed with status 8
% 1.41/0.73  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 31642 completed with status 0
% 1.41/0.73  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.41/0.73  # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.41/0.73  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.41/0.73  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.41/0.73  # No SInE strategy applied
% 1.41/0.73  # Search class: FGHSF-FSLM21-SFFFFFNN
% 1.41/0.73  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.41/0.73  # Starting SAT001_MinMin_p005000_rr_RG with 811s (1) cores
% 1.41/0.73  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.41/0.73  # Starting new_bool_3 with 136s (1) cores
% 1.41/0.73  # Starting new_bool_1 with 136s (1) cores
% 1.41/0.73  # Starting sh5l with 136s (1) cores
% 1.41/0.73  # new_bool_1 with pid 31668 completed with status 0
% 1.41/0.73  # Result found by new_bool_1
% 1.41/0.73  # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.41/0.73  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.41/0.73  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.41/0.73  # No SInE strategy applied
% 1.41/0.73  # Search class: FGHSF-FSLM21-SFFFFFNN
% 1.41/0.73  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.41/0.73  # Starting SAT001_MinMin_p005000_rr_RG with 811s (1) cores
% 1.41/0.73  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.41/0.73  # Starting new_bool_3 with 136s (1) cores
% 1.41/0.73  # Starting new_bool_1 with 136s (1) cores
% 1.41/0.73  # Preprocessing time       : 0.003 s
% 1.41/0.73  # Presaturation interreduction done
% 1.41/0.73  
% 1.41/0.73  # Proof found!
% 1.41/0.73  # SZS status Unsatisfiable
% 1.41/0.73  # SZS output start CNFRefutation
% See solution above
% 1.41/0.73  # Parsed axioms                        : 35
% 1.41/0.73  # Removed by relevancy pruning/SinE    : 0
% 1.41/0.73  # Initial clauses                      : 270
% 1.41/0.73  # Removed in clause preprocessing      : 0
% 1.41/0.73  # Initial clauses in saturation        : 270
% 1.41/0.73  # Processed clauses                    : 5296
% 1.41/0.73  # ...of these trivial                  : 140
% 1.41/0.73  # ...subsumed                          : 3131
% 1.41/0.73  # ...remaining for further processing  : 2024
% 1.41/0.73  # Other redundant clauses eliminated   : 0
% 1.41/0.73  # Clauses deleted for lack of memory   : 0
% 1.41/0.73  # Backward-subsumed                    : 396
% 1.41/0.73  # Backward-rewritten                   : 1220
% 1.41/0.73  # Generated clauses                    : 12971
% 1.41/0.73  # ...of the previous two non-redundant : 13112
% 1.41/0.73  # ...aggressively subsumed             : 0
% 1.41/0.73  # Contextual simplify-reflections      : 89
% 1.41/0.73  # Paramodulations                      : 12727
% 1.41/0.73  # Factorizations                       : 201
% 1.41/0.73  # NegExts                              : 0
% 1.41/0.73  # Equation resolutions                 : 0
% 1.41/0.73  # Disequality decompositions           : 0
% 1.41/0.73  # Total rewrite steps                  : 2038
% 1.41/0.73  # ...of those cached                   : 1981
% 1.41/0.73  # Propositional unsat checks           : 0
% 1.41/0.73  #    Propositional check models        : 0
% 1.41/0.73  #    Propositional check unsatisfiable : 0
% 1.41/0.73  #    Propositional clauses             : 0
% 1.41/0.73  #    Propositional clauses after purity: 0
% 1.41/0.73  #    Propositional unsat core size     : 0
% 1.41/0.73  #    Propositional preprocessing time  : 0.000
% 1.41/0.73  #    Propositional encoding time       : 0.000
% 1.41/0.73  #    Propositional solver time         : 0.000
% 1.41/0.73  #    Success case prop preproc time    : 0.000
% 1.41/0.73  #    Success case prop encoding time   : 0.000
% 1.41/0.73  #    Success case prop solver time     : 0.000
% 1.41/0.73  # Current number of processed clauses  : 95
% 1.41/0.73  #    Positive orientable unit clauses  : 46
% 1.41/0.73  #    Positive unorientable unit clauses: 0
% 1.41/0.73  #    Negative unit clauses             : 42
% 1.41/0.73  #    Non-unit-clauses                  : 7
% 1.41/0.73  # Current number of unprocessed clauses: 6539
% 1.41/0.73  # ...number of literals in the above   : 35524
% 1.41/0.73  # Current number of archived formulas  : 0
% 1.41/0.73  # Current number of archived clauses   : 1929
% 1.41/0.73  # Clause-clause subsumption calls (NU) : 32357
% 1.41/0.73  # Rec. Clause-clause subsumption calls : 13974
% 1.41/0.73  # Non-unit clause-clause subsumptions  : 2095
% 1.41/0.73  # Unit Clause-clause subsumption calls : 1296
% 1.41/0.73  # Rewrite failures with RHS unbound    : 0
% 1.41/0.73  # BW rewrite match attempts            : 13
% 1.41/0.73  # BW rewrite match successes           : 13
% 1.41/0.73  # Condensation attempts                : 0
% 1.41/0.73  # Condensation successes               : 0
% 1.41/0.73  # Termbank termtop insertions          : 158896
% 1.41/0.73  # Search garbage collected termcells   : 785
% 1.41/0.73  
% 1.41/0.73  # -------------------------------------------------
% 1.41/0.73  # User time                : 0.225 s
% 1.41/0.73  # System time              : 0.013 s
% 1.41/0.73  # Total time               : 0.238 s
% 1.41/0.73  # Maximum resident set size: 2108 pages
% 1.41/0.73  
% 1.41/0.73  # -------------------------------------------------
% 1.41/0.73  # User time                : 1.160 s
% 1.41/0.73  # System time              : 0.071 s
% 1.41/0.73  # Total time               : 1.232 s
% 1.41/0.73  # Maximum resident set size: 1776 pages
% 1.41/0.73  % E---3.1 exiting
%------------------------------------------------------------------------------