TSTP Solution File: SET746+4 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : SET746+4 : TPTP v8.2.0. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n027.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 : Tue May 21 02:59:24 EDT 2024

% Result   : Theorem 0.21s 0.53s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   62 (  23 unt;   0 def)
%            Number of atoms       :  278 (  12 equ)
%            Maximal formula atoms :   55 (   4 avg)
%            Number of connectives :  347 ( 131   ~; 157   |;  49   &)
%                                         (   3 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-5 aty)
%            Number of functors    :   19 (  19 usr;   8 con; 0-7 aty)
%            Number of variables   :  189 (   0 sgn  72   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(thII37,conjecture,
    ! [X6,X10,X1,X2,X11,X15,X16,X17] :
      ( ( maps(X6,X1,X2)
        & maps(X10,X2,X11)
        & increasing(X6,X1,X15,X2,X16)
        & increasing(X10,X2,X16,X11,X17) )
     => increasing(compose_function(X10,X6,X1,X2,X11),X1,X15,X11,X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII37) ).

fof(increasing_function,axiom,
    ! [X6,X1,X15,X2,X16] :
      ( increasing(X6,X1,X15,X2,X16)
    <=> ! [X13,X7,X14,X8] :
          ( ( member(X13,X1)
            & member(X7,X2)
            & member(X14,X1)
            & member(X8,X2)
            & apply(X15,X13,X14)
            & apply(X6,X13,X7)
            & apply(X6,X14,X8) )
         => apply(X16,X7,X8) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',increasing_function) ).

fof(compose_function,axiom,
    ! [X10,X6,X1,X2,X11,X3,X12] :
      ( ( member(X3,X1)
        & member(X12,X11) )
     => ( apply(compose_function(X10,X6,X1,X2,X11),X3,X12)
      <=> ? [X5] :
            ( member(X5,X2)
            & apply(X6,X3,X5)
            & apply(X10,X5,X12) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',compose_function) ).

fof(maps,axiom,
    ! [X6,X1,X2] :
      ( maps(X6,X1,X2)
    <=> ( ! [X3] :
            ( member(X3,X1)
           => ? [X5] :
                ( member(X5,X2)
                & apply(X6,X3,X5) ) )
        & ! [X3,X7,X8] :
            ( ( member(X3,X1)
              & member(X7,X2)
              & member(X8,X2) )
           => ( ( apply(X6,X3,X7)
                & apply(X6,X3,X8) )
             => X7 = X8 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',maps) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X6,X10,X1,X2,X11,X15,X16,X17] :
        ( ( maps(X6,X1,X2)
          & maps(X10,X2,X11)
          & increasing(X6,X1,X15,X2,X16)
          & increasing(X10,X2,X16,X11,X17) )
       => increasing(compose_function(X10,X6,X1,X2,X11),X1,X15,X11,X17) ),
    inference(assume_negation,[status(cth)],[thII37]) ).

fof(c_0_5,plain,
    ! [X26,X27,X28,X29,X30,X31,X32,X33,X34,X35,X36,X37,X38,X39] :
      ( ( ~ increasing(X26,X27,X28,X29,X30)
        | ~ member(X31,X27)
        | ~ member(X32,X29)
        | ~ member(X33,X27)
        | ~ member(X34,X29)
        | ~ apply(X28,X31,X33)
        | ~ apply(X26,X31,X32)
        | ~ apply(X26,X33,X34)
        | apply(X30,X32,X34) )
      & ( member(esk9_5(X35,X36,X37,X38,X39),X36)
        | increasing(X35,X36,X37,X38,X39) )
      & ( member(esk10_5(X35,X36,X37,X38,X39),X38)
        | increasing(X35,X36,X37,X38,X39) )
      & ( member(esk11_5(X35,X36,X37,X38,X39),X36)
        | increasing(X35,X36,X37,X38,X39) )
      & ( member(esk12_5(X35,X36,X37,X38,X39),X38)
        | increasing(X35,X36,X37,X38,X39) )
      & ( apply(X37,esk9_5(X35,X36,X37,X38,X39),esk11_5(X35,X36,X37,X38,X39))
        | increasing(X35,X36,X37,X38,X39) )
      & ( apply(X35,esk9_5(X35,X36,X37,X38,X39),esk10_5(X35,X36,X37,X38,X39))
        | increasing(X35,X36,X37,X38,X39) )
      & ( apply(X35,esk11_5(X35,X36,X37,X38,X39),esk12_5(X35,X36,X37,X38,X39))
        | increasing(X35,X36,X37,X38,X39) )
      & ( ~ apply(X39,esk10_5(X35,X36,X37,X38,X39),esk12_5(X35,X36,X37,X38,X39))
        | increasing(X35,X36,X37,X38,X39) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[increasing_function])])])])])])]) ).

fof(c_0_6,negated_conjecture,
    ( maps(esk1_0,esk3_0,esk4_0)
    & maps(esk2_0,esk4_0,esk5_0)
    & increasing(esk1_0,esk3_0,esk6_0,esk4_0,esk7_0)
    & increasing(esk2_0,esk4_0,esk7_0,esk5_0,esk8_0)
    & ~ increasing(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0) ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).

cnf(c_0_7,plain,
    ( apply(X5,X7,X9)
    | ~ increasing(X1,X2,X3,X4,X5)
    | ~ member(X6,X2)
    | ~ member(X7,X4)
    | ~ member(X8,X2)
    | ~ member(X9,X4)
    | ~ apply(X3,X6,X8)
    | ~ apply(X1,X6,X7)
    | ~ apply(X1,X8,X9) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,negated_conjecture,
    increasing(esk1_0,esk3_0,esk6_0,esk4_0,esk7_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_9,negated_conjecture,
    ~ increasing(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    ( apply(X1,esk9_5(X2,X3,X1,X4,X5),esk11_5(X2,X3,X1,X4,X5))
    | increasing(X2,X3,X1,X4,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_11,plain,
    ( member(esk11_5(X1,X2,X3,X4,X5),X2)
    | increasing(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_12,plain,
    ( member(esk9_5(X1,X2,X3,X4,X5),X2)
    | increasing(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

fof(c_0_13,plain,
    ! [X44,X45,X46,X47,X48,X49,X50,X52] :
      ( ( member(esk13_7(X44,X45,X46,X47,X48,X49,X50),X47)
        | ~ apply(compose_function(X44,X45,X46,X47,X48),X49,X50)
        | ~ member(X49,X46)
        | ~ member(X50,X48) )
      & ( apply(X45,X49,esk13_7(X44,X45,X46,X47,X48,X49,X50))
        | ~ apply(compose_function(X44,X45,X46,X47,X48),X49,X50)
        | ~ member(X49,X46)
        | ~ member(X50,X48) )
      & ( apply(X44,esk13_7(X44,X45,X46,X47,X48,X49,X50),X50)
        | ~ apply(compose_function(X44,X45,X46,X47,X48),X49,X50)
        | ~ member(X49,X46)
        | ~ member(X50,X48) )
      & ( ~ member(X52,X47)
        | ~ apply(X45,X49,X52)
        | ~ apply(X44,X52,X50)
        | apply(compose_function(X44,X45,X46,X47,X48),X49,X50)
        | ~ member(X49,X46)
        | ~ member(X50,X48) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[compose_function])])])])])]) ).

cnf(c_0_14,plain,
    ( apply(X1,esk11_5(X1,X2,X3,X4,X5),esk12_5(X1,X2,X3,X4,X5))
    | increasing(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_15,plain,
    ( member(esk12_5(X1,X2,X3,X4,X5),X4)
    | increasing(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

fof(c_0_16,plain,
    ! [X53,X54,X55,X56,X58,X59,X60,X61,X62,X63,X65] :
      ( ( member(esk14_4(X53,X54,X55,X56),X55)
        | ~ member(X56,X54)
        | ~ maps(X53,X54,X55) )
      & ( apply(X53,X56,esk14_4(X53,X54,X55,X56))
        | ~ member(X56,X54)
        | ~ maps(X53,X54,X55) )
      & ( ~ member(X58,X54)
        | ~ member(X59,X55)
        | ~ member(X60,X55)
        | ~ apply(X53,X58,X59)
        | ~ apply(X53,X58,X60)
        | X59 = X60
        | ~ maps(X53,X54,X55) )
      & ( member(esk16_3(X61,X62,X63),X62)
        | member(esk15_3(X61,X62,X63),X62)
        | maps(X61,X62,X63) )
      & ( member(esk17_3(X61,X62,X63),X63)
        | member(esk15_3(X61,X62,X63),X62)
        | maps(X61,X62,X63) )
      & ( member(esk18_3(X61,X62,X63),X63)
        | member(esk15_3(X61,X62,X63),X62)
        | maps(X61,X62,X63) )
      & ( apply(X61,esk16_3(X61,X62,X63),esk17_3(X61,X62,X63))
        | member(esk15_3(X61,X62,X63),X62)
        | maps(X61,X62,X63) )
      & ( apply(X61,esk16_3(X61,X62,X63),esk18_3(X61,X62,X63))
        | member(esk15_3(X61,X62,X63),X62)
        | maps(X61,X62,X63) )
      & ( esk17_3(X61,X62,X63) != esk18_3(X61,X62,X63)
        | member(esk15_3(X61,X62,X63),X62)
        | maps(X61,X62,X63) )
      & ( member(esk16_3(X61,X62,X63),X62)
        | ~ member(X65,X63)
        | ~ apply(X61,esk15_3(X61,X62,X63),X65)
        | maps(X61,X62,X63) )
      & ( member(esk17_3(X61,X62,X63),X63)
        | ~ member(X65,X63)
        | ~ apply(X61,esk15_3(X61,X62,X63),X65)
        | maps(X61,X62,X63) )
      & ( member(esk18_3(X61,X62,X63),X63)
        | ~ member(X65,X63)
        | ~ apply(X61,esk15_3(X61,X62,X63),X65)
        | maps(X61,X62,X63) )
      & ( apply(X61,esk16_3(X61,X62,X63),esk17_3(X61,X62,X63))
        | ~ member(X65,X63)
        | ~ apply(X61,esk15_3(X61,X62,X63),X65)
        | maps(X61,X62,X63) )
      & ( apply(X61,esk16_3(X61,X62,X63),esk18_3(X61,X62,X63))
        | ~ member(X65,X63)
        | ~ apply(X61,esk15_3(X61,X62,X63),X65)
        | maps(X61,X62,X63) )
      & ( esk17_3(X61,X62,X63) != esk18_3(X61,X62,X63)
        | ~ member(X65,X63)
        | ~ apply(X61,esk15_3(X61,X62,X63),X65)
        | maps(X61,X62,X63) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[maps])])])])])])]) ).

cnf(c_0_17,negated_conjecture,
    ( apply(esk7_0,X1,X2)
    | ~ apply(esk6_0,X3,X4)
    | ~ apply(esk1_0,X4,X2)
    | ~ apply(esk1_0,X3,X1)
    | ~ member(X2,esk4_0)
    | ~ member(X4,esk3_0)
    | ~ member(X1,esk4_0)
    | ~ member(X3,esk3_0) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_18,negated_conjecture,
    apply(esk6_0,esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk11_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_19,negated_conjecture,
    member(esk11_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk3_0),
    inference(spm,[status(thm)],[c_0_9,c_0_11]) ).

cnf(c_0_20,negated_conjecture,
    member(esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk3_0),
    inference(spm,[status(thm)],[c_0_9,c_0_12]) ).

cnf(c_0_21,plain,
    ( apply(X1,X2,esk13_7(X3,X1,X4,X5,X6,X2,X7))
    | ~ apply(compose_function(X3,X1,X4,X5,X6),X2,X7)
    | ~ member(X2,X4)
    | ~ member(X7,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_22,negated_conjecture,
    apply(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk11_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk12_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)),
    inference(spm,[status(thm)],[c_0_9,c_0_14]) ).

cnf(c_0_23,negated_conjecture,
    member(esk12_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk5_0),
    inference(spm,[status(thm)],[c_0_9,c_0_15]) ).

cnf(c_0_24,plain,
    ( member(esk13_7(X1,X2,X3,X4,X5,X6,X7),X4)
    | ~ apply(compose_function(X1,X2,X3,X4,X5),X6,X7)
    | ~ member(X6,X3)
    | ~ member(X7,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_25,plain,
    ( X3 = X5
    | ~ member(X1,X2)
    | ~ member(X3,X4)
    | ~ member(X5,X4)
    | ~ apply(X6,X1,X3)
    | ~ apply(X6,X1,X5)
    | ~ maps(X6,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_26,negated_conjecture,
    maps(esk2_0,esk4_0,esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_27,plain,
    ( apply(X1,X2,esk14_4(X1,X3,X4,X2))
    | ~ member(X2,X3)
    | ~ maps(X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_28,plain,
    ( member(esk14_4(X1,X2,X3,X4),X3)
    | ~ member(X4,X2)
    | ~ maps(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_29,negated_conjecture,
    increasing(esk2_0,esk4_0,esk7_0,esk5_0,esk8_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_30,negated_conjecture,
    ( apply(esk7_0,X1,X2)
    | ~ apply(esk1_0,esk11_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),X2)
    | ~ apply(esk1_0,esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),X1)
    | ~ member(X2,esk4_0)
    | ~ member(X1,esk4_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]) ).

cnf(c_0_31,negated_conjecture,
    apply(esk1_0,esk11_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk13_7(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0,esk11_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk12_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_19])]) ).

cnf(c_0_32,negated_conjecture,
    member(esk13_7(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0,esk11_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk12_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)),esk4_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_22]),c_0_23]),c_0_19])]) ).

cnf(c_0_33,negated_conjecture,
    ( X1 = X2
    | ~ apply(esk2_0,X3,X2)
    | ~ apply(esk2_0,X3,X1)
    | ~ member(X2,esk5_0)
    | ~ member(X1,esk5_0)
    | ~ member(X3,esk4_0) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_34,negated_conjecture,
    ( apply(esk2_0,X1,esk14_4(esk2_0,esk4_0,esk5_0,X1))
    | ~ member(X1,esk4_0) ),
    inference(spm,[status(thm)],[c_0_27,c_0_26]) ).

cnf(c_0_35,negated_conjecture,
    ( member(esk14_4(esk2_0,esk4_0,esk5_0,X1),esk5_0)
    | ~ member(X1,esk4_0) ),
    inference(spm,[status(thm)],[c_0_28,c_0_26]) ).

cnf(c_0_36,plain,
    ( apply(X1,esk13_7(X1,X2,X3,X4,X5,X6,X7),X7)
    | ~ apply(compose_function(X1,X2,X3,X4,X5),X6,X7)
    | ~ member(X6,X3)
    | ~ member(X7,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_37,negated_conjecture,
    maps(esk1_0,esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_38,plain,
    ( apply(X1,esk9_5(X1,X2,X3,X4,X5),esk10_5(X1,X2,X3,X4,X5))
    | increasing(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_39,plain,
    ( member(esk10_5(X1,X2,X3,X4,X5),X4)
    | increasing(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_40,negated_conjecture,
    ( apply(esk8_0,X1,X2)
    | ~ apply(esk7_0,X3,X4)
    | ~ apply(esk2_0,X4,X2)
    | ~ apply(esk2_0,X3,X1)
    | ~ member(X2,esk5_0)
    | ~ member(X4,esk4_0)
    | ~ member(X1,esk5_0)
    | ~ member(X3,esk4_0) ),
    inference(spm,[status(thm)],[c_0_7,c_0_29]) ).

cnf(c_0_41,negated_conjecture,
    ( apply(esk7_0,X1,esk13_7(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0,esk11_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk12_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)))
    | ~ apply(esk1_0,esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),X1)
    | ~ member(X1,esk4_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).

cnf(c_0_42,negated_conjecture,
    ( X1 = esk14_4(esk2_0,esk4_0,esk5_0,X2)
    | ~ apply(esk2_0,X2,X1)
    | ~ member(X1,esk5_0)
    | ~ member(X2,esk4_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).

cnf(c_0_43,negated_conjecture,
    apply(esk2_0,esk13_7(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0,esk11_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk12_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)),esk12_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_22]),c_0_23]),c_0_19])]) ).

cnf(c_0_44,negated_conjecture,
    ( X1 = X2
    | ~ apply(esk1_0,X3,X2)
    | ~ apply(esk1_0,X3,X1)
    | ~ member(X2,esk4_0)
    | ~ member(X1,esk4_0)
    | ~ member(X3,esk3_0) ),
    inference(spm,[status(thm)],[c_0_25,c_0_37]) ).

cnf(c_0_45,negated_conjecture,
    ( apply(esk1_0,X1,esk14_4(esk1_0,esk3_0,esk4_0,X1))
    | ~ member(X1,esk3_0) ),
    inference(spm,[status(thm)],[c_0_27,c_0_37]) ).

cnf(c_0_46,negated_conjecture,
    ( member(esk14_4(esk1_0,esk3_0,esk4_0,X1),esk4_0)
    | ~ member(X1,esk3_0) ),
    inference(spm,[status(thm)],[c_0_28,c_0_37]) ).

cnf(c_0_47,negated_conjecture,
    apply(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk10_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)),
    inference(spm,[status(thm)],[c_0_9,c_0_38]) ).

cnf(c_0_48,negated_conjecture,
    member(esk10_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk5_0),
    inference(spm,[status(thm)],[c_0_9,c_0_39]) ).

cnf(c_0_49,negated_conjecture,
    ( apply(esk8_0,X1,X2)
    | ~ apply(esk2_0,esk13_7(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0,esk11_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk12_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)),X2)
    | ~ apply(esk1_0,esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),X3)
    | ~ apply(esk2_0,X3,X1)
    | ~ member(X2,esk5_0)
    | ~ member(X1,esk5_0)
    | ~ member(X3,esk4_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_32])]) ).

cnf(c_0_50,negated_conjecture,
    esk14_4(esk2_0,esk4_0,esk5_0,esk13_7(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0,esk11_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk12_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0))) = esk12_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_23]),c_0_32])]) ).

cnf(c_0_51,negated_conjecture,
    ( X1 = esk14_4(esk1_0,esk3_0,esk4_0,X2)
    | ~ apply(esk1_0,X2,X1)
    | ~ member(X1,esk4_0)
    | ~ member(X2,esk3_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).

cnf(c_0_52,negated_conjecture,
    apply(esk1_0,esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk13_7(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0,esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk10_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_47]),c_0_48]),c_0_20])]) ).

cnf(c_0_53,negated_conjecture,
    member(esk13_7(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0,esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk10_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)),esk4_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_47]),c_0_48]),c_0_20])]) ).

cnf(c_0_54,negated_conjecture,
    ( apply(esk8_0,X1,esk12_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0))
    | ~ apply(esk1_0,esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),X2)
    | ~ apply(esk2_0,X2,X1)
    | ~ member(X1,esk5_0)
    | ~ member(X2,esk4_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_34]),c_0_50]),c_0_50]),c_0_23]),c_0_32])]) ).

cnf(c_0_55,negated_conjecture,
    esk14_4(esk1_0,esk3_0,esk4_0,esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)) = esk13_7(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0,esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk10_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_20])]) ).

cnf(c_0_56,negated_conjecture,
    apply(esk2_0,esk13_7(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0,esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk10_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)),esk10_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_47]),c_0_48]),c_0_20])]) ).

cnf(c_0_57,plain,
    ( increasing(X2,X3,X4,X5,X1)
    | ~ apply(X1,esk10_5(X2,X3,X4,X5,X1),esk12_5(X2,X3,X4,X5,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_58,negated_conjecture,
    ( apply(esk8_0,X1,esk12_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0))
    | ~ apply(esk2_0,esk13_7(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0,esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk10_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)),X1)
    | ~ member(X1,esk5_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_45]),c_0_55]),c_0_55]),c_0_53]),c_0_20])]) ).

cnf(c_0_59,negated_conjecture,
    esk14_4(esk2_0,esk4_0,esk5_0,esk13_7(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0,esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk10_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0))) = esk10_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_56]),c_0_48]),c_0_53])]) ).

cnf(c_0_60,negated_conjecture,
    ~ apply(esk8_0,esk10_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk12_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)),
    inference(spm,[status(thm)],[c_0_9,c_0_57]) ).

cnf(c_0_61,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_34]),c_0_59]),c_0_59]),c_0_48]),c_0_53])]),c_0_60]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET746+4 : TPTP v8.2.0. Bugfixed v2.2.1.
% 0.13/0.13  % Command    : run_E %s %d THM
% 0.14/0.34  % Computer : n027.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Mon May 20 12:12:08 EDT 2024
% 0.14/0.34  % CPUTime    : 
% 0.21/0.47  Running first-order model finding
% 0.21/0.47  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
% 0.21/0.53  # Version: 3.1.0
% 0.21/0.53  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.21/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.53  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.21/0.53  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.53  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.53  # Starting sh5l with 300s (1) cores
% 0.21/0.53  # new_bool_1 with pid 28530 completed with status 0
% 0.21/0.53  # Result found by new_bool_1
% 0.21/0.53  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.21/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.53  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.21/0.53  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.53  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.53  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.53  # Search class: FGUSF-FFMS33-SFFFFFNN
% 0.21/0.53  # partial match(1): FGUSS-FFMS33-SFFFFFNN
% 0.21/0.53  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.53  # Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 150s (1) cores
% 0.21/0.53  # G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with pid 28534 completed with status 0
% 0.21/0.53  # Result found by G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI
% 0.21/0.53  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.21/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.53  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.21/0.53  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.53  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.53  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.53  # Search class: FGUSF-FFMS33-SFFFFFNN
% 0.21/0.53  # partial match(1): FGUSS-FFMS33-SFFFFFNN
% 0.21/0.53  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.53  # Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 150s (1) cores
% 0.21/0.53  # Preprocessing time       : 0.002 s
% 0.21/0.53  # Presaturation interreduction done
% 0.21/0.53  
% 0.21/0.53  # Proof found!
% 0.21/0.53  # SZS status Theorem
% 0.21/0.53  # SZS output start CNFRefutation
% See solution above
% 0.21/0.53  # Parsed axioms                        : 29
% 0.21/0.53  # Removed by relevancy pruning/SinE    : 25
% 0.21/0.53  # Initial clauses                      : 33
% 0.21/0.53  # Removed in clause preprocessing      : 0
% 0.21/0.53  # Initial clauses in saturation        : 33
% 0.21/0.53  # Processed clauses                    : 154
% 0.21/0.53  # ...of these trivial                  : 0
% 0.21/0.53  # ...subsumed                          : 2
% 0.21/0.53  # ...remaining for further processing  : 152
% 0.21/0.53  # Other redundant clauses eliminated   : 0
% 0.21/0.53  # Clauses deleted for lack of memory   : 0
% 0.21/0.53  # Backward-subsumed                    : 0
% 0.21/0.53  # Backward-rewritten                   : 0
% 0.21/0.53  # Generated clauses                    : 825
% 0.21/0.53  # ...of the previous two non-redundant : 763
% 0.21/0.53  # ...aggressively subsumed             : 0
% 0.21/0.53  # Contextual simplify-reflections      : 2
% 0.21/0.53  # Paramodulations                      : 825
% 0.21/0.53  # Factorizations                       : 0
% 0.21/0.53  # NegExts                              : 0
% 0.21/0.53  # Equation resolutions                 : 0
% 0.21/0.53  # Disequality decompositions           : 0
% 0.21/0.53  # Total rewrite steps                  : 193
% 0.21/0.53  # ...of those cached                   : 179
% 0.21/0.53  # Propositional unsat checks           : 0
% 0.21/0.53  #    Propositional check models        : 0
% 0.21/0.53  #    Propositional check unsatisfiable : 0
% 0.21/0.53  #    Propositional clauses             : 0
% 0.21/0.53  #    Propositional clauses after purity: 0
% 0.21/0.53  #    Propositional unsat core size     : 0
% 0.21/0.53  #    Propositional preprocessing time  : 0.000
% 0.21/0.53  #    Propositional encoding time       : 0.000
% 0.21/0.53  #    Propositional solver time         : 0.000
% 0.21/0.53  #    Success case prop preproc time    : 0.000
% 0.21/0.53  #    Success case prop encoding time   : 0.000
% 0.21/0.53  #    Success case prop solver time     : 0.000
% 0.21/0.53  # Current number of processed clauses  : 119
% 0.21/0.53  #    Positive orientable unit clauses  : 21
% 0.21/0.53  #    Positive unorientable unit clauses: 0
% 0.21/0.53  #    Negative unit clauses             : 2
% 0.21/0.53  #    Non-unit-clauses                  : 96
% 0.21/0.53  # Current number of unprocessed clauses: 668
% 0.21/0.53  # ...number of literals in the above   : 5334
% 0.21/0.53  # Current number of archived formulas  : 0
% 0.21/0.53  # Current number of archived clauses   : 33
% 0.21/0.53  # Clause-clause subsumption calls (NU) : 1984
% 0.21/0.53  # Rec. Clause-clause subsumption calls : 218
% 0.21/0.53  # Non-unit clause-clause subsumptions  : 4
% 0.21/0.53  # Unit Clause-clause subsumption calls : 0
% 0.21/0.53  # Rewrite failures with RHS unbound    : 0
% 0.21/0.53  # BW rewrite match attempts            : 13
% 0.21/0.53  # BW rewrite match successes           : 0
% 0.21/0.53  # Condensation attempts                : 0
% 0.21/0.53  # Condensation successes               : 0
% 0.21/0.53  # Termbank termtop insertions          : 44379
% 0.21/0.53  # Search garbage collected termcells   : 991
% 0.21/0.53  
% 0.21/0.53  # -------------------------------------------------
% 0.21/0.53  # User time                : 0.039 s
% 0.21/0.53  # System time              : 0.005 s
% 0.21/0.53  # Total time               : 0.043 s
% 0.21/0.53  # Maximum resident set size: 1900 pages
% 0.21/0.53  
% 0.21/0.53  # -------------------------------------------------
% 0.21/0.53  # User time                : 0.040 s
% 0.21/0.53  # System time              : 0.007 s
% 0.21/0.53  # Total time               : 0.047 s
% 0.21/0.53  # Maximum resident set size: 1764 pages
% 0.21/0.53  % E---3.1 exiting
%------------------------------------------------------------------------------