TSTP Solution File: SWW319+1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SWW319+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n028.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 : Sat May  4 10:00:45 EDT 2024

% Result   : Theorem 5.22s 3.59s
% Output   : CNFRefutation 5.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   44 (  16 unt;   0 def)
%            Number of atoms       :   97 (  28 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :   89 (  36   ~;  29   |;   9   &)
%                                         (   4 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   16 (  16 usr;   5 con; 0-3 aty)
%            Number of variables   :  121 (   8 sgn  71   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_ex__in__conv,axiom,
    ! [X10,X5] :
      ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X5),X3),X10))
    <=> X10 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/tmp/tmp.xBbPpquvr6/E---3.1_16150.p',fact_ex__in__conv) ).

fof(fact_disjoint__iff__not__equal,axiom,
    ! [X39,X10,X5] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X10),X39) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X10))
         => ! [X104] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X104),X39))
             => X3 != X104 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.xBbPpquvr6/E---3.1_16150.p',fact_disjoint__iff__not__equal) ).

fof(fact_Int__insert__right,axiom,
    ! [X39,X10,X6,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X10))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X10),hAPP(hAPP(c_Set_Oinsert(X5),X6),X39)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X10),X39)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X10))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X10),hAPP(hAPP(c_Set_Oinsert(X5),X6),X39)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X10),X39) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.xBbPpquvr6/E---3.1_16150.p',fact_Int__insert__right) ).

fof(fact_asm,axiom,
    ! [X4,X7,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)),X7),X4))
     => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X7) ),
    file('/export/starexec/sandbox2/tmp/tmp.xBbPpquvr6/E---3.1_16150.p',fact_asm) ).

fof(fact_Int__lower1,axiom,
    ! [X39,X10,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X10),X39)),X10)),
    file('/export/starexec/sandbox2/tmp/tmp.xBbPpquvr6/E---3.1_16150.p',fact_Int__lower1) ).

fof(fact_cut,axiom,
    ! [X4,X7,X8,X5] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X8,X7)
     => ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X8)
       => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X7) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.xBbPpquvr6/E---3.1_16150.p',fact_cut) ).

fof(fact_subset__insertI,axiom,
    ! [X6,X39,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X39),hAPP(hAPP(c_Set_Oinsert(X5),X6),X39))),
    file('/export/starexec/sandbox2/tmp/tmp.xBbPpquvr6/E---3.1_16150.p',fact_subset__insertI) ).

fof(conj_1,conjecture,
    ( c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
    & c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,v_ts) ),
    file('/export/starexec/sandbox2/tmp/tmp.xBbPpquvr6/E---3.1_16150.p',conj_1) ).

fof(conj_0,hypothesis,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts)),
    file('/export/starexec/sandbox2/tmp/tmp.xBbPpquvr6/E---3.1_16150.p',conj_0) ).

fof(fact_insertI1,axiom,
    ! [X39,X6,X5] : hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X6),X39))),
    file('/export/starexec/sandbox2/tmp/tmp.xBbPpquvr6/E---3.1_16150.p',fact_insertI1) ).

fof(c_0_10,plain,
    ! [X10,X5] :
      ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X5),X3),X10))
    <=> X10 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    inference(fof_simplification,[status(thm)],[fact_ex__in__conv]) ).

fof(c_0_11,plain,
    ! [X39,X10,X5] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X10),X39) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X10))
         => ! [X104] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X104),X39))
             => X3 != X104 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_disjoint__iff__not__equal]) ).

fof(c_0_12,plain,
    ! [X39,X10,X6,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X10))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X10),hAPP(hAPP(c_Set_Oinsert(X5),X6),X39)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X10),X39)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X10))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X10),hAPP(hAPP(c_Set_Oinsert(X5),X6),X39)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X10),X39) ) ),
    inference(fof_simplification,[status(thm)],[fact_Int__insert__right]) ).

fof(c_0_13,plain,
    ! [X562,X563,X564,X565,X566] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X563),X564),X562))
        | X562 != c_Orderings_Obot__class_Obot(tc_fun(X563,tc_HOL_Obool)) )
      & ( X565 = c_Orderings_Obot__class_Obot(tc_fun(X566,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(X566),esk18_2(X565,X566)),X565)) ) ),
    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)],[c_0_10])])])])])]) ).

fof(c_0_14,plain,
    ! [X1413,X1414,X1415,X1416,X1417,X1418,X1419,X1420] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1415,tc_HOL_Obool)),X1414),X1413) != c_Orderings_Obot__class_Obot(tc_fun(X1415,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(X1415),X1416),X1414))
        | ~ hBOOL(hAPP(hAPP(c_member(X1415),X1417),X1413))
        | X1416 != X1417 )
      & ( hBOOL(hAPP(hAPP(c_member(X1420),esk34_3(X1418,X1419,X1420)),X1419))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1420,tc_HOL_Obool)),X1419),X1418) = c_Orderings_Obot__class_Obot(tc_fun(X1420,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(X1420),esk35_3(X1418,X1419,X1420)),X1418))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1420,tc_HOL_Obool)),X1419),X1418) = c_Orderings_Obot__class_Obot(tc_fun(X1420,tc_HOL_Obool)) )
      & ( esk34_3(X1418,X1419,X1420) = esk35_3(X1418,X1419,X1420)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1420,tc_HOL_Obool)),X1419),X1418) = c_Orderings_Obot__class_Obot(tc_fun(X1420,tc_HOL_Obool)) ) ),
    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)],[c_0_11])])])])])])]) ).

fof(c_0_15,plain,
    ! [X344,X345,X346] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X346),tc_HOL_Obool)),X345),X344))
      | c_Hoare__Mirabelle_Ohoare__derivs(X346,X344,X345) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_asm])])]) ).

fof(c_0_16,plain,
    ! [X1481,X1482,X1483] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1483,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1483,tc_HOL_Obool)),X1482),X1481)),X1482)),
    inference(variable_rename,[status(thm)],[fact_Int__lower1]) ).

fof(c_0_17,plain,
    ! [X523,X524,X525,X526] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X526),X525),X524))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X526,tc_HOL_Obool)),X524),hAPP(hAPP(c_Set_Oinsert(X526),X525),X523)) = hAPP(hAPP(c_Set_Oinsert(X526),X525),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X526,tc_HOL_Obool)),X524),X523)) )
      & ( hBOOL(hAPP(hAPP(c_member(X526),X525),X524))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X526,tc_HOL_Obool)),X524),hAPP(hAPP(c_Set_Oinsert(X526),X525),X523)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X526,tc_HOL_Obool)),X524),X523) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).

cnf(c_0_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | X3 != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_19,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk35_3(X2,X3,X1)),X2))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_20,plain,
    ! [X309,X310,X311,X312] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X312,X311,X310)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(X312,X309,X311)
      | c_Hoare__Mirabelle_Ohoare__derivs(X312,X309,X310) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_cut])])]) ).

fof(c_0_21,plain,
    ! [X426,X427,X428] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X428,tc_HOL_Obool)),X427),hAPP(hAPP(c_Set_Oinsert(X428),X426),X427))),
    inference(variable_rename,[status(thm)],[fact_subset__insertI]) ).

cnf(c_0_22,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_23,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X2)),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_24,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_25,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X3 != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

fof(c_0_26,negated_conjecture,
    ~ ( c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
      & c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,v_ts) ),
    inference(assume_negation,[status(cth)],[conj_1]) ).

cnf(c_0_27,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_28,hypothesis,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts)),
    inference(split_conjunct,[status(thm)],[conj_0]) ).

cnf(c_0_29,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_30,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X2),X3)),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_31,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))
    | X4 != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

fof(c_0_32,negated_conjecture,
    ( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,v_ts) ),
    inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])]) ).

cnf(c_0_33,hypothesis,
    ( c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,X1)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts),X1) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_34,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X2),X3),X3),
    inference(spm,[status(thm)],[c_0_22,c_0_29]) ).

cnf(c_0_35,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
    | X4 != c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),X3),X2)) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_36,negated_conjecture,
    ( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,v_ts) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_37,hypothesis,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,v_ts),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_38,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),X3),X2)) ),
    inference(er,[status(thm)],[c_0_35]) ).

fof(c_0_39,plain,
    ! [X408,X409,X410] : hBOOL(hAPP(hAPP(c_member(X410),X409),hAPP(hAPP(c_Set_Oinsert(X410),X409),X408))),
    inference(variable_rename,[status(thm)],[fact_insertI1]) ).

cnf(c_0_40,negated_conjecture,
    ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]) ).

cnf(c_0_41,hypothesis,
    ( c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts))) ),
    inference(spm,[status(thm)],[c_0_33,c_0_38]) ).

cnf(c_0_42,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_43,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 1.16/1.21  % Problem    : SWW319+1 : TPTP v8.1.2. Released v5.2.0.
% 1.16/1.22  % Command    : run_E %s %d THM
% 1.23/1.42  % Computer : n028.cluster.edu
% 1.23/1.42  % Model    : x86_64 x86_64
% 1.23/1.42  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 1.23/1.42  % Memory   : 8042.1875MB
% 1.23/1.42  % OS       : Linux 3.10.0-693.el7.x86_64
% 1.23/1.42  % CPULimit   : 300
% 1.23/1.42  % WCLimit    : 300
% 1.23/1.42  % DateTime   : Fri May  3 13:26:35 EDT 2024
% 1.23/1.42  % CPUTime    : 
% 2.34/2.58  Running first-order theorem proving
% 2.34/2.58  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.xBbPpquvr6/E---3.1_16150.p
% 5.22/3.59  # Version: 3.1.0
% 5.22/3.59  # Preprocessing class: FMLMSMSMSSSNFFN.
% 5.22/3.59  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.22/3.59  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 5.22/3.59  # Starting new_bool_3 with 300s (1) cores
% 5.22/3.59  # Starting new_bool_1 with 300s (1) cores
% 5.22/3.59  # Starting sh5l with 300s (1) cores
% 5.22/3.59  # new_bool_1 with pid 16231 completed with status 0
% 5.22/3.59  # Result found by new_bool_1
% 5.22/3.59  # Preprocessing class: FMLMSMSMSSSNFFN.
% 5.22/3.59  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.22/3.59  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 5.22/3.59  # Starting new_bool_3 with 300s (1) cores
% 5.22/3.59  # Starting new_bool_1 with 300s (1) cores
% 5.22/3.59  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 5.22/3.59  # Search class: FGHSM-FSLM32-DFFFFFNN
% 5.22/3.59  # Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 5.22/3.59  # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 23s (1) cores
% 5.22/3.59  # G-E--_301_C18_F1_URBAN_S5PRR_S0Y with pid 16234 completed with status 0
% 5.22/3.59  # Result found by G-E--_301_C18_F1_URBAN_S5PRR_S0Y
% 5.22/3.59  # Preprocessing class: FMLMSMSMSSSNFFN.
% 5.22/3.59  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.22/3.59  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 5.22/3.59  # Starting new_bool_3 with 300s (1) cores
% 5.22/3.59  # Starting new_bool_1 with 300s (1) cores
% 5.22/3.59  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 5.22/3.59  # Search class: FGHSM-FSLM32-DFFFFFNN
% 5.22/3.59  # Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 5.22/3.59  # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 23s (1) cores
% 5.22/3.59  # Preprocessing time       : 0.028 s
% 5.22/3.59  
% 5.22/3.59  # Proof found!
% 5.22/3.59  # SZS status Theorem
% 5.22/3.59  # SZS output start CNFRefutation
% See solution above
% 5.22/3.59  # Parsed axioms                        : 5227
% 5.22/3.59  # Removed by relevancy pruning/SinE    : 4597
% 5.22/3.59  # Initial clauses                      : 924
% 5.22/3.59  # Removed in clause preprocessing      : 39
% 5.22/3.59  # Initial clauses in saturation        : 885
% 5.22/3.59  # Processed clauses                    : 2073
% 5.22/3.59  # ...of these trivial                  : 137
% 5.22/3.59  # ...subsumed                          : 906
% 5.22/3.59  # ...remaining for further processing  : 1030
% 5.22/3.59  # Other redundant clauses eliminated   : 185
% 5.22/3.59  # Clauses deleted for lack of memory   : 0
% 5.22/3.59  # Backward-subsumed                    : 36
% 5.22/3.59  # Backward-rewritten                   : 71
% 5.22/3.59  # Generated clauses                    : 23310
% 5.22/3.59  # ...of the previous two non-redundant : 20609
% 5.22/3.59  # ...aggressively subsumed             : 0
% 5.22/3.59  # Contextual simplify-reflections      : 19
% 5.22/3.59  # Paramodulations                      : 23038
% 5.22/3.59  # Factorizations                       : 10
% 5.22/3.59  # NegExts                              : 0
% 5.22/3.59  # Equation resolutions                 : 263
% 5.22/3.59  # Disequality decompositions           : 0
% 5.22/3.59  # Total rewrite steps                  : 7965
% 5.22/3.59  # ...of those cached                   : 6237
% 5.22/3.59  # Propositional unsat checks           : 0
% 5.22/3.59  #    Propositional check models        : 0
% 5.22/3.59  #    Propositional check unsatisfiable : 0
% 5.22/3.59  #    Propositional clauses             : 0
% 5.22/3.59  #    Propositional clauses after purity: 0
% 5.22/3.59  #    Propositional unsat core size     : 0
% 5.22/3.59  #    Propositional preprocessing time  : 0.000
% 5.22/3.59  #    Propositional encoding time       : 0.000
% 5.22/3.59  #    Propositional solver time         : 0.000
% 5.22/3.59  #    Success case prop preproc time    : 0.000
% 5.22/3.59  #    Success case prop encoding time   : 0.000
% 5.22/3.59  #    Success case prop solver time     : 0.000
% 5.22/3.59  # Current number of processed clauses  : 896
% 5.22/3.59  #    Positive orientable unit clauses  : 204
% 5.22/3.59  #    Positive unorientable unit clauses: 17
% 5.22/3.59  #    Negative unit clauses             : 46
% 5.22/3.59  #    Non-unit-clauses                  : 629
% 5.22/3.59  # Current number of unprocessed clauses: 19257
% 5.22/3.59  # ...number of literals in the above   : 56405
% 5.22/3.59  # Current number of archived formulas  : 0
% 5.22/3.59  # Current number of archived clauses   : 107
% 5.22/3.59  # Clause-clause subsumption calls (NU) : 35210
% 5.22/3.59  # Rec. Clause-clause subsumption calls : 28678
% 5.22/3.59  # Non-unit clause-clause subsumptions  : 625
% 5.22/3.59  # Unit Clause-clause subsumption calls : 3786
% 5.22/3.59  # Rewrite failures with RHS unbound    : 36
% 5.22/3.59  # BW rewrite match attempts            : 3375
% 5.22/3.59  # BW rewrite match successes           : 112
% 5.22/3.59  # Condensation attempts                : 0
% 5.22/3.59  # Condensation successes               : 0
% 5.22/3.59  # Termbank termtop insertions          : 882006
% 5.22/3.59  # Search garbage collected termcells   : 55247
% 5.22/3.59  
% 5.22/3.59  # -------------------------------------------------
% 5.22/3.59  # User time                : 0.705 s
% 5.22/3.59  # System time              : 0.030 s
% 5.22/3.59  # Total time               : 0.734 s
% 5.22/3.59  # Maximum resident set size: 11500 pages
% 5.22/3.59  
% 5.22/3.59  # -------------------------------------------------
% 5.22/3.59  # User time                : 0.952 s
% 5.22/3.59  # System time              : 0.040 s
% 5.22/3.59  # Total time               : 0.992 s
% 5.22/3.59  # Maximum resident set size: 9496 pages
% 5.22/3.59  % E---3.1 exiting
% 5.22/3.59  % E exiting
%------------------------------------------------------------------------------