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E---3.5.1.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : E---3.5.1
% Problem  : LAT304+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 24 01:04:48 PM UTC 2026

% Result   : Theorem 61.89s 11.31s
% Output   : CNFRefutation 61.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   63 (  10 unt;   0 def)
%            Number of atoms       :  266 (  11 equ)
%            Maximal formula atoms :   36 (   4 avg)
%            Number of connectives :  320 ( 117   ~; 106   |;  71   &)
%                                         (   5 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   19 (  17 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-1 aty)
%            Number of variables   :   55 (   0 sgn  38   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(fc1_struct_0,axiom,
    ! [X1] :
      ( ( l1_struct_0(X1)
        & ~ v3_struct_0(X1) )
     => ~ v1_xboole_0(u1_struct_0(X1)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+200.ax',fc1_struct_0) ).

fof(t28_filter_2,conjecture,
    ! [X1] :
      ( ( l3_lattices(X1)
        & v10_lattices(X1)
        & ~ v3_struct_0(X1) )
     => m2_filter_2(u1_struct_0(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_filter_2) ).

fof(dt_l1_lattices,axiom,
    ! [X1] :
      ( l1_lattices(X1)
     => l1_struct_0(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+205.ax',dt_l1_lattices) ).

fof(t18_lattice2,axiom,
    ! [X1] :
      ( ( l3_lattices(X1)
        & ~ v3_struct_0(X1) )
     => ( u1_lattices(X1) = u2_lattices(k1_lattice2(X1))
        & u2_lattices(X1) = u1_lattices(k1_lattice2(X1))
        & u1_struct_0(X1) = u1_struct_0(k1_lattice2(X1)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+253.ax',t18_lattice2) ).

fof(dt_l3_lattices,axiom,
    ! [X1] :
      ( l3_lattices(X1)
     => ( l2_lattices(X1)
        & l1_lattices(X1) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+205.ax',dt_l3_lattices) ).

fof(d1_struct_0,axiom,
    ! [X1] :
      ( l1_struct_0(X1)
     => ( v3_struct_0(X1)
      <=> v1_xboole_0(u1_struct_0(X1)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+200.ax',d1_struct_0) ).

fof(fc1_lattice2,axiom,
    ! [X1] :
      ( ( l3_lattices(X1)
        & ~ v3_struct_0(X1) )
     => ( v3_lattices(k1_lattice2(X1))
        & ~ v3_struct_0(k1_lattice2(X1)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+253.ax',fc1_lattice2) ).

fof(dt_k1_lattice2,axiom,
    ! [X1] :
      ( l3_lattices(X1)
     => ( l3_lattices(k1_lattice2(X1))
        & v3_lattices(k1_lattice2(X1)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+253.ax',dt_k1_lattice2) ).

fof(fc6_lattice2,axiom,
    ! [X1] :
      ( ( l3_lattices(X1)
        & v10_lattices(X1)
        & ~ v3_struct_0(X1) )
     => ( v10_lattices(k1_lattice2(X1))
        & v9_lattices(k1_lattice2(X1))
        & v8_lattices(k1_lattice2(X1))
        & v7_lattices(k1_lattice2(X1))
        & v6_lattices(k1_lattice2(X1))
        & v5_lattices(k1_lattice2(X1))
        & v4_lattices(k1_lattice2(X1))
        & v3_lattices(k1_lattice2(X1))
        & ~ v3_struct_0(k1_lattice2(X1)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+253.ax',fc6_lattice2) ).

fof(t15_filter_0,axiom,
    ! [X1] :
      ( ( l3_lattices(X1)
        & v10_lattices(X1)
        & ~ v3_struct_0(X1) )
     => m1_filter_0(u1_struct_0(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+242.ax',t15_filter_0) ).

fof(redefinition_m1_filter_2,axiom,
    ! [X1] :
      ( ( l3_lattices(X1)
        & v10_lattices(X1)
        & ~ v3_struct_0(X1) )
     => ! [X2] :
          ( m1_filter_2(X2,X1)
        <=> m1_filter_0(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m1_filter_2) ).

fof(t21_filter_2,axiom,
    ! [X1] :
      ( ( l3_lattices(X1)
        & v10_lattices(X1)
        & ~ v3_struct_0(X1) )
     => ! [X2] :
          ( m2_filter_2(X2,X1)
        <=> m1_filter_2(X2,k1_lattice2(X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_filter_2) ).

fof(c_0_12,plain,
    ! [X1] :
      ( ( l1_struct_0(X1)
        & ~ v3_struct_0(X1) )
     => ~ v1_xboole_0(u1_struct_0(X1)) ),
    inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).

fof(c_0_13,negated_conjecture,
    ~ ! [X1] :
        ( ( l3_lattices(X1)
          & v10_lattices(X1)
          & ~ v3_struct_0(X1) )
       => m2_filter_2(u1_struct_0(X1),X1) ),
    inference(assume_negation,[status(cth)],[t28_filter_2]) ).

fof(c_0_14,plain,
    ! [X5791] :
      ( ~ v1_xboole_0(u1_struct_0(X5791))
      | ~ l1_struct_0(X5791)
      | v3_struct_0(X5791) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).

fof(c_0_15,plain,
    ! [X3895] :
      ( l1_struct_0(X3895)
      | ~ l1_lattices(X3895) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_lattices])])]) ).

fof(c_0_16,plain,
    ! [X1] :
      ( ( l3_lattices(X1)
        & ~ v3_struct_0(X1) )
     => ( u1_lattices(X1) = u2_lattices(k1_lattice2(X1))
        & u2_lattices(X1) = u1_lattices(k1_lattice2(X1))
        & u1_struct_0(X1) = u1_struct_0(k1_lattice2(X1)) ) ),
    inference(fof_simplification,[status(thm)],[t18_lattice2]) ).

fof(c_0_17,negated_conjecture,
    ~ ! [X1] :
        ( ( l3_lattices(X1)
          & v10_lattices(X1)
          & ~ v3_struct_0(X1) )
       => m2_filter_2(u1_struct_0(X1),X1) ),
    inference(fof_simplification,[status(thm)],[c_0_13]) ).

cnf(c_0_18,plain,
    ( ~ v1_xboole_0(u1_struct_0(X1))
    | ~ l1_struct_0(X1)
    | v3_struct_0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_19,plain,
    ( ~ l1_lattices(X1)
    | l1_struct_0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_20,plain,
    ! [X3386] :
      ( ( ~ l3_lattices(X3386)
        | l2_lattices(X3386) )
      & ( ~ l3_lattices(X3386)
        | l1_lattices(X3386) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])])]) ).

fof(c_0_21,plain,
    ! [X849] :
      ( ( ~ l3_lattices(X849)
        | v3_struct_0(X849)
        | u1_lattices(X849) = u2_lattices(k1_lattice2(X849)) )
      & ( ~ l3_lattices(X849)
        | v3_struct_0(X849)
        | u2_lattices(X849) = u1_lattices(k1_lattice2(X849)) )
      & ( ~ l3_lattices(X849)
        | v3_struct_0(X849)
        | u1_struct_0(X849) = u1_struct_0(k1_lattice2(X849)) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).

fof(c_0_22,negated_conjecture,
    ( ~ m2_filter_2(u1_struct_0(esk1_0),esk1_0)
    & l3_lattices(esk1_0)
    & v10_lattices(esk1_0)
    & ~ v3_struct_0(esk1_0) ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])]) ).

cnf(c_0_23,plain,
    ( ~ v1_xboole_0(u1_struct_0(X1))
    | ~ l1_lattices(X1)
    | v3_struct_0(X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_24,plain,
    ( ~ l3_lattices(X1)
    | l1_lattices(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_25,plain,
    ( ~ l3_lattices(X1)
    | v3_struct_0(X1)
    | u1_struct_0(X1) = u1_struct_0(k1_lattice2(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_26,negated_conjecture,
    l3_lattices(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_27,negated_conjecture,
    ~ v3_struct_0(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

fof(c_0_28,plain,
    ! [X5794] :
      ( ( ~ l1_struct_0(X5794)
        | v3_struct_0(X5794)
        | ~ v1_xboole_0(u1_struct_0(X5794)) )
      & ( ~ l1_struct_0(X5794)
        | v1_xboole_0(u1_struct_0(X5794))
        | ~ v3_struct_0(X5794) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_struct_0])])])]) ).

fof(c_0_29,plain,
    ! [X1] :
      ( ( l3_lattices(X1)
        & ~ v3_struct_0(X1) )
     => ( v3_lattices(k1_lattice2(X1))
        & ~ v3_struct_0(k1_lattice2(X1)) ) ),
    inference(fof_simplification,[status(thm)],[fc1_lattice2]) ).

cnf(c_0_30,plain,
    ( ~ v1_xboole_0(u1_struct_0(X1))
    | ~ l3_lattices(X1)
    | v3_struct_0(X1) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_31,negated_conjecture,
    u1_struct_0(k1_lattice2(esk1_0)) = u1_struct_0(esk1_0),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).

fof(c_0_32,plain,
    ! [X916] :
      ( ( ~ l3_lattices(X916)
        | l3_lattices(k1_lattice2(X916)) )
      & ( ~ l3_lattices(X916)
        | v3_lattices(k1_lattice2(X916)) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_lattice2])])])]) ).

cnf(c_0_33,plain,
    ( ~ l1_struct_0(X1)
    | ~ v3_struct_0(X1)
    | v1_xboole_0(u1_struct_0(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

fof(c_0_34,plain,
    ! [X893] :
      ( ( ~ l3_lattices(X893)
        | v3_struct_0(X893)
        | v3_lattices(k1_lattice2(X893)) )
      & ( ~ l3_lattices(X893)
        | v3_struct_0(X893)
        | ~ v3_struct_0(k1_lattice2(X893)) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])])]) ).

cnf(c_0_35,negated_conjecture,
    ( ~ v1_xboole_0(u1_struct_0(esk1_0))
    | ~ l3_lattices(k1_lattice2(esk1_0))
    | v3_struct_0(k1_lattice2(esk1_0)) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_36,plain,
    ( ~ l3_lattices(X1)
    | l3_lattices(k1_lattice2(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

fof(c_0_37,plain,
    ! [X1] :
      ( ( l3_lattices(X1)
        & v10_lattices(X1)
        & ~ v3_struct_0(X1) )
     => ( v10_lattices(k1_lattice2(X1))
        & v9_lattices(k1_lattice2(X1))
        & v8_lattices(k1_lattice2(X1))
        & v7_lattices(k1_lattice2(X1))
        & v6_lattices(k1_lattice2(X1))
        & v5_lattices(k1_lattice2(X1))
        & v4_lattices(k1_lattice2(X1))
        & v3_lattices(k1_lattice2(X1))
        & ~ v3_struct_0(k1_lattice2(X1)) ) ),
    inference(fof_simplification,[status(thm)],[fc6_lattice2]) ).

cnf(c_0_38,plain,
    ( ~ v3_struct_0(X1)
    | ~ l1_lattices(X1)
    | v1_xboole_0(u1_struct_0(X1)) ),
    inference(spm,[status(thm)],[c_0_33,c_0_19]) ).

cnf(c_0_39,plain,
    ( ~ l3_lattices(X1)
    | ~ v3_struct_0(k1_lattice2(X1))
    | v3_struct_0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_40,negated_conjecture,
    ( ~ v1_xboole_0(u1_struct_0(esk1_0))
    | v3_struct_0(k1_lattice2(esk1_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_26])]) ).

fof(c_0_41,plain,
    ! [X1] :
      ( ( l3_lattices(X1)
        & v10_lattices(X1)
        & ~ v3_struct_0(X1) )
     => m1_filter_0(u1_struct_0(X1),X1) ),
    inference(fof_simplification,[status(thm)],[t15_filter_0]) ).

fof(c_0_42,plain,
    ! [X894] :
      ( ( ~ l3_lattices(X894)
        | ~ v10_lattices(X894)
        | v3_struct_0(X894)
        | v10_lattices(k1_lattice2(X894)) )
      & ( ~ l3_lattices(X894)
        | ~ v10_lattices(X894)
        | v3_struct_0(X894)
        | v9_lattices(k1_lattice2(X894)) )
      & ( ~ l3_lattices(X894)
        | ~ v10_lattices(X894)
        | v3_struct_0(X894)
        | v8_lattices(k1_lattice2(X894)) )
      & ( ~ l3_lattices(X894)
        | ~ v10_lattices(X894)
        | v3_struct_0(X894)
        | v7_lattices(k1_lattice2(X894)) )
      & ( ~ l3_lattices(X894)
        | ~ v10_lattices(X894)
        | v3_struct_0(X894)
        | v6_lattices(k1_lattice2(X894)) )
      & ( ~ l3_lattices(X894)
        | ~ v10_lattices(X894)
        | v3_struct_0(X894)
        | v5_lattices(k1_lattice2(X894)) )
      & ( ~ l3_lattices(X894)
        | ~ v10_lattices(X894)
        | v3_struct_0(X894)
        | v4_lattices(k1_lattice2(X894)) )
      & ( ~ l3_lattices(X894)
        | ~ v10_lattices(X894)
        | v3_struct_0(X894)
        | v3_lattices(k1_lattice2(X894)) )
      & ( ~ l3_lattices(X894)
        | ~ v10_lattices(X894)
        | v3_struct_0(X894)
        | ~ v3_struct_0(k1_lattice2(X894)) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])]) ).

cnf(c_0_43,plain,
    ( ~ v3_struct_0(X1)
    | ~ l3_lattices(X1)
    | v1_xboole_0(u1_struct_0(X1)) ),
    inference(spm,[status(thm)],[c_0_38,c_0_24]) ).

cnf(c_0_44,negated_conjecture,
    ~ v1_xboole_0(u1_struct_0(esk1_0)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_26])]),c_0_27]) ).

fof(c_0_45,plain,
    ! [X1] :
      ( ( l3_lattices(X1)
        & v10_lattices(X1)
        & ~ v3_struct_0(X1) )
     => ! [X2] :
          ( m1_filter_2(X2,X1)
        <=> m1_filter_0(X2,X1) ) ),
    inference(fof_simplification,[status(thm)],[redefinition_m1_filter_2]) ).

fof(c_0_46,plain,
    ! [X51] :
      ( m1_filter_0(u1_struct_0(X51),X51)
      | ~ l3_lattices(X51)
      | ~ v10_lattices(X51)
      | v3_struct_0(X51) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])]) ).

cnf(c_0_47,plain,
    ( ~ l3_lattices(X1)
    | ~ v10_lattices(X1)
    | v3_struct_0(X1)
    | v10_lattices(k1_lattice2(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

cnf(c_0_48,negated_conjecture,
    v10_lattices(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_49,negated_conjecture,
    ( ~ v3_struct_0(k1_lattice2(esk1_0))
    | ~ l3_lattices(k1_lattice2(esk1_0)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_31]),c_0_44]) ).

fof(c_0_50,plain,
    ! [X1] :
      ( ( l3_lattices(X1)
        & v10_lattices(X1)
        & ~ v3_struct_0(X1) )
     => ! [X2] :
          ( m2_filter_2(X2,X1)
        <=> m1_filter_2(X2,k1_lattice2(X1)) ) ),
    inference(fof_simplification,[status(thm)],[t21_filter_2]) ).

fof(c_0_51,plain,
    ! [X879,X880] :
      ( ( ~ l3_lattices(X879)
        | ~ v10_lattices(X879)
        | v3_struct_0(X879)
        | m1_filter_2(X880,X879)
        | ~ m1_filter_0(X880,X879) )
      & ( ~ l3_lattices(X879)
        | ~ v10_lattices(X879)
        | v3_struct_0(X879)
        | m1_filter_0(X880,X879)
        | ~ m1_filter_2(X880,X879) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])])]) ).

cnf(c_0_52,plain,
    ( ~ l3_lattices(X1)
    | ~ v10_lattices(X1)
    | m1_filter_0(u1_struct_0(X1),X1)
    | v3_struct_0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_53,negated_conjecture,
    v10_lattices(k1_lattice2(esk1_0)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_26])]),c_0_27]) ).

cnf(c_0_54,negated_conjecture,
    ~ v3_struct_0(k1_lattice2(esk1_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_36]),c_0_26])]) ).

fof(c_0_55,plain,
    ! [X32,X33] :
      ( ( ~ l3_lattices(X32)
        | ~ v10_lattices(X32)
        | v3_struct_0(X32)
        | m2_filter_2(X33,X32)
        | ~ m1_filter_2(X33,k1_lattice2(X32)) )
      & ( ~ l3_lattices(X32)
        | ~ v10_lattices(X32)
        | v3_struct_0(X32)
        | m1_filter_2(X33,k1_lattice2(X32))
        | ~ m2_filter_2(X33,X32) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])])])])]) ).

cnf(c_0_56,plain,
    ( ~ l3_lattices(X2)
    | ~ v10_lattices(X2)
    | ~ m1_filter_0(X1,X2)
    | v3_struct_0(X2)
    | m1_filter_2(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

cnf(c_0_57,negated_conjecture,
    ( ~ l3_lattices(k1_lattice2(esk1_0))
    | m1_filter_0(u1_struct_0(esk1_0),k1_lattice2(esk1_0)) ),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_31]),c_0_54]) ).

cnf(c_0_58,plain,
    ( ~ l3_lattices(X2)
    | ~ v10_lattices(X2)
    | ~ m1_filter_2(X1,k1_lattice2(X2))
    | v3_struct_0(X2)
    | m2_filter_2(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_55]) ).

cnf(c_0_59,negated_conjecture,
    ( ~ l3_lattices(k1_lattice2(esk1_0))
    | m1_filter_2(u1_struct_0(esk1_0),k1_lattice2(esk1_0)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_53])]),c_0_54]) ).

cnf(c_0_60,negated_conjecture,
    ~ m2_filter_2(u1_struct_0(esk1_0),esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_61,negated_conjecture,
    ~ l3_lattices(k1_lattice2(esk1_0)),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_48]),c_0_26])]),c_0_60]),c_0_27]) ).

cnf(c_0_62,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_36]),c_0_26])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LAT304+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06  % Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.47  % Computer : n009.cluster.edu
% 0.19/0.47  % Model    : x86_64 x86_64
% 0.19/0.47  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.47  % Memory   : 8046.5625MB
% 0.19/0.47  % OS       : Linux 6.8.0-71-generic
% 0.19/0.47  % CPULimit : 300
% 0.19/0.47  % WCLimit  : 300
% 0.19/0.47  % DateTime : Sun Sep 20 23:31:44 UTC 2026
% 0.19/0.48  % CPUTime  : 
% 0.19/0.48  Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.56  Running first-order theorem proving
% 0.23/0.56  Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 61.89/11.31  % Version: 3.5.1
% 61.89/11.31  % Preprocessing class: FMLMSMSLSSSNFFN.
% 61.89/11.31  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 61.89/11.31  % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 61.89/11.31  % Starting new_bool_3 with 600s (2) cores
% 61.89/11.31  % Starting new_bool_1 with 600s (2) cores
% 61.89/11.31  % Starting sh5l with 300s (1) cores
% 61.89/11.31  % G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 296909 completed with status 0
% 61.89/11.31  % Result found by G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 61.89/11.31  % Preprocessing class: FMLMSMSLSSSNFFN.
% 61.89/11.31  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 61.89/11.31  % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 61.89/11.31  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 61.89/11.31  % SinE strategy is gf600_h_gu_R05_F100_L20000
% 61.89/11.31  % Search class: FGHSM-SMLM32-DFFFFFNN
% 61.89/11.31  % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 61.89/11.31  % Starting SubtermCWHack with 82s (1) cores
% 61.89/11.31  % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 91s (1) cores
% 61.89/11.31  % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 68s (1) cores
% 61.89/11.31  % G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 296919 completed with status 0
% 61.89/11.31  % Result found by G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 61.89/11.31  % Preprocessing class: FMLMSMSLSSSNFFN.
% 61.89/11.31  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 61.89/11.31  % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 61.89/11.31  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 61.89/11.31  % SinE strategy is gf600_h_gu_R05_F100_L20000
% 61.89/11.31  % Search class: FGHSM-SMLM32-DFFFFFNN
% 61.89/11.31  % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 61.89/11.31  % Starting SubtermCWHack with 82s (1) cores
% 61.89/11.31  % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 91s (1) cores
% 61.89/11.31  % Preprocessing time       : 0.170 s
% 61.89/11.31  % Presaturation interreduction done
% 61.89/11.31  
% 61.89/11.31  % Proof found!
% 61.89/11.31  % SZS status Theorem
% 61.89/11.31  % SZS output start CNFRefutation
% See solution above
% 61.89/11.31  % Parsed axioms                        : 2952
% 61.89/11.31  % Removed by relevancy pruning/SinE    : 890
% 61.89/11.31  % Initial clauses                      : 4408
% 61.89/11.31  % Removed in clause preprocessing      : 138
% 61.89/11.31  % Initial clauses in saturation        : 4270
% 61.89/11.31  % Processed clauses                    : 9078
% 61.89/11.31  % ...of these trivial                  : 84
% 61.89/11.31  % ...subsumed                          : 1851
% 61.89/11.31  % ...remaining for further processing  : 7143
% 61.89/11.31  % Other redundant clauses eliminated   : 640
% 61.89/11.31  % Clauses deleted for lack of memory   : 0
% 61.89/11.31  % Backward-subsumed                    : 82
% 61.89/11.31  % Backward-rewritten                   : 141
% 61.89/11.31  % Generated clauses                    : 45660
% 61.89/11.31  % ...of the previous two non-redundant : 37892
% 61.89/11.31  % ...aggressively subsumed             : 0
% 61.89/11.31  % Contextual simplify-reflections      : 294
% 61.89/11.31  % Paramodulations                      : 45116
% 61.89/11.31  % Factorizations                       : 0
% 61.89/11.31  % NegExts                              : 0
% 61.89/11.31  % Equation resolutions                 : 643
% 61.89/11.31  % Disequality decompositions           : 0
% 61.89/11.31  % Total rewrite steps                  : 129846
% 61.89/11.31  % ...of those cached                   : 123140
% 61.89/11.31  % Propositional unsat checks           : 1
% 61.89/11.31  %    Propositional check models        : 1
% 61.89/11.31  %    Propositional check unsatisfiable : 0
% 61.89/11.31  %    Propositional clauses             : 0
% 61.89/11.31  %    Propositional clauses after purity: 0
% 61.89/11.31  %    Propositional unsat core size     : 0
% 61.89/11.31  %    Propositional preprocessing time  : 0.000
% 61.89/11.31  %    Propositional encoding time       : 0.034
% 61.89/11.31  %    Propositional solver time         : 0.017
% 61.89/11.31  %    Success case prop preproc time    : 0.000
% 61.89/11.31  %    Success case prop encoding time   : 0.000
% 61.89/11.31  %    Success case prop solver time     : 0.000
% 61.89/11.31  % Current number of processed clauses  : 2516
% 61.89/11.31  %    Positive orientable unit clauses  : 1090
% 61.89/11.31  %    Positive unorientable unit clauses: 57
% 61.89/11.31  %    Negative unit clauses             : 255
% 61.89/11.31  %    Non-unit-clauses                  : 1114
% 61.89/11.31  % Current number of unprocessed clauses: 36904
% 61.89/11.31  % ...number of literals in the above   : 61063
% 61.89/11.31  % Current number of archived formulas  : 0
% 61.89/11.31  % Current number of archived clauses   : 4119
% 61.89/11.31  % Clause-clause subsumption calls (NU) : 4811049
% 61.89/11.31  % Rec. Clause-clause subsumption calls : 426325
% 61.89/11.31  % Non-unit clause-clause subsumptions  : 1244
% 61.89/11.31  % Unit Clause-clause subsumption calls : 167816
% 61.89/11.31  % Rewrite failures with RHS unbound    : 0
% 61.89/11.31  % BW rewrite match attempts            : 14561
% 61.89/11.31  % BW rewrite match successes           : 8562
% 61.89/11.31  % Condensation attempts                : 0
% 61.89/11.31  % Condensation successes               : 0
% 61.89/11.31  % Termbank termtop insertions          : 2589741
% 61.89/11.31  % Search garbage collected termcells   : 89654
% 61.89/11.31  
% 61.89/11.31  % -------------------------------------------------
% 61.89/11.31  % User time                : 8.667 s
% 61.89/11.31  % System time              : 0.178 s
% 61.89/11.31  % Total time               : 8.845 s
% 61.89/11.31  % Maximum resident set size: 24532 pages
% 61.89/11.31  
% 61.89/11.31  % -------------------------------------------------
% 61.89/11.31  % User time                : 24.203 s
% 61.89/11.31  % System time              : 0.538 s
% 61.89/11.31  % Total time               : 24.741 s
% 61.89/11.31  % Maximum resident set size: 8448 pages
% 61.89/11.31  % E exiting
%------------------------------------------------------------------------------