TSTP Solution File: ALG045+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : ALG045+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n029.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 : Wed Aug 30 16:00:36 EDT 2023

% Result   : Unsatisfiable 0.20s 0.70s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :   18
% Syntax   : Number of formulae    :  112 (  31 unt;   7 typ;   0 def)
%            Number of atoms       :  784 ( 694 equ)
%            Maximal formula atoms :  256 (   7 avg)
%            Number of connectives :  848 ( 169   ~; 468   |; 209   &)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   68 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   1   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   2 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    e0: $i ).

tff(decl_23,type,
    op: ( $i * $i ) > $i ).

tff(decl_24,type,
    e1: $i ).

tff(decl_25,type,
    e2: $i ).

tff(decl_26,type,
    e3: $i ).

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

tff(decl_28,type,
    epred1_0: $o ).

fof(ax6,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/sandbox2/benchmark/theBenchmark.p',ax6) ).

fof(ax28,axiom,
    ~ ( e3 = op(e1,e1)
      & e2 = op(e0,e1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).

fof(ax2,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/sandbox2/benchmark/theBenchmark.p',ax2) ).

fof(ax4,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/sandbox2/benchmark/theBenchmark.p',ax4) ).

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/sandbox2/benchmark/theBenchmark.p',ax1) ).

fof(ax5,axiom,
    ( e0 != e1
    & e0 != e2
    & e0 != e3
    & e1 != e2
    & e1 != e3
    & e2 != e3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).

fof(ax21,axiom,
    ~ ( e2 = op(e1,e1)
      & e0 = op(e3,e1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).

fof(ax3,axiom,
    ( ( op(e0,e0) = e0
      | op(e0,e1) = e0
      | op(e0,e2) = e0
      | op(e0,e3) = e0 )
    & ( op(e0,e0) = e0
      | op(e1,e0) = e0
      | op(e2,e0) = e0
      | op(e3,e0) = e0 )
    & ( op(e0,e0) = e1
      | op(e0,e1) = e1
      | op(e0,e2) = e1
      | op(e0,e3) = e1 )
    & ( op(e0,e0) = e1
      | op(e1,e0) = e1
      | op(e2,e0) = e1
      | op(e3,e0) = e1 )
    & ( op(e0,e0) = e2
      | op(e0,e1) = e2
      | op(e0,e2) = e2
      | op(e0,e3) = e2 )
    & ( op(e0,e0) = e2
      | op(e1,e0) = e2
      | op(e2,e0) = e2
      | op(e3,e0) = e2 )
    & ( op(e0,e0) = e3
      | op(e0,e1) = e3
      | op(e0,e2) = e3
      | op(e0,e3) = e3 )
    & ( op(e0,e0) = e3
      | op(e1,e0) = e3
      | op(e2,e0) = e3
      | op(e3,e0) = e3 )
    & ( op(e1,e0) = e0
      | op(e1,e1) = e0
      | op(e1,e2) = e0
      | op(e1,e3) = e0 )
    & ( op(e0,e1) = e0
      | op(e1,e1) = e0
      | op(e2,e1) = e0
      | op(e3,e1) = e0 )
    & ( op(e1,e0) = e1
      | op(e1,e1) = e1
      | op(e1,e2) = e1
      | op(e1,e3) = e1 )
    & ( op(e0,e1) = e1
      | op(e1,e1) = e1
      | op(e2,e1) = e1
      | op(e3,e1) = e1 )
    & ( op(e1,e0) = e2
      | op(e1,e1) = e2
      | op(e1,e2) = e2
      | op(e1,e3) = e2 )
    & ( op(e0,e1) = e2
      | op(e1,e1) = e2
      | op(e2,e1) = e2
      | op(e3,e1) = e2 )
    & ( op(e1,e0) = e3
      | op(e1,e1) = e3
      | op(e1,e2) = e3
      | op(e1,e3) = e3 )
    & ( op(e0,e1) = e3
      | op(e1,e1) = e3
      | op(e2,e1) = e3
      | op(e3,e1) = e3 )
    & ( op(e2,e0) = e0
      | op(e2,e1) = e0
      | op(e2,e2) = e0
      | op(e2,e3) = e0 )
    & ( op(e0,e2) = e0
      | op(e1,e2) = e0
      | op(e2,e2) = e0
      | op(e3,e2) = e0 )
    & ( op(e2,e0) = e1
      | op(e2,e1) = e1
      | op(e2,e2) = e1
      | op(e2,e3) = e1 )
    & ( op(e0,e2) = e1
      | op(e1,e2) = e1
      | op(e2,e2) = e1
      | op(e3,e2) = e1 )
    & ( op(e2,e0) = e2
      | op(e2,e1) = e2
      | op(e2,e2) = e2
      | op(e2,e3) = e2 )
    & ( op(e0,e2) = e2
      | op(e1,e2) = e2
      | op(e2,e2) = e2
      | op(e3,e2) = e2 )
    & ( op(e2,e0) = e3
      | op(e2,e1) = e3
      | op(e2,e2) = e3
      | op(e2,e3) = e3 )
    & ( op(e0,e2) = e3
      | op(e1,e2) = e3
      | op(e2,e2) = e3
      | op(e3,e2) = e3 )
    & ( op(e3,e0) = e0
      | op(e3,e1) = e0
      | op(e3,e2) = e0
      | op(e3,e3) = e0 )
    & ( op(e0,e3) = e0
      | op(e1,e3) = e0
      | op(e2,e3) = e0
      | op(e3,e3) = e0 )
    & ( op(e3,e0) = e1
      | op(e3,e1) = e1
      | op(e3,e2) = e1
      | op(e3,e3) = e1 )
    & ( op(e0,e3) = e1
      | op(e1,e3) = e1
      | op(e2,e3) = e1
      | op(e3,e3) = e1 )
    & ( op(e3,e0) = e2
      | op(e3,e1) = e2
      | op(e3,e2) = e2
      | op(e3,e3) = e2 )
    & ( op(e0,e3) = e2
      | op(e1,e3) = e2
      | op(e2,e3) = e2
      | op(e3,e3) = e2 )
    & ( op(e3,e0) = e3
      | op(e3,e1) = e3
      | op(e3,e2) = e3
      | op(e3,e3) = e3 )
    & ( op(e0,e3) = e3
      | op(e1,e3) = e3
      | op(e2,e3) = e3
      | op(e3,e3) = e3 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).

fof(ax13,axiom,
    ~ ( e1 = op(e0,e0)
      & e2 = op(e3,e0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax13) ).

fof(ax12,axiom,
    ~ ( e0 = op(e3,e3)
      & e2 = op(e1,e3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax12) ).

fof(c_0_10,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_11,axiom,
    ( epred1_0
    | ( op(e0,e0) = e3
      & op(e1,e1) = e3
      & op(e2,e2) = e3
      & op(e3,e3) = e3 ) ),
    inference(apply_def,[status(thm)],[ax6,c_0_10]) ).

fof(c_0_12,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_11]) ).

fof(c_0_13,plain,
    ( e3 != op(e1,e1)
    | e2 != op(e0,e1) ),
    inference(fof_nnf,[status(thm)],[ax28]) ).

cnf(c_0_14,plain,
    op(unit,e1) = e1,
    inference(split_conjunct,[status(thm)],[ax2]) ).

cnf(c_0_15,plain,
    ( unit = e0
    | unit = e1
    | unit = e2
    | unit = e3 ),
    inference(split_conjunct,[status(thm)],[ax2]) ).

cnf(c_0_16,plain,
    op(e0,e1) != op(e1,e1),
    inference(split_conjunct,[status(thm)],[ax4]) ).

cnf(c_0_17,plain,
    ( op(e1,e1) = e3
    | epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_18,plain,
    ( e3 != op(e1,e1)
    | e2 != op(e0,e1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_19,plain,
    op(e0,unit) = e0,
    inference(split_conjunct,[status(thm)],[ax2]) ).

cnf(c_0_20,plain,
    op(e0,e1) != op(e3,e1),
    inference(split_conjunct,[status(thm)],[ax4]) ).

cnf(c_0_21,plain,
    ( op(e3,e1) = e1
    | unit = e2
    | unit = e1
    | unit = e0 ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_22,plain,
    ( epred1_0
    | op(e0,e1) != e3 ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_23,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_24,plain,
    ( epred1_0
    | op(e0,e1) != e2 ),
    inference(spm,[status(thm)],[c_0_18,c_0_17]) ).

cnf(c_0_25,plain,
    op(e0,e1) != op(e0,e3),
    inference(split_conjunct,[status(thm)],[ax4]) ).

cnf(c_0_26,plain,
    ( op(e0,e3) = e0
    | unit = e2
    | unit = e1
    | unit = e0 ),
    inference(spm,[status(thm)],[c_0_19,c_0_15]) ).

cnf(c_0_27,plain,
    ( unit = e0
    | unit = e1
    | unit = e2
    | op(e0,e1) != e1 ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_28,plain,
    ( op(e0,e1) = e1
    | op(e0,e1) = e0
    | epred1_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).

cnf(c_0_29,plain,
    ( unit = e0
    | unit = e1
    | unit = e2
    | op(e0,e1) != e0 ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_30,plain,
    op(e2,unit) = e2,
    inference(split_conjunct,[status(thm)],[ax2]) ).

cnf(c_0_31,plain,
    ( unit = e2
    | unit = e1
    | unit = e0
    | epred1_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).

cnf(c_0_32,plain,
    ( op(e2,e2) = e3
    | epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_33,plain,
    ( op(e2,e2) = e2
    | unit = e0
    | unit = e1
    | epred1_0 ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_34,plain,
    e2 != e3,
    inference(split_conjunct,[status(thm)],[ax5]) ).

cnf(c_0_35,plain,
    op(e1,unit) = e1,
    inference(split_conjunct,[status(thm)],[ax2]) ).

cnf(c_0_36,plain,
    ( unit = e1
    | unit = e0
    | epred1_0 ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).

cnf(c_0_37,plain,
    ( op(e1,e1) = e1
    | unit = e0
    | epred1_0 ),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_38,plain,
    e1 != e3,
    inference(split_conjunct,[status(thm)],[ax5]) ).

fof(c_0_39,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_10]) ).

cnf(c_0_40,plain,
    ( unit = e0
    | epred1_0 ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_37]),c_0_38]) ).

fof(c_0_41,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)],[c_0_39])]) ).

cnf(c_0_42,plain,
    ( op(e0,e0) = e3
    | epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_43,plain,
    ( op(e0,e0) = e0
    | epred1_0 ),
    inference(spm,[status(thm)],[c_0_19,c_0_40]) ).

cnf(c_0_44,plain,
    e0 != e3,
    inference(split_conjunct,[status(thm)],[ax5]) ).

cnf(c_0_45,plain,
    op(e3,unit) = e3,
    inference(split_conjunct,[status(thm)],[ax2]) ).

cnf(c_0_46,plain,
    ( op(e3,e3) = e2
    | op(e3,e3) = e1
    | op(e3,e3) = e0
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_47,plain,
    epred1_0,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).

cnf(c_0_48,plain,
    ( op(e3,e3) = e3
    | unit = e2
    | unit = e1
    | unit = e0 ),
    inference(spm,[status(thm)],[c_0_45,c_0_15]) ).

cnf(c_0_49,plain,
    ( op(e3,e3) = e2
    | op(e3,e3) = e1
    | op(e3,e3) = e0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).

cnf(c_0_50,plain,
    ( op(e3,e3) = e0
    | op(e3,e3) = e1
    | unit = e0
    | unit = e1
    | unit = e2 ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_34]) ).

cnf(c_0_51,plain,
    ( op(e3,e3) = e0
    | unit = e0
    | unit = e1
    | unit = e2 ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_50]),c_0_38]) ).

fof(c_0_52,plain,
    ( e2 != op(e1,e1)
    | e0 != op(e3,e1) ),
    inference(fof_nnf,[status(thm)],[ax21]) ).

cnf(c_0_53,plain,
    ( op(e1,e1) = e2
    | op(e2,e2) = e1
    | op(e2,e2) = e0
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_54,plain,
    ( unit = e0
    | unit = e1
    | unit = e2 ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_51]),c_0_44]) ).

cnf(c_0_55,plain,
    ( e2 != op(e1,e1)
    | e0 != op(e3,e1) ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_56,plain,
    ( op(e0,e1) = e0
    | op(e1,e1) = e0
    | op(e2,e1) = e0
    | op(e3,e1) = e0 ),
    inference(split_conjunct,[status(thm)],[ax3]) ).

cnf(c_0_57,plain,
    ( op(e2,e2) = e1
    | op(e2,e2) = e0
    | op(e1,e1) = e2 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_47])]) ).

cnf(c_0_58,plain,
    ( op(e2,e2) = e2
    | unit = e1
    | unit = e0 ),
    inference(spm,[status(thm)],[c_0_30,c_0_54]) ).

cnf(c_0_59,plain,
    e1 != e2,
    inference(split_conjunct,[status(thm)],[ax5]) ).

cnf(c_0_60,plain,
    e0 != e2,
    inference(split_conjunct,[status(thm)],[ax5]) ).

cnf(c_0_61,plain,
    op(e0,e1) != op(e0,e2),
    inference(split_conjunct,[status(thm)],[ax4]) ).

cnf(c_0_62,plain,
    ( op(e0,e2) = e0
    | unit = e1
    | unit = e0 ),
    inference(spm,[status(thm)],[c_0_19,c_0_54]) ).

cnf(c_0_63,plain,
    ( op(e2,e1) = e0
    | op(e1,e1) = e0
    | op(e0,e1) = e0
    | op(e1,e1) != e2 ),
    inference(spm,[status(thm)],[c_0_55,c_0_56]) ).

cnf(c_0_64,plain,
    ( op(e1,e1) = e2
    | unit = e0
    | unit = e1 ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_60]) ).

cnf(c_0_65,plain,
    ( unit = e0
    | unit = e1
    | op(e0,e1) != e0 ),
    inference(spm,[status(thm)],[c_0_61,c_0_62]) ).

cnf(c_0_66,plain,
    ( op(e2,e1) = e1
    | unit = e1
    | unit = e0 ),
    inference(spm,[status(thm)],[c_0_14,c_0_54]) ).

cnf(c_0_67,plain,
    ( op(e2,e1) = e0
    | unit = e1
    | unit = e0 ),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_60]),c_0_65]) ).

cnf(c_0_68,plain,
    e0 != e1,
    inference(split_conjunct,[status(thm)],[ax5]) ).

fof(c_0_69,plain,
    ( e1 != op(e0,e0)
    | e2 != op(e3,e0) ),
    inference(fof_nnf,[status(thm)],[ax13]) ).

cnf(c_0_70,plain,
    ( op(e1,e1) = e2
    | op(e0,e0) = e1
    | op(e1,e1) = e0
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_71,plain,
    ( unit = e0
    | unit = e1 ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]) ).

cnf(c_0_72,plain,
    op(unit,e2) = e2,
    inference(split_conjunct,[status(thm)],[ax2]) ).

cnf(c_0_73,plain,
    ( e1 != op(e0,e0)
    | e2 != op(e3,e0) ),
    inference(split_conjunct,[status(thm)],[c_0_69]) ).

cnf(c_0_74,plain,
    ( op(e0,e0) = e2
    | op(e1,e0) = e2
    | op(e2,e0) = e2
    | op(e3,e0) = e2 ),
    inference(split_conjunct,[status(thm)],[ax3]) ).

cnf(c_0_75,plain,
    ( op(e1,e1) = e2
    | op(e1,e1) = e0
    | op(e0,e0) = e1 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_47])]) ).

cnf(c_0_76,plain,
    ( op(e1,e1) = e1
    | unit = e0 ),
    inference(spm,[status(thm)],[c_0_35,c_0_71]) ).

cnf(c_0_77,plain,
    op(e1,e0) != op(e1,e2),
    inference(split_conjunct,[status(thm)],[ax4]) ).

cnf(c_0_78,plain,
    ( op(e1,e2) = e2
    | unit = e0 ),
    inference(spm,[status(thm)],[c_0_72,c_0_71]) ).

cnf(c_0_79,plain,
    op(e2,e0) != op(e2,e1),
    inference(split_conjunct,[status(thm)],[ax4]) ).

cnf(c_0_80,plain,
    ( op(e2,e1) = e2
    | unit = e0 ),
    inference(spm,[status(thm)],[c_0_30,c_0_71]) ).

cnf(c_0_81,plain,
    ( op(e2,e0) = e2
    | op(e1,e0) = e2
    | op(e0,e0) = e2
    | op(e0,e0) != e1 ),
    inference(spm,[status(thm)],[c_0_73,c_0_74]) ).

cnf(c_0_82,plain,
    ( op(e0,e0) = e1
    | unit = e0 ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_59]),c_0_68]) ).

cnf(c_0_83,plain,
    ( unit = e0
    | op(e1,e0) != e2 ),
    inference(spm,[status(thm)],[c_0_77,c_0_78]) ).

cnf(c_0_84,plain,
    ( unit = e0
    | op(e2,e0) != e2 ),
    inference(spm,[status(thm)],[c_0_79,c_0_80]) ).

cnf(c_0_85,plain,
    ( op(e3,e3) = e2
    | op(e0,e0) = e1
    | op(e3,e3) = e0
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

fof(c_0_86,plain,
    ( e0 != op(e3,e3)
    | e2 != op(e1,e3) ),
    inference(fof_nnf,[status(thm)],[ax12]) ).

cnf(c_0_87,plain,
    ( op(e0,e0) = e2
    | op(e0,e0) = e1
    | op(e3,e3) = e0
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_88,plain,
    op(unit,e0) = e0,
    inference(split_conjunct,[status(thm)],[ax2]) ).

cnf(c_0_89,plain,
    unit = e0,
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_59]),c_0_83]),c_0_84]) ).

cnf(c_0_90,plain,
    op(e1,e3) != op(e3,e3),
    inference(split_conjunct,[status(thm)],[ax4]) ).

cnf(c_0_91,plain,
    ( op(e3,e3) = e2
    | op(e3,e3) = e0
    | op(e0,e0) = e1 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_47])]) ).

cnf(c_0_92,plain,
    ( e0 != op(e3,e3)
    | e2 != op(e1,e3) ),
    inference(split_conjunct,[status(thm)],[c_0_86]) ).

cnf(c_0_93,plain,
    op(unit,e3) = e3,
    inference(split_conjunct,[status(thm)],[ax2]) ).

cnf(c_0_94,plain,
    ( op(e3,e3) = e0
    | op(e0,e0) = e2
    | op(e0,e0) = e1 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_47])]) ).

cnf(c_0_95,plain,
    op(e0,e0) = e0,
    inference(rw,[status(thm)],[c_0_88,c_0_89]) ).

cnf(c_0_96,plain,
    ( op(e0,e0) = e1
    | op(e1,e3) != e2 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]) ).

cnf(c_0_97,plain,
    op(e2,e0) != op(e2,e3),
    inference(split_conjunct,[status(thm)],[ax4]) ).

cnf(c_0_98,plain,
    op(e2,e0) = e2,
    inference(rw,[status(thm)],[c_0_30,c_0_89]) ).

cnf(c_0_99,plain,
    ( op(e0,e3) = e2
    | op(e1,e3) = e2
    | op(e2,e3) = e2
    | op(e3,e3) = e2 ),
    inference(split_conjunct,[status(thm)],[ax3]) ).

cnf(c_0_100,plain,
    op(e0,e3) = e3,
    inference(rw,[status(thm)],[c_0_93,c_0_89]) ).

cnf(c_0_101,plain,
    op(e3,e3) = e0,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95]),c_0_95]),c_0_60]),c_0_68]) ).

cnf(c_0_102,plain,
    op(e1,e3) != e2,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_95]),c_0_68]) ).

cnf(c_0_103,plain,
    op(e2,e3) != e2,
    inference(rw,[status(thm)],[c_0_97,c_0_98]) ).

cnf(c_0_104,plain,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_100]),c_0_34]),c_0_101]),c_0_102]),c_0_103]),c_0_60]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : ALG045+1 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n029.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Mon Aug 28 04:29:26 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.20/0.70  % Version  : CSE_E---1.5
% 0.20/0.70  % Problem  : theBenchmark.p
% 0.20/0.70  % Proof found
% 0.20/0.70  % SZS status Theorem for theBenchmark.p
% 0.20/0.70  % SZS output start Proof
% See solution above
% 0.20/0.71  % Total time : 0.139000 s
% 0.20/0.71  % SZS output end Proof
% 0.20/0.71  % Total time : 0.143000 s
%------------------------------------------------------------------------------