TSTP Solution File: LCL874^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : LCL874^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n032.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 : Mon May 20 23:54:33 EDT 2024

% Result   : Theorem 0.16s 0.41s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   33
% Syntax   : Number of formulae    :   84 (  36 unt;  17 typ;   0 def)
%            Number of atoms       :  147 (  19 equ;   0 cnn)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  428 (  59   ~;  64   |;   8   &; 293   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  108 ( 108   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  17 usr;   3 con; 0-3 aty)
%            Number of variables   :  141 (  39   ^  99   !;   3   ?; 141   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_24,type,
    mnot: ( $i > $o ) > $i > $o ).

thf(decl_25,type,
    mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(decl_27,type,
    mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(decl_32,type,
    mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).

thf(decl_37,type,
    mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).

thf(decl_39,type,
    mreflexive: ( $i > $i > $o ) > $o ).

thf(decl_41,type,
    mserial: ( $i > $i > $o ) > $o ).

thf(decl_43,type,
    meuclidean: ( $i > $i > $o ) > $o ).

thf(decl_49,type,
    mvalid: ( $i > $o ) > $o ).

thf(decl_53,type,
    rk: $i > $i > $o ).

thf(decl_54,type,
    rb: $i > $i > $o ).

thf(decl_55,type,
    esk1_1: $i > $i ).

thf(decl_56,type,
    esk2_2: $i > ( $i > $o ) > $i ).

thf(decl_57,type,
    esk3_2: $i > ( $i > $o ) > $i ).

thf(decl_58,type,
    esk4_0: $i ).

thf(decl_59,type,
    epred1_0: $i > $o ).

thf(decl_60,type,
    esk5_0: $i ).

thf(meuclidean,axiom,
    ( meuclidean
    = ( ^ [X13: $i > $i > $o] :
        ! [X15: $i,X16: $i,X17: $i] :
          ( ( ( X13 @ X15 @ X16 )
            & ( X13 @ X15 @ X17 ) )
         => ( X13 @ X16 @ X17 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',meuclidean) ).

thf(mreflexive,axiom,
    ( mreflexive
    = ( ^ [X13: $i > $i > $o] :
        ! [X15: $i] : ( X13 @ X15 @ X15 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mreflexive) ).

thf(mimplies,axiom,
    ( mimplies
    = ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).

thf(mnot,axiom,
    ( mnot
    = ( ^ [X6: $i > $o,X3: $i] :
          ~ ( X6 @ X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).

thf(mor,axiom,
    ( mor
    = ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
          ( ( X6 @ X3 )
          | ( X7 @ X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).

thf(ax5,axiom,
    meuclidean @ rk,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).

thf(ax1,axiom,
    mreflexive @ rk,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).

thf(mforall_prop,axiom,
    ( mforall_prop
    = ( ^ [X9: ( $i > $o ) > $i > $o,X3: $i] :
        ! [X10: $i > $o] : ( X9 @ X10 @ X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mforall_prop) ).

thf(mbox,axiom,
    ( mbox
    = ( ^ [X13: $i > $i > $o,X6: $i > $o,X3: $i] :
        ! [X14: $i] :
          ( ~ ( X13 @ X3 @ X14 )
          | ( X6 @ X14 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mbox) ).

thf(mvalid,axiom,
    ( mvalid
    = ( ^ [X6: $i > $o] :
        ! [X3: $i] : ( X6 @ X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).

thf(mserial,axiom,
    ( mserial
    = ( ^ [X13: $i > $i > $o] :
        ! [X15: $i] :
        ? [X16: $i] : ( X13 @ X15 @ X16 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mserial) ).

thf(conj,conjecture,
    ( mvalid
    @ ( mforall_prop
      @ ^ [X18: $i > $o] : ( mimplies @ ( mbox @ rb @ X18 ) @ ( mbox @ rk @ X18 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

thf(ax7,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [X18: $i > $o] : ( mimplies @ ( mbox @ rk @ X18 ) @ ( mbox @ rb @ X18 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7) ).

thf(ax2,axiom,
    mserial @ rb,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).

thf(ax8,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [X18: $i > $o] : ( mimplies @ ( mbox @ rb @ X18 ) @ ( mbox @ rb @ ( mbox @ rk @ X18 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8) ).

thf(ax6,axiom,
    meuclidean @ rb,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).

thf(c_0_16,plain,
    ( meuclidean
    = ( ^ [Z0: $i > $i > $o] :
        ! [X15: $i,X16: $i,X17: $i] :
          ( ( ( Z0 @ X15 @ X16 )
            & ( Z0 @ X15 @ X17 ) )
         => ( Z0 @ X16 @ X17 ) ) ) ),
    inference(fof_simplification,[status(thm)],[meuclidean]) ).

thf(c_0_17,plain,
    ( mreflexive
    = ( ^ [Z0: $i > $i > $o] :
        ! [X15: $i] : ( Z0 @ X15 @ X15 ) ) ),
    inference(fof_simplification,[status(thm)],[mreflexive]) ).

thf(c_0_18,plain,
    ( mimplies
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ~ ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mimplies]) ).

thf(c_0_19,plain,
    ( mnot
    = ( ^ [Z0: $i > $o,Z1: $i] :
          ~ ( Z0 @ Z1 ) ) ),
    inference(fof_simplification,[status(thm)],[mnot]) ).

thf(c_0_20,plain,
    ( mor
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mor]) ).

thf(c_0_21,plain,
    ! [X31: $i,X32: $i,X33: $i] :
      ( ( ( rk @ X31 @ X32 )
        & ( rk @ X31 @ X33 ) )
     => ( rk @ X32 @ X33 ) ),
    inference(apply_def,[status(thm)],[ax5,c_0_16]) ).

thf(c_0_22,plain,
    ! [X22: $i] : ( rk @ X22 @ X22 ),
    inference(apply_def,[status(thm)],[ax1,c_0_17]) ).

thf(c_0_23,plain,
    ( mimplies
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ~ ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).

thf(c_0_24,plain,
    ( mforall_prop
    = ( ^ [Z0: ( $i > $o ) > $i > $o,Z1: $i] :
        ! [X10: $i > $o] : ( Z0 @ X10 @ Z1 ) ) ),
    inference(fof_simplification,[status(thm)],[mforall_prop]) ).

thf(c_0_25,plain,
    ( mbox
    = ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
        ! [X14: $i] :
          ( ~ ( Z0 @ Z2 @ X14 )
          | ( Z1 @ X14 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mbox]) ).

thf(c_0_26,plain,
    ( mvalid
    = ( ^ [Z0: $i > $o] :
        ! [X3: $i] : ( Z0 @ X3 ) ) ),
    inference(fof_simplification,[status(thm)],[mvalid]) ).

thf(c_0_27,plain,
    ( mserial
    = ( ^ [Z0: $i > $i > $o] :
        ! [X15: $i] :
        ? [X16: $i] : ( Z0 @ X15 @ X16 ) ) ),
    inference(fof_simplification,[status(thm)],[mserial]) ).

thf(c_0_28,plain,
    ! [X59: $i,X60: $i,X61: $i] :
      ( ~ ( rk @ X59 @ X60 )
      | ~ ( rk @ X59 @ X61 )
      | ( rk @ X60 @ X61 ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).

thf(c_0_29,plain,
    ! [X50: $i] : ( rk @ X50 @ X50 ),
    inference(variable_rename,[status(thm)],[c_0_22]) ).

thf(c_0_30,negated_conjecture,
    ~ ! [X49: $i,X48: $i > $o] :
        ( ~ ! [X46: $i] :
              ( ~ ( rb @ X49 @ X46 )
              | ( X48 @ X46 ) )
        | ! [X47: $i] :
            ( ~ ( rk @ X49 @ X47 )
            | ( X48 @ X47 ) ) ),
    inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj])]),c_0_23]),c_0_24]),c_0_25]),c_0_26])]) ).

thf(c_0_31,plain,
    ! [X40: $i,X39: $i > $o] :
      ( ~ ! [X37: $i] :
            ( ~ ( rk @ X40 @ X37 )
            | ( X39 @ X37 ) )
      | ! [X38: $i] :
          ( ~ ( rb @ X40 @ X38 )
          | ( X39 @ X38 ) ) ),
    inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[ax7]),c_0_23]),c_0_24]),c_0_25]),c_0_26])]) ).

thf(c_0_32,plain,
    ! [X23: $i] :
    ? [X24: $i] : ( rb @ X23 @ X24 ),
    inference(apply_def,[status(thm)],[ax2,c_0_27]) ).

thf(c_0_33,plain,
    ! [X14: $i,X3: $i,X15: $i] :
      ( ( rk @ X14 @ X15 )
      | ~ ( rk @ X3 @ X14 )
      | ~ ( rk @ X3 @ X15 ) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

thf(c_0_34,plain,
    ! [X3: $i] : ( rk @ X3 @ X3 ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

thf(c_0_35,negated_conjecture,
    ! [X76: $i] :
      ( ( ~ ( rb @ esk4_0 @ X76 )
        | ( epred1_0 @ X76 ) )
      & ( rk @ esk4_0 @ esk5_0 )
      & ~ ( epred1_0 @ esk5_0 ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])])])]) ).

thf(c_0_36,plain,
    ! [X65: $i,X66: $i > $o,X68: $i] :
      ( ( ( rk @ X65 @ ( esk2_2 @ X65 @ X66 ) )
        | ~ ( rb @ X65 @ X68 )
        | ( X66 @ X68 ) )
      & ( ~ ( X66 @ ( esk2_2 @ X65 @ X66 ) )
        | ~ ( rb @ X65 @ X68 )
        | ( X66 @ X68 ) ) ),
    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)],[c_0_31])])])])])]) ).

thf(c_0_37,plain,
    ! [X51: $i] : ( rb @ X51 @ ( esk1_1 @ X51 ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_32])]) ).

thf(c_0_38,plain,
    ! [X45: $i,X44: $i > $o] :
      ( ~ ! [X41: $i] :
            ( ~ ( rb @ X45 @ X41 )
            | ( X44 @ X41 ) )
      | ! [X43: $i] :
          ( ~ ( rb @ X45 @ X43 )
          | ! [X42: $i] :
              ( ~ ( rk @ X43 @ X42 )
              | ( X44 @ X42 ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[ax8]),c_0_23]),c_0_24]),c_0_25]),c_0_26])]) ).

thf(c_0_39,plain,
    ! [X14: $i,X3: $i] :
      ( ( rk @ X3 @ X14 )
      | ~ ( rk @ X14 @ X3 ) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

thf(c_0_40,negated_conjecture,
    rk @ esk4_0 @ esk5_0,
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

thf(c_0_41,plain,
    ! [X4: $i > $o,X3: $i,X14: $i] :
      ( ( X4 @ X14 )
      | ~ ( X4 @ ( esk2_2 @ X3 @ X4 ) )
      | ~ ( rb @ X3 @ X14 ) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

thf(c_0_42,plain,
    ! [X3: $i] : ( rb @ X3 @ ( esk1_1 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

thf(c_0_43,plain,
    ! [X4: $i > $o,X3: $i,X14: $i] :
      ( ( rk @ X3 @ ( esk2_2 @ X3 @ X4 ) )
      | ( X4 @ X14 )
      | ~ ( rb @ X3 @ X14 ) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

thf(c_0_44,plain,
    ! [X34: $i,X35: $i,X36: $i] :
      ( ( ( rb @ X34 @ X35 )
        & ( rb @ X34 @ X36 ) )
     => ( rb @ X35 @ X36 ) ),
    inference(apply_def,[status(thm)],[ax6,c_0_16]) ).

thf(c_0_45,plain,
    ! [X69: $i,X70: $i > $o,X72: $i,X73: $i] :
      ( ( ( rb @ X69 @ ( esk3_2 @ X69 @ X70 ) )
        | ~ ( rb @ X69 @ X72 )
        | ~ ( rk @ X72 @ X73 )
        | ( X70 @ X73 ) )
      & ( ~ ( X70 @ ( esk3_2 @ X69 @ X70 ) )
        | ~ ( rb @ X69 @ X72 )
        | ~ ( rk @ X72 @ X73 )
        | ( X70 @ X73 ) ) ),
    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)],[c_0_38])])])])])]) ).

thf(c_0_46,negated_conjecture,
    rk @ esk5_0 @ esk4_0,
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

thf(c_0_47,plain,
    ! [X3: $i,X4: $i > $o] :
      ( ( X4 @ ( esk1_1 @ X3 ) )
      | ~ ( X4 @ ( esk2_2 @ X3 @ X4 ) ) ),
    inference(spm,[status(thm)],[c_0_41,c_0_42]) ).

thf(c_0_48,plain,
    ! [X4: $i > $o,X3: $i] :
      ( ( rk @ X3 @ ( esk2_2 @ X3 @ X4 ) )
      | ( X4 @ ( esk1_1 @ X3 ) ) ),
    inference(spm,[status(thm)],[c_0_43,c_0_42]) ).

thf(c_0_49,plain,
    ! [X62: $i,X63: $i,X64: $i] :
      ( ~ ( rb @ X62 @ X63 )
      | ~ ( rb @ X62 @ X64 )
      | ( rb @ X63 @ X64 ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])]) ).

thf(c_0_50,plain,
    ! [X14: $i,X4: $i > $o,X3: $i,X15: $i] :
      ( ( rb @ X3 @ ( esk3_2 @ X3 @ X4 ) )
      | ( X4 @ X15 )
      | ~ ( rb @ X3 @ X14 )
      | ~ ( rk @ X14 @ X15 ) ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

thf(c_0_51,negated_conjecture,
    ! [X3: $i] :
      ( ( rk @ X3 @ esk4_0 )
      | ~ ( rk @ esk5_0 @ X3 ) ),
    inference(spm,[status(thm)],[c_0_33,c_0_46]) ).

thf(c_0_52,plain,
    ! [X3: $i] : ( rk @ X3 @ ( esk1_1 @ X3 ) ),
    inference(spm,[status(thm)],[c_0_47,c_0_48]) ).

thf(c_0_53,plain,
    ! [X14: $i,X3: $i,X15: $i] :
      ( ( rb @ X14 @ X15 )
      | ~ ( rb @ X3 @ X14 )
      | ~ ( rb @ X3 @ X15 ) ),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

thf(c_0_54,negated_conjecture,
    ! [X4: $i > $o,X3: $i] :
      ( ( rb @ X3 @ ( esk3_2 @ X3 @ X4 ) )
      | ( X4 @ esk5_0 )
      | ~ ( rb @ X3 @ esk4_0 ) ),
    inference(spm,[status(thm)],[c_0_50,c_0_40]) ).

thf(c_0_55,plain,
    ! [X14: $i,X4: $i > $o,X3: $i,X15: $i] :
      ( ( X4 @ X15 )
      | ~ ( X4 @ ( esk3_2 @ X3 @ X4 ) )
      | ~ ( rb @ X3 @ X14 )
      | ~ ( rk @ X14 @ X15 ) ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

thf(c_0_56,negated_conjecture,
    rk @ ( esk1_1 @ esk5_0 ) @ esk4_0,
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

thf(c_0_57,negated_conjecture,
    ! [X3: $i] :
      ( ( epred1_0 @ X3 )
      | ~ ( rb @ esk4_0 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

thf(c_0_58,negated_conjecture,
    ! [X14: $i,X4: $i > $o,X3: $i] :
      ( ( rb @ X3 @ ( esk3_2 @ X14 @ X4 ) )
      | ( X4 @ esk5_0 )
      | ~ ( rb @ X14 @ esk4_0 )
      | ~ ( rb @ X14 @ X3 ) ),
    inference(spm,[status(thm)],[c_0_53,c_0_54]) ).

thf(c_0_59,negated_conjecture,
    ! [X3: $i,X4: $i > $o] :
      ( ( X4 @ esk4_0 )
      | ~ ( rb @ X3 @ ( esk1_1 @ esk5_0 ) )
      | ~ ( X4 @ ( esk3_2 @ X3 @ X4 ) ) ),
    inference(spm,[status(thm)],[c_0_55,c_0_56]) ).

thf(c_0_60,negated_conjecture,
    ! [X4: $i > $o,X3: $i] :
      ( ( X4 @ esk5_0 )
      | ~ ( X4 @ ( esk3_2 @ X3 @ X4 ) )
      | ~ ( rb @ X3 @ esk4_0 ) ),
    inference(spm,[status(thm)],[c_0_55,c_0_40]) ).

thf(c_0_61,negated_conjecture,
    ! [X4: $i > $o,X3: $i] :
      ( ( epred1_0 @ ( esk3_2 @ X3 @ X4 ) )
      | ( X4 @ esk5_0 )
      | ~ ( rb @ X3 @ esk4_0 ) ),
    inference(spm,[status(thm)],[c_0_57,c_0_58]) ).

thf(c_0_62,negated_conjecture,
    ~ ( epred1_0 @ esk5_0 ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

thf(c_0_63,negated_conjecture,
    ! [X4: $i > $o] :
      ( ( X4 @ esk4_0 )
      | ~ ( X4 @ ( esk3_2 @ esk5_0 @ X4 ) ) ),
    inference(spm,[status(thm)],[c_0_59,c_0_42]) ).

thf(c_0_64,negated_conjecture,
    ! [X4: $i > $o,X3: $i] :
      ( ( rb @ X3 @ ( esk3_2 @ X3 @ X4 ) )
      | ( X4 @ esk4_0 )
      | ~ ( rb @ X3 @ ( esk1_1 @ esk5_0 ) ) ),
    inference(spm,[status(thm)],[c_0_50,c_0_56]) ).

thf(c_0_65,negated_conjecture,
    ! [X3: $i] :
      ~ ( rb @ X3 @ esk4_0 ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]) ).

thf(c_0_66,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_42])]),c_0_65]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : LCL874^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 0.10/0.11  % Command    : run_E %s %d THM
% 0.11/0.31  % Computer : n032.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit   : 300
% 0.11/0.31  % WCLimit    : 300
% 0.11/0.31  % DateTime   : Mon May 20 02:01:52 EDT 2024
% 0.11/0.31  % CPUTime    : 
% 0.16/0.39  Running higher-order theorem proving
% 0.16/0.39  Running: /export/starexec/sandbox/solver/bin/eprover-ho --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
% 0.16/0.41  # Version: 3.1.0-ho
% 0.16/0.41  # Preprocessing class: HSMSSMSSMLMNHHN.
% 0.16/0.41  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.41  # Starting ehoh_best2_full_lfho with 1500s (5) cores
% 0.16/0.41  # Starting lpo9_lambda_fix with 300s (1) cores
% 0.16/0.41  # Starting sh5l with 300s (1) cores
% 0.16/0.41  # Starting ho_unfolding_6 with 300s (1) cores
% 0.16/0.41  # ho_unfolding_6 with pid 26018 completed with status 0
% 0.16/0.41  # Result found by ho_unfolding_6
% 0.16/0.41  # Preprocessing class: HSMSSMSSMLMNHHN.
% 0.16/0.41  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.41  # Starting ehoh_best2_full_lfho with 1500s (5) cores
% 0.16/0.41  # Starting lpo9_lambda_fix with 300s (1) cores
% 0.16/0.41  # Starting sh5l with 300s (1) cores
% 0.16/0.41  # Starting ho_unfolding_6 with 300s (1) cores
% 0.16/0.41  # No SInE strategy applied
% 0.16/0.41  # Search class: HGUNS-FFSF21-SHHSMSBN
% 0.16/0.41  # partial match(3): HGUNF-FFSF22-SHHSMMBN
% 0.16/0.41  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.41  # Starting new_ho_10 with 163s (1) cores
% 0.16/0.41  # new_ho_10 with pid 26022 completed with status 0
% 0.16/0.41  # Result found by new_ho_10
% 0.16/0.41  # Preprocessing class: HSMSSMSSMLMNHHN.
% 0.16/0.41  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.41  # Starting ehoh_best2_full_lfho with 1500s (5) cores
% 0.16/0.41  # Starting lpo9_lambda_fix with 300s (1) cores
% 0.16/0.41  # Starting sh5l with 300s (1) cores
% 0.16/0.41  # Starting ho_unfolding_6 with 300s (1) cores
% 0.16/0.41  # No SInE strategy applied
% 0.16/0.41  # Search class: HGUNS-FFSF21-SHHSMSBN
% 0.16/0.41  # partial match(3): HGUNF-FFSF22-SHHSMMBN
% 0.16/0.41  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.41  # Starting new_ho_10 with 163s (1) cores
% 0.16/0.41  # Preprocessing time       : 0.001 s
% 0.16/0.41  # Presaturation interreduction done
% 0.16/0.41  
% 0.16/0.41  # Proof found!
% 0.16/0.41  # SZS status Theorem
% 0.16/0.41  # SZS output start CNFRefutation
% See solution above
% 0.16/0.42  # Parsed axioms                        : 74
% 0.16/0.42  # Removed by relevancy pruning/SinE    : 0
% 0.16/0.42  # Initial clauses                      : 47
% 0.16/0.42  # Removed in clause preprocessing      : 34
% 0.16/0.42  # Initial clauses in saturation        : 13
% 0.16/0.42  # Processed clauses                    : 191
% 0.16/0.42  # ...of these trivial                  : 4
% 0.16/0.42  # ...subsumed                          : 29
% 0.16/0.42  # ...remaining for further processing  : 158
% 0.16/0.42  # Other redundant clauses eliminated   : 0
% 0.16/0.42  # Clauses deleted for lack of memory   : 0
% 0.16/0.42  # Backward-subsumed                    : 33
% 0.16/0.42  # Backward-rewritten                   : 4
% 0.16/0.42  # Generated clauses                    : 920
% 0.16/0.42  # ...of the previous two non-redundant : 782
% 0.16/0.42  # ...aggressively subsumed             : 0
% 0.16/0.42  # Contextual simplify-reflections      : 1
% 0.16/0.42  # Paramodulations                      : 920
% 0.16/0.42  # Factorizations                       : 0
% 0.16/0.42  # NegExts                              : 0
% 0.16/0.42  # Equation resolutions                 : 0
% 0.16/0.42  # Disequality decompositions           : 0
% 0.16/0.42  # Total rewrite steps                  : 140
% 0.16/0.42  # ...of those cached                   : 105
% 0.16/0.42  # Propositional unsat checks           : 0
% 0.16/0.42  #    Propositional check models        : 0
% 0.16/0.42  #    Propositional check unsatisfiable : 0
% 0.16/0.42  #    Propositional clauses             : 0
% 0.16/0.42  #    Propositional clauses after purity: 0
% 0.16/0.42  #    Propositional unsat core size     : 0
% 0.16/0.42  #    Propositional preprocessing time  : 0.000
% 0.16/0.42  #    Propositional encoding time       : 0.000
% 0.16/0.42  #    Propositional solver time         : 0.000
% 0.16/0.42  #    Success case prop preproc time    : 0.000
% 0.16/0.42  #    Success case prop encoding time   : 0.000
% 0.16/0.42  #    Success case prop solver time     : 0.000
% 0.16/0.42  # Current number of processed clauses  : 108
% 0.16/0.42  #    Positive orientable unit clauses  : 21
% 0.16/0.42  #    Positive unorientable unit clauses: 0
% 0.16/0.42  #    Negative unit clauses             : 3
% 0.16/0.42  #    Non-unit-clauses                  : 84
% 0.16/0.42  # Current number of unprocessed clauses: 610
% 0.16/0.42  # ...number of literals in the above   : 2005
% 0.16/0.42  # Current number of archived formulas  : 0
% 0.16/0.42  # Current number of archived clauses   : 50
% 0.16/0.42  # Clause-clause subsumption calls (NU) : 1190
% 0.16/0.42  # Rec. Clause-clause subsumption calls : 1061
% 0.16/0.42  # Non-unit clause-clause subsumptions  : 28
% 0.16/0.42  # Unit Clause-clause subsumption calls : 82
% 0.16/0.42  # Rewrite failures with RHS unbound    : 0
% 0.16/0.42  # BW rewrite match attempts            : 16
% 0.16/0.42  # BW rewrite match successes           : 4
% 0.16/0.42  # Condensation attempts                : 191
% 0.16/0.42  # Condensation successes               : 0
% 0.16/0.42  # Termbank termtop insertions          : 15416
% 0.16/0.42  # Search garbage collected termcells   : 959
% 0.16/0.42  
% 0.16/0.42  # -------------------------------------------------
% 0.16/0.42  # User time                : 0.016 s
% 0.16/0.42  # System time              : 0.002 s
% 0.16/0.42  # Total time               : 0.018 s
% 0.16/0.42  # Maximum resident set size: 2040 pages
% 0.16/0.42  
% 0.16/0.42  # -------------------------------------------------
% 0.16/0.42  # User time                : 0.017 s
% 0.16/0.42  # System time              : 0.003 s
% 0.16/0.42  # Total time               : 0.021 s
% 0.16/0.42  # Maximum resident set size: 1800 pages
% 0.16/0.42  % E---3.1 exiting
% 0.16/0.42  % E exiting
%------------------------------------------------------------------------------