TSTP Solution File: ALG045+1 by iProver---3.9

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%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : ALG045+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n002.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May  3 02:03:24 EDT 2024

% Result   : Unsatisfiable 2.25s 1.18s
% Output   : CNFRefutation 2.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   15
% Syntax   : Number of formulae    :  169 (  63 unt;   0 def)
%            Number of atoms       :  642 ( 592 equ)
%            Maximal formula atoms :  128 (   3 avg)
%            Number of connectives :  651 ( 178   ~; 329   |; 144   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   49 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   4 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :    4 (   0 sgn   0   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ( ( e3 = op(e3,e3)
      | e2 = op(e3,e3)
      | e1 = op(e3,e3)
      | e0 = op(e3,e3) )
    & ( e3 = op(e3,e2)
      | e2 = op(e3,e2)
      | e1 = op(e3,e2)
      | e0 = op(e3,e2) )
    & ( e3 = op(e3,e1)
      | e2 = op(e3,e1)
      | e1 = op(e3,e1)
      | e0 = op(e3,e1) )
    & ( e3 = op(e3,e0)
      | e2 = op(e3,e0)
      | e1 = op(e3,e0)
      | e0 = op(e3,e0) )
    & ( e3 = op(e2,e3)
      | e2 = op(e2,e3)
      | e1 = op(e2,e3)
      | e0 = op(e2,e3) )
    & ( e3 = op(e2,e2)
      | e2 = op(e2,e2)
      | e1 = op(e2,e2)
      | e0 = op(e2,e2) )
    & ( e3 = op(e2,e1)
      | e2 = op(e2,e1)
      | e1 = op(e2,e1)
      | e0 = op(e2,e1) )
    & ( e3 = op(e2,e0)
      | e2 = op(e2,e0)
      | e1 = op(e2,e0)
      | e0 = op(e2,e0) )
    & ( e3 = op(e1,e3)
      | e2 = op(e1,e3)
      | e1 = op(e1,e3)
      | e0 = op(e1,e3) )
    & ( e3 = op(e1,e2)
      | e2 = op(e1,e2)
      | e1 = op(e1,e2)
      | e0 = op(e1,e2) )
    & ( e3 = op(e1,e1)
      | e2 = op(e1,e1)
      | e1 = op(e1,e1)
      | e0 = op(e1,e1) )
    & ( e3 = op(e1,e0)
      | e2 = op(e1,e0)
      | e1 = op(e1,e0)
      | e0 = op(e1,e0) )
    & ( e3 = op(e0,e3)
      | e2 = op(e0,e3)
      | e1 = op(e0,e3)
      | e0 = op(e0,e3) )
    & ( e3 = op(e0,e2)
      | e2 = op(e0,e2)
      | e1 = op(e0,e2)
      | e0 = op(e0,e2) )
    & ( e3 = op(e0,e1)
      | e2 = op(e0,e1)
      | e1 = op(e0,e1)
      | e0 = op(e0,e1) )
    & ( op(e0,e0) = e3
      | op(e0,e0) = e2
      | op(e0,e0) = e1
      | e0 = op(e0,e0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).

fof(f2,axiom,
    ( ( e3 = unit
      | e2 = unit
      | e1 = unit
      | e0 = unit )
    & e3 = op(e3,unit)
    & e3 = op(unit,e3)
    & e2 = op(e2,unit)
    & e2 = op(unit,e2)
    & e1 = op(e1,unit)
    & e1 = op(unit,e1)
    & e0 = op(e0,unit)
    & e0 = op(unit,e0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).

fof(f3,axiom,
    ( ( e3 = op(e3,e3)
      | e3 = op(e2,e3)
      | e3 = op(e1,e3)
      | e3 = op(e0,e3) )
    & ( e3 = op(e3,e3)
      | e3 = op(e3,e2)
      | e3 = op(e3,e1)
      | e3 = op(e3,e0) )
    & ( e2 = op(e3,e3)
      | e2 = op(e2,e3)
      | e2 = op(e1,e3)
      | e2 = op(e0,e3) )
    & ( e2 = op(e3,e3)
      | e2 = op(e3,e2)
      | e2 = op(e3,e1)
      | e2 = op(e3,e0) )
    & ( e1 = op(e3,e3)
      | e1 = op(e2,e3)
      | e1 = op(e1,e3)
      | e1 = op(e0,e3) )
    & ( e1 = op(e3,e3)
      | e1 = op(e3,e2)
      | e1 = op(e3,e1)
      | e1 = op(e3,e0) )
    & ( e0 = op(e3,e3)
      | e0 = op(e2,e3)
      | e0 = op(e1,e3)
      | e0 = op(e0,e3) )
    & ( e0 = op(e3,e3)
      | e0 = op(e3,e2)
      | e0 = op(e3,e1)
      | e0 = op(e3,e0) )
    & ( e3 = op(e3,e2)
      | e3 = op(e2,e2)
      | e3 = op(e1,e2)
      | e3 = op(e0,e2) )
    & ( e3 = op(e2,e3)
      | e3 = op(e2,e2)
      | e3 = op(e2,e1)
      | e3 = op(e2,e0) )
    & ( e2 = op(e3,e2)
      | e2 = op(e2,e2)
      | e2 = op(e1,e2)
      | e2 = op(e0,e2) )
    & ( e2 = op(e2,e3)
      | e2 = op(e2,e2)
      | e2 = op(e2,e1)
      | e2 = op(e2,e0) )
    & ( e1 = op(e3,e2)
      | e1 = op(e2,e2)
      | e1 = op(e1,e2)
      | e1 = op(e0,e2) )
    & ( e1 = op(e2,e3)
      | e1 = op(e2,e2)
      | e1 = op(e2,e1)
      | e1 = op(e2,e0) )
    & ( e0 = op(e3,e2)
      | e0 = op(e2,e2)
      | e0 = op(e1,e2)
      | e0 = op(e0,e2) )
    & ( e0 = op(e2,e3)
      | e0 = op(e2,e2)
      | e0 = op(e2,e1)
      | e0 = op(e2,e0) )
    & ( e3 = op(e3,e1)
      | e3 = op(e2,e1)
      | e3 = op(e1,e1)
      | e3 = op(e0,e1) )
    & ( e3 = op(e1,e3)
      | e3 = op(e1,e2)
      | e3 = op(e1,e1)
      | e3 = op(e1,e0) )
    & ( e2 = op(e3,e1)
      | e2 = op(e2,e1)
      | e2 = op(e1,e1)
      | e2 = op(e0,e1) )
    & ( e2 = op(e1,e3)
      | e2 = op(e1,e2)
      | e2 = op(e1,e1)
      | e2 = op(e1,e0) )
    & ( e1 = op(e3,e1)
      | e1 = op(e2,e1)
      | e1 = op(e1,e1)
      | e1 = op(e0,e1) )
    & ( e1 = op(e1,e3)
      | e1 = op(e1,e2)
      | e1 = op(e1,e1)
      | e1 = op(e1,e0) )
    & ( e0 = op(e3,e1)
      | e0 = op(e2,e1)
      | e0 = op(e1,e1)
      | e0 = op(e0,e1) )
    & ( e0 = op(e1,e3)
      | e0 = op(e1,e2)
      | e0 = op(e1,e1)
      | e0 = op(e1,e0) )
    & ( e3 = op(e3,e0)
      | e3 = op(e2,e0)
      | e3 = op(e1,e0)
      | op(e0,e0) = e3 )
    & ( e3 = op(e0,e3)
      | e3 = op(e0,e2)
      | e3 = op(e0,e1)
      | op(e0,e0) = e3 )
    & ( e2 = op(e3,e0)
      | e2 = op(e2,e0)
      | e2 = op(e1,e0)
      | op(e0,e0) = e2 )
    & ( e2 = op(e0,e3)
      | e2 = op(e0,e2)
      | e2 = op(e0,e1)
      | op(e0,e0) = e2 )
    & ( e1 = op(e3,e0)
      | e1 = op(e2,e0)
      | e1 = op(e1,e0)
      | op(e0,e0) = e1 )
    & ( e1 = op(e0,e3)
      | e1 = op(e0,e2)
      | e1 = op(e0,e1)
      | op(e0,e0) = e1 )
    & ( e0 = op(e3,e0)
      | e0 = op(e2,e0)
      | e0 = op(e1,e0)
      | e0 = op(e0,e0) )
    & ( e0 = op(e0,e3)
      | e0 = op(e0,e2)
      | e0 = op(e0,e1)
      | e0 = op(e0,e0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).

fof(f4,axiom,
    ( op(e3,e2) != op(e3,e3)
    & op(e3,e1) != op(e3,e3)
    & op(e3,e1) != op(e3,e2)
    & op(e3,e0) != op(e3,e3)
    & op(e3,e0) != op(e3,e2)
    & op(e3,e0) != op(e3,e1)
    & op(e2,e2) != op(e2,e3)
    & op(e2,e1) != op(e2,e3)
    & op(e2,e1) != op(e2,e2)
    & op(e2,e0) != op(e2,e3)
    & op(e2,e0) != op(e2,e2)
    & op(e2,e0) != op(e2,e1)
    & op(e1,e2) != op(e1,e3)
    & op(e1,e1) != op(e1,e3)
    & op(e1,e1) != op(e1,e2)
    & op(e1,e0) != op(e1,e3)
    & op(e1,e0) != op(e1,e2)
    & op(e1,e0) != op(e1,e1)
    & op(e0,e2) != op(e0,e3)
    & op(e0,e1) != op(e0,e3)
    & op(e0,e1) != op(e0,e2)
    & op(e0,e0) != op(e0,e3)
    & op(e0,e0) != op(e0,e2)
    & op(e0,e0) != op(e0,e1)
    & op(e2,e3) != op(e3,e3)
    & op(e1,e3) != op(e3,e3)
    & op(e1,e3) != op(e2,e3)
    & op(e0,e3) != op(e3,e3)
    & op(e0,e3) != op(e2,e3)
    & op(e0,e3) != op(e1,e3)
    & op(e2,e2) != op(e3,e2)
    & op(e1,e2) != op(e3,e2)
    & op(e1,e2) != op(e2,e2)
    & op(e0,e2) != op(e3,e2)
    & op(e0,e2) != op(e2,e2)
    & op(e0,e2) != op(e1,e2)
    & op(e2,e1) != op(e3,e1)
    & op(e1,e1) != op(e3,e1)
    & op(e1,e1) != op(e2,e1)
    & op(e0,e1) != op(e3,e1)
    & op(e0,e1) != op(e2,e1)
    & op(e0,e1) != op(e1,e1)
    & op(e2,e0) != op(e3,e0)
    & op(e1,e0) != op(e3,e0)
    & op(e1,e0) != op(e2,e0)
    & op(e0,e0) != op(e3,e0)
    & op(e0,e0) != op(e2,e0)
    & op(e0,e0) != op(e1,e0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).

fof(f5,axiom,
    ( e2 != e3
    & e1 != e3
    & e1 != e2
    & e0 != e3
    & e0 != e2
    & e0 != e1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).

fof(f6,axiom,
    ( ( e3 = op(e3,e3)
      & e3 = op(e2,e2)
      & e3 = op(e1,e1)
      & op(e0,e0) = e3 )
    | ( e2 = op(e3,e3)
      & e2 = op(e2,e2)
      & e2 = op(e1,e1)
      & op(e0,e0) = e2 )
    | ( e1 = op(e3,e3)
      & e1 = op(e2,e2)
      & e1 = op(e1,e1)
      & op(e0,e0) = e1 )
    | ( e0 = op(e3,e3)
      & e0 = op(e2,e2)
      & e0 = op(e1,e1)
      & e0 = op(e0,e0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).

fof(f10,axiom,
    ~ ( e3 = op(e1,e2)
      & e0 = op(e2,e2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10) ).

fof(f11,axiom,
    ~ ( e1 = op(e2,e3)
      & e0 = op(e3,e3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11) ).

fof(f17,axiom,
    ~ ( e0 = op(e2,e3)
      & e1 = op(e3,e3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).

fof(f23,axiom,
    ~ ( e0 = op(e1,e3)
      & e2 = op(e3,e3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).

fof(f28,axiom,
    ~ ( e2 = op(e0,e1)
      & e3 = op(e1,e1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).

fof(f34,plain,
    ( e3 != op(e1,e2)
    | e0 != op(e2,e2) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f35,plain,
    ( e1 != op(e2,e3)
    | e0 != op(e3,e3) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f41,plain,
    ( e0 != op(e2,e3)
    | e1 != op(e3,e3) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f47,plain,
    ( e0 != op(e1,e3)
    | e2 != op(e3,e3) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f52,plain,
    ( e2 != op(e0,e1)
    | e3 != op(e1,e1) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f55,plain,
    ( ( e0 = op(e3,e3)
      & e0 = op(e2,e2)
      & e0 = op(e1,e1)
      & e0 = op(e0,e0) )
    | ~ sP0 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f56,plain,
    ( ( e1 = op(e3,e3)
      & e1 = op(e2,e2)
      & e1 = op(e1,e1)
      & op(e0,e0) = e1 )
    | ~ sP1 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f57,plain,
    ( ( e2 = op(e3,e3)
      & e2 = op(e2,e2)
      & e2 = op(e1,e1)
      & op(e0,e0) = e2 )
    | ~ sP2 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f58,plain,
    ( ( e3 = op(e3,e3)
      & e3 = op(e2,e2)
      & e3 = op(e1,e1)
      & op(e0,e0) = e3 )
    | sP2
    | sP1
    | sP0 ),
    inference(definition_folding,[],[f6,f57,f56,f55]) ).

fof(f59,plain,
    ( ( e2 = op(e3,e3)
      & e2 = op(e2,e2)
      & e2 = op(e1,e1)
      & op(e0,e0) = e2 )
    | ~ sP2 ),
    inference(nnf_transformation,[],[f57]) ).

fof(f60,plain,
    ( ( e1 = op(e3,e3)
      & e1 = op(e2,e2)
      & e1 = op(e1,e1)
      & op(e0,e0) = e1 )
    | ~ sP1 ),
    inference(nnf_transformation,[],[f56]) ).

fof(f61,plain,
    ( ( e0 = op(e3,e3)
      & e0 = op(e2,e2)
      & e0 = op(e1,e1)
      & e0 = op(e0,e0) )
    | ~ sP0 ),
    inference(nnf_transformation,[],[f55]) ).

fof(f68,plain,
    ( e3 = op(e1,e2)
    | e2 = op(e1,e2)
    | e1 = op(e1,e2)
    | e0 = op(e1,e2) ),
    inference(cnf_transformation,[],[f1]) ).

fof(f73,plain,
    ( e3 = op(e2,e3)
    | e2 = op(e2,e3)
    | e1 = op(e2,e3)
    | e0 = op(e2,e3) ),
    inference(cnf_transformation,[],[f1]) ).

fof(f78,plain,
    e0 = op(unit,e0),
    inference(cnf_transformation,[],[f2]) ).

fof(f79,plain,
    e0 = op(e0,unit),
    inference(cnf_transformation,[],[f2]) ).

fof(f80,plain,
    e1 = op(unit,e1),
    inference(cnf_transformation,[],[f2]) ).

fof(f81,plain,
    e1 = op(e1,unit),
    inference(cnf_transformation,[],[f2]) ).

fof(f82,plain,
    e2 = op(unit,e2),
    inference(cnf_transformation,[],[f2]) ).

fof(f83,plain,
    e2 = op(e2,unit),
    inference(cnf_transformation,[],[f2]) ).

fof(f84,plain,
    e3 = op(unit,e3),
    inference(cnf_transformation,[],[f2]) ).

fof(f85,plain,
    e3 = op(e3,unit),
    inference(cnf_transformation,[],[f2]) ).

fof(f86,plain,
    ( e3 = unit
    | e2 = unit
    | e1 = unit
    | e0 = unit ),
    inference(cnf_transformation,[],[f2]) ).

fof(f91,plain,
    ( e2 = op(e0,e3)
    | e2 = op(e0,e2)
    | e2 = op(e0,e1)
    | op(e0,e0) = e2 ),
    inference(cnf_transformation,[],[f3]) ).

fof(f112,plain,
    ( e0 = op(e3,e3)
    | e0 = op(e2,e3)
    | e0 = op(e1,e3)
    | e0 = op(e0,e3) ),
    inference(cnf_transformation,[],[f3]) ).

fof(f121,plain,
    op(e0,e0) != op(e3,e0),
    inference(cnf_transformation,[],[f4]) ).

fof(f125,plain,
    op(e0,e1) != op(e1,e1),
    inference(cnf_transformation,[],[f4]) ).

fof(f129,plain,
    op(e1,e1) != op(e3,e1),
    inference(cnf_transformation,[],[f4]) ).

fof(f131,plain,
    op(e0,e2) != op(e1,e2),
    inference(cnf_transformation,[],[f4]) ).

fof(f132,plain,
    op(e0,e2) != op(e2,e2),
    inference(cnf_transformation,[],[f4]) ).

fof(f133,plain,
    op(e0,e2) != op(e3,e2),
    inference(cnf_transformation,[],[f4]) ).

fof(f134,plain,
    op(e1,e2) != op(e2,e2),
    inference(cnf_transformation,[],[f4]) ).

fof(f136,plain,
    op(e2,e2) != op(e3,e2),
    inference(cnf_transformation,[],[f4]) ).

fof(f139,plain,
    op(e0,e3) != op(e3,e3),
    inference(cnf_transformation,[],[f4]) ).

fof(f140,plain,
    op(e1,e3) != op(e2,e3),
    inference(cnf_transformation,[],[f4]) ).

fof(f141,plain,
    op(e1,e3) != op(e3,e3),
    inference(cnf_transformation,[],[f4]) ).

fof(f142,plain,
    op(e2,e3) != op(e3,e3),
    inference(cnf_transformation,[],[f4]) ).

fof(f143,plain,
    op(e0,e0) != op(e0,e1),
    inference(cnf_transformation,[],[f4]) ).

fof(f147,plain,
    op(e0,e1) != op(e0,e3),
    inference(cnf_transformation,[],[f4]) ).

fof(f148,plain,
    op(e0,e2) != op(e0,e3),
    inference(cnf_transformation,[],[f4]) ).

fof(f150,plain,
    op(e1,e0) != op(e1,e2),
    inference(cnf_transformation,[],[f4]) ).

fof(f151,plain,
    op(e1,e0) != op(e1,e3),
    inference(cnf_transformation,[],[f4]) ).

fof(f156,plain,
    op(e2,e0) != op(e2,e2),
    inference(cnf_transformation,[],[f4]) ).

fof(f157,plain,
    op(e2,e0) != op(e2,e3),
    inference(cnf_transformation,[],[f4]) ).

fof(f158,plain,
    op(e2,e1) != op(e2,e2),
    inference(cnf_transformation,[],[f4]) ).

fof(f159,plain,
    op(e2,e1) != op(e2,e3),
    inference(cnf_transformation,[],[f4]) ).

fof(f168,plain,
    e0 != e2,
    inference(cnf_transformation,[],[f5]) ).

fof(f172,plain,
    e2 != e3,
    inference(cnf_transformation,[],[f5]) ).

fof(f175,plain,
    ( e2 = op(e2,e2)
    | ~ sP2 ),
    inference(cnf_transformation,[],[f59]) ).

fof(f176,plain,
    ( e2 = op(e3,e3)
    | ~ sP2 ),
    inference(cnf_transformation,[],[f59]) ).

fof(f178,plain,
    ( e1 = op(e1,e1)
    | ~ sP1 ),
    inference(cnf_transformation,[],[f60]) ).

fof(f179,plain,
    ( e1 = op(e2,e2)
    | ~ sP1 ),
    inference(cnf_transformation,[],[f60]) ).

fof(f180,plain,
    ( e1 = op(e3,e3)
    | ~ sP1 ),
    inference(cnf_transformation,[],[f60]) ).

fof(f181,plain,
    ( e0 = op(e0,e0)
    | ~ sP0 ),
    inference(cnf_transformation,[],[f61]) ).

fof(f183,plain,
    ( e0 = op(e2,e2)
    | ~ sP0 ),
    inference(cnf_transformation,[],[f61]) ).

fof(f185,plain,
    ( op(e0,e0) = e3
    | sP2
    | sP1
    | sP0 ),
    inference(cnf_transformation,[],[f58]) ).

fof(f186,plain,
    ( e3 = op(e1,e1)
    | sP2
    | sP1
    | sP0 ),
    inference(cnf_transformation,[],[f58]) ).

fof(f188,plain,
    ( e3 = op(e3,e3)
    | sP2
    | sP1
    | sP0 ),
    inference(cnf_transformation,[],[f58]) ).

fof(f192,plain,
    ( e3 != op(e1,e2)
    | e0 != op(e2,e2) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f193,plain,
    ( e1 != op(e2,e3)
    | e0 != op(e3,e3) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f199,plain,
    ( e0 != op(e2,e3)
    | e1 != op(e3,e3) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f205,plain,
    ( e0 != op(e1,e3)
    | e2 != op(e3,e3) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f210,plain,
    ( e2 != op(e0,e1)
    | e3 != op(e1,e1) ),
    inference(cnf_transformation,[],[f52]) ).

cnf(c_53,plain,
    ( op(e2,e3) = e3
    | op(e2,e3) = e2
    | op(e2,e3) = e1
    | op(e2,e3) = e0 ),
    inference(cnf_transformation,[],[f73]) ).

cnf(c_58,plain,
    ( op(e1,e2) = e3
    | op(e1,e2) = e2
    | op(e1,e2) = e1
    | op(e1,e2) = e0 ),
    inference(cnf_transformation,[],[f68]) ).

cnf(c_65,plain,
    ( e3 = unit
    | e2 = unit
    | e1 = unit
    | e0 = unit ),
    inference(cnf_transformation,[],[f86]) ).

cnf(c_66,plain,
    op(e3,unit) = e3,
    inference(cnf_transformation,[],[f85]) ).

cnf(c_67,plain,
    op(unit,e3) = e3,
    inference(cnf_transformation,[],[f84]) ).

cnf(c_68,plain,
    op(e2,unit) = e2,
    inference(cnf_transformation,[],[f83]) ).

cnf(c_69,plain,
    op(unit,e2) = e2,
    inference(cnf_transformation,[],[f82]) ).

cnf(c_70,plain,
    op(e1,unit) = e1,
    inference(cnf_transformation,[],[f81]) ).

cnf(c_71,plain,
    op(unit,e1) = e1,
    inference(cnf_transformation,[],[f80]) ).

cnf(c_72,plain,
    op(e0,unit) = e0,
    inference(cnf_transformation,[],[f79]) ).

cnf(c_73,plain,
    op(unit,e0) = e0,
    inference(cnf_transformation,[],[f78]) ).

cnf(c_80,plain,
    ( op(e3,e3) = e0
    | op(e2,e3) = e0
    | op(e1,e3) = e0
    | op(e0,e3) = e0 ),
    inference(cnf_transformation,[],[f112]) ).

cnf(c_101,plain,
    ( op(e0,e3) = e2
    | op(e0,e2) = e2
    | op(e0,e1) = e2
    | op(e0,e0) = e2 ),
    inference(cnf_transformation,[],[f91]) ).

cnf(c_113,plain,
    op(e2,e3) != op(e2,e1),
    inference(cnf_transformation,[],[f159]) ).

cnf(c_114,plain,
    op(e2,e2) != op(e2,e1),
    inference(cnf_transformation,[],[f158]) ).

cnf(c_115,plain,
    op(e2,e3) != op(e2,e0),
    inference(cnf_transformation,[],[f157]) ).

cnf(c_116,plain,
    op(e2,e2) != op(e2,e0),
    inference(cnf_transformation,[],[f156]) ).

cnf(c_121,plain,
    op(e1,e3) != op(e1,e0),
    inference(cnf_transformation,[],[f151]) ).

cnf(c_122,plain,
    op(e1,e2) != op(e1,e0),
    inference(cnf_transformation,[],[f150]) ).

cnf(c_124,plain,
    op(e0,e3) != op(e0,e2),
    inference(cnf_transformation,[],[f148]) ).

cnf(c_125,plain,
    op(e0,e3) != op(e0,e1),
    inference(cnf_transformation,[],[f147]) ).

cnf(c_129,plain,
    op(e0,e1) != op(e0,e0),
    inference(cnf_transformation,[],[f143]) ).

cnf(c_130,plain,
    op(e3,e3) != op(e2,e3),
    inference(cnf_transformation,[],[f142]) ).

cnf(c_131,plain,
    op(e3,e3) != op(e1,e3),
    inference(cnf_transformation,[],[f141]) ).

cnf(c_132,plain,
    op(e2,e3) != op(e1,e3),
    inference(cnf_transformation,[],[f140]) ).

cnf(c_133,plain,
    op(e3,e3) != op(e0,e3),
    inference(cnf_transformation,[],[f139]) ).

cnf(c_136,plain,
    op(e3,e2) != op(e2,e2),
    inference(cnf_transformation,[],[f136]) ).

cnf(c_138,plain,
    op(e2,e2) != op(e1,e2),
    inference(cnf_transformation,[],[f134]) ).

cnf(c_139,plain,
    op(e3,e2) != op(e0,e2),
    inference(cnf_transformation,[],[f133]) ).

cnf(c_140,plain,
    op(e2,e2) != op(e0,e2),
    inference(cnf_transformation,[],[f132]) ).

cnf(c_141,plain,
    op(e1,e2) != op(e0,e2),
    inference(cnf_transformation,[],[f131]) ).

cnf(c_143,plain,
    op(e3,e1) != op(e1,e1),
    inference(cnf_transformation,[],[f129]) ).

cnf(c_147,plain,
    op(e1,e1) != op(e0,e1),
    inference(cnf_transformation,[],[f125]) ).

cnf(c_151,plain,
    op(e3,e0) != op(e0,e0),
    inference(cnf_transformation,[],[f121]) ).

cnf(c_154,plain,
    e3 != e2,
    inference(cnf_transformation,[],[f172]) ).

cnf(c_158,plain,
    e2 != e0,
    inference(cnf_transformation,[],[f168]) ).

cnf(c_160,plain,
    ( ~ sP2
    | op(e3,e3) = e2 ),
    inference(cnf_transformation,[],[f176]) ).

cnf(c_161,plain,
    ( ~ sP2
    | op(e2,e2) = e2 ),
    inference(cnf_transformation,[],[f175]) ).

cnf(c_164,plain,
    ( ~ sP1
    | op(e3,e3) = e1 ),
    inference(cnf_transformation,[],[f180]) ).

cnf(c_165,plain,
    ( ~ sP1
    | op(e2,e2) = e1 ),
    inference(cnf_transformation,[],[f179]) ).

cnf(c_166,plain,
    ( ~ sP1
    | op(e1,e1) = e1 ),
    inference(cnf_transformation,[],[f178]) ).

cnf(c_169,plain,
    ( ~ sP0
    | op(e2,e2) = e0 ),
    inference(cnf_transformation,[],[f183]) ).

cnf(c_171,plain,
    ( ~ sP0
    | op(e0,e0) = e0 ),
    inference(cnf_transformation,[],[f181]) ).

cnf(c_172,plain,
    ( op(e3,e3) = e3
    | sP2
    | sP1
    | sP0 ),
    inference(cnf_transformation,[],[f188]) ).

cnf(c_174,plain,
    ( op(e1,e1) = e3
    | sP2
    | sP1
    | sP0 ),
    inference(cnf_transformation,[],[f186]) ).

cnf(c_175,plain,
    ( op(e0,e0) = e3
    | sP2
    | sP1
    | sP0 ),
    inference(cnf_transformation,[],[f185]) ).

cnf(c_179,plain,
    ( op(e2,e2) != e0
    | op(e1,e2) != e3 ),
    inference(cnf_transformation,[],[f192]) ).

cnf(c_180,plain,
    ( op(e3,e3) != e0
    | op(e2,e3) != e1 ),
    inference(cnf_transformation,[],[f193]) ).

cnf(c_186,plain,
    ( op(e3,e3) != e1
    | op(e2,e3) != e0 ),
    inference(cnf_transformation,[],[f199]) ).

cnf(c_192,plain,
    ( op(e3,e3) != e2
    | op(e1,e3) != e0 ),
    inference(cnf_transformation,[],[f205]) ).

cnf(c_197,plain,
    ( op(e1,e1) != e3
    | op(e0,e1) != e2 ),
    inference(cnf_transformation,[],[f210]) ).

cnf(c_2187,plain,
    ( op(e3,e3) = e3
    | op(e2,e2) = e0
    | sP2
    | sP1 ),
    inference(resolution,[status(thm)],[c_172,c_169]) ).

cnf(c_2278,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_3115,plain,
    ( op(e3,e3) = e3
    | op(e0,e0) = e0
    | sP2
    | sP1 ),
    inference(superposition,[status(thm)],[c_172,c_171]) ).

cnf(c_3117,plain,
    ( op(e3,e3) = e3
    | op(e2,e2) = e0
    | sP2
    | sP1 ),
    inference(superposition,[status(thm)],[c_172,c_169]) ).

cnf(c_3365,plain,
    ( op(e3,e3) = e3
    | op(e3,e3) = e1
    | op(e0,e0) = e0
    | sP2 ),
    inference(superposition,[status(thm)],[c_3115,c_164]) ).

cnf(c_3443,plain,
    ( op(e0,e1) = e1
    | e3 = unit
    | e2 = unit
    | e1 = unit ),
    inference(superposition,[status(thm)],[c_65,c_71]) ).

cnf(c_3444,plain,
    ( op(e1,e0) = e1
    | e3 = unit
    | e2 = unit
    | e1 = unit ),
    inference(superposition,[status(thm)],[c_65,c_70]) ).

cnf(c_3445,plain,
    ( op(e0,e2) = e2
    | e3 = unit
    | e2 = unit
    | e1 = unit ),
    inference(superposition,[status(thm)],[c_65,c_69]) ).

cnf(c_3447,plain,
    ( op(e0,e3) = e3
    | e3 = unit
    | e2 = unit
    | e1 = unit ),
    inference(superposition,[status(thm)],[c_65,c_67]) ).

cnf(c_3448,plain,
    ( op(e3,e0) = e3
    | e3 = unit
    | e2 = unit
    | e1 = unit ),
    inference(superposition,[status(thm)],[c_65,c_66]) ).

cnf(c_3531,plain,
    ( op(e2,e2) != e0
    | op(e1,e2) = e3
    | op(e1,e2) = e2
    | op(e1,e2) = e1 ),
    inference(superposition,[status(thm)],[c_58,c_138]) ).

cnf(c_3556,plain,
    ( op(e3,e3) = e3
    | op(e2,e2) = e1
    | op(e2,e2) = e0
    | sP2 ),
    inference(superposition,[status(thm)],[c_3117,c_165]) ).

cnf(c_4049,plain,
    ( op(e0,e1) != X0
    | op(e0,e0) != X0
    | op(e0,e1) = op(e0,e0) ),
    inference(instantiation,[status(thm)],[c_2278]) ).

cnf(c_4050,plain,
    ( op(e0,e1) != e0
    | op(e0,e0) != e0
    | op(e0,e1) = op(e0,e0) ),
    inference(instantiation,[status(thm)],[c_4049]) ).

cnf(c_4263,plain,
    ( op(e1,e1) != e1
    | e3 = unit
    | e2 = unit
    | e1 = unit ),
    inference(superposition,[status(thm)],[c_3443,c_147]) ).

cnf(c_4302,plain,
    ( op(e1,e2) != e1
    | e3 = unit
    | e2 = unit
    | e1 = unit ),
    inference(superposition,[status(thm)],[c_3444,c_122]) ).

cnf(c_4331,plain,
    ( op(e1,e2) != e2
    | e3 = unit
    | e2 = unit
    | e1 = unit ),
    inference(superposition,[status(thm)],[c_3445,c_141]) ).

cnf(c_4332,plain,
    ( op(e2,e2) != e2
    | e3 = unit
    | e2 = unit
    | e1 = unit ),
    inference(superposition,[status(thm)],[c_3445,c_140]) ).

cnf(c_4403,plain,
    ( op(e3,e3) != e3
    | e3 = unit
    | e2 = unit
    | e1 = unit ),
    inference(superposition,[status(thm)],[c_3447,c_133]) ).

cnf(c_4423,plain,
    ( e3 = unit
    | e2 = unit
    | e1 = unit ),
    inference(global_subsumption_just,[status(thm)],[c_3448,c_166,c_161,c_179,c_2187,c_3531,c_4263,c_4302,c_4332,c_4331,c_4403]) ).

cnf(c_4431,plain,
    ( op(e1,e0) = e0
    | e3 = unit
    | e2 = unit ),
    inference(superposition,[status(thm)],[c_4423,c_73]) ).

cnf(c_4432,plain,
    ( op(e0,e1) = e0
    | e3 = unit
    | e2 = unit ),
    inference(superposition,[status(thm)],[c_4423,c_72]) ).

cnf(c_4435,plain,
    ( op(e1,e2) = e2
    | e3 = unit
    | e2 = unit ),
    inference(superposition,[status(thm)],[c_4423,c_69]) ).

cnf(c_4436,plain,
    ( op(e2,e1) = e2
    | e3 = unit
    | e2 = unit ),
    inference(superposition,[status(thm)],[c_4423,c_68]) ).

cnf(c_4437,plain,
    ( op(e1,e3) = e3
    | e3 = unit
    | e2 = unit ),
    inference(superposition,[status(thm)],[c_4423,c_67]) ).

cnf(c_4438,plain,
    ( op(e3,e1) = e3
    | e3 = unit
    | e2 = unit ),
    inference(superposition,[status(thm)],[c_4423,c_66]) ).

cnf(c_4470,plain,
    ( op(e1,e3) != e0
    | e3 = unit
    | e2 = unit ),
    inference(superposition,[status(thm)],[c_4431,c_121]) ).

cnf(c_4496,plain,
    ( op(e0,e3) != e0
    | e3 = unit
    | e2 = unit ),
    inference(superposition,[status(thm)],[c_4432,c_125]) ).

cnf(c_4674,plain,
    ( op(e2,e2) != e2
    | e3 = unit
    | e2 = unit ),
    inference(superposition,[status(thm)],[c_4435,c_138]) ).

cnf(c_4702,plain,
    ( op(e2,e3) != e2
    | e3 = unit
    | e2 = unit ),
    inference(superposition,[status(thm)],[c_4436,c_113]) ).

cnf(c_4723,plain,
    ( op(e2,e3) != e3
    | e3 = unit
    | e2 = unit ),
    inference(superposition,[status(thm)],[c_4437,c_132]) ).

cnf(c_4724,plain,
    ( op(e3,e3) != e3
    | e3 = unit
    | e2 = unit ),
    inference(superposition,[status(thm)],[c_4437,c_131]) ).

cnf(c_4737,plain,
    ( e3 = unit
    | e2 = unit ),
    inference(global_subsumption_just,[status(thm)],[c_4438,c_161,c_129,c_186,c_180,c_80,c_53,c_3365,c_4050,c_4432,c_4470,c_4496,c_4674,c_4702,c_4724,c_4723]) ).

cnf(c_4743,plain,
    ( op(e2,e0) = e0
    | e3 = unit ),
    inference(superposition,[status(thm)],[c_4737,c_73]) ).

cnf(c_4744,plain,
    ( op(e0,e2) = e0
    | e3 = unit ),
    inference(superposition,[status(thm)],[c_4737,c_72]) ).

cnf(c_4745,plain,
    ( op(e2,e1) = e1
    | e3 = unit ),
    inference(superposition,[status(thm)],[c_4737,c_71]) ).

cnf(c_4749,plain,
    ( op(e2,e3) = e3
    | e3 = unit ),
    inference(superposition,[status(thm)],[c_4737,c_67]) ).

cnf(c_4771,plain,
    ( op(e2,e2) != e0
    | e3 = unit ),
    inference(superposition,[status(thm)],[c_4743,c_116]) ).

cnf(c_4772,plain,
    ( op(e2,e3) != e0
    | e3 = unit ),
    inference(superposition,[status(thm)],[c_4743,c_115]) ).

cnf(c_4788,plain,
    ( op(e0,e3) != e0
    | e3 = unit ),
    inference(superposition,[status(thm)],[c_4744,c_124]) ).

cnf(c_4802,plain,
    ( op(e2,e2) != e1
    | e3 = unit ),
    inference(superposition,[status(thm)],[c_4745,c_114]) ).

cnf(c_4852,plain,
    ( op(e3,e3) != e3
    | e3 = unit ),
    inference(superposition,[status(thm)],[c_4749,c_130]) ).

cnf(c_5104,plain,
    ( op(e3,e3) = e0
    | op(e2,e3) = e0
    | op(e1,e3) = e0
    | e3 = unit ),
    inference(superposition,[status(thm)],[c_80,c_4788]) ).

cnf(c_6365,plain,
    $false,
    inference(smt_impl_just,[status(thm)],[c_5104,c_4852,c_4802,c_4772,c_4771,c_3556,c_197,c_192,c_175,c_174,c_172,c_171,c_166,c_161,c_160,c_158,c_154,c_151,c_143,c_139,c_136,c_101,c_73,c_72,c_71,c_69]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : ALG045+1 : TPTP v8.1.2. Released v2.7.0.
% 0.03/0.12  % Command  : run_iprover %s %d THM
% 0.13/0.33  % Computer : n002.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Thu May  2 23:05:57 EDT 2024
% 0.13/0.33  % CPUTime  : 
% 0.20/0.45  Running first-order theorem proving
% 0.20/0.45  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.25/1.18  % SZS status Started for theBenchmark.p
% 2.25/1.18  % SZS status Unsatisfiable for theBenchmark.p
% 2.25/1.18  
% 2.25/1.18  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 2.25/1.18  
% 2.25/1.18  ------  iProver source info
% 2.25/1.18  
% 2.25/1.18  git: date: 2024-05-02 19:28:25 +0000
% 2.25/1.18  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 2.25/1.18  git: non_committed_changes: false
% 2.25/1.18  
% 2.25/1.18  ------ Parsing...
% 2.25/1.18  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.25/1.18  
% 2.25/1.18  ------ Preprocessing... sup_sim: 0  sf_s  rm: 0 0s  sf_e  pe_s  pe_e 
% 2.25/1.18  
% 2.25/1.18  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.25/1.18  
% 2.25/1.18  ------ Preprocessing... sf_s  rm: 0 0s  sf_e 
% 2.25/1.18  ------ Proving...
% 2.25/1.18  ------ Problem Properties 
% 2.25/1.18  
% 2.25/1.18  
% 2.25/1.18  clauses                                 151
% 2.25/1.18  conjectures                             0
% 2.25/1.18  EPR                                     7
% 2.25/1.18  Horn                                    98
% 2.25/1.18  unary                                   62
% 2.25/1.18  binary                                  36
% 2.25/1.18  lits                                    346
% 2.25/1.18  lits eq                                 322
% 2.25/1.18  fd_pure                                 0
% 2.25/1.18  fd_pseudo                               0
% 2.25/1.18  fd_cond                                 0
% 2.25/1.18  fd_pseudo_cond                          0
% 2.25/1.18  AC symbols                              0
% 2.25/1.18  
% 2.25/1.18  ------ Schedule dynamic 5 is on 
% 2.25/1.18  
% 2.25/1.18  ------ no conjectures: strip conj schedule 
% 2.25/1.18  
% 2.25/1.18  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.25/1.18  
% 2.25/1.18  
% 2.25/1.18  ------ 
% 2.25/1.18  Current options:
% 2.25/1.18  ------ 
% 2.25/1.18  
% 2.25/1.18  
% 2.25/1.18  
% 2.25/1.18  
% 2.25/1.18  ------ Proving...
% 2.25/1.18  
% 2.25/1.18  
% 2.25/1.18  % SZS status Unsatisfiable for theBenchmark.p
% 2.25/1.18  
% 2.25/1.18  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.25/1.18  
% 2.25/1.18  
%------------------------------------------------------------------------------