TSTP Solution File: SYN367^7 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SYN367^7 : TPTP v8.2.0. Released v5.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n024.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 07:44:28 EDT 2024

% Result   : Theorem 13.43s 2.23s
% Output   : CNFRefutation 13.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :   39
% Syntax   : Number of formulae    :  112 (  39 unt;  25 typ;   0 def)
%            Number of atoms       :  315 (  20 equ;   0 cnn)
%            Maximal formula atoms :   45 (   3 avg)
%            Number of connectives :  980 ( 140   ~; 157   |;  18   &; 656   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   6 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   80 (  80   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   26 (  24 usr;   9 con; 0-3 aty)
%            Number of variables   :  165 (  43   ^ 121   !;   1   ?; 165   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_sort1,type,
    mu: $tType ).

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

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

thf(decl_30,type,
    mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(decl_31,type,
    mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(decl_36,type,
    exists_in_world: mu > $i > $o ).

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

thf(decl_40,type,
    mreflexive: ( $i > $i > $o ) > $o ).

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

thf(decl_50,type,
    mvalid: ( $i > $o ) > $o ).

thf(decl_54,type,
    rel_s4: $i > $i > $o ).

thf(decl_55,type,
    mbox_s4: ( $i > $o ) > $i > $o ).

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

thf(decl_58,type,
    big_r: mu > $i > $o ).

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

thf(decl_60,type,
    esk1_1: $i > mu ).

thf(decl_61,type,
    esk2_0: $i ).

thf(decl_62,type,
    esk3_0: $i ).

thf(decl_63,type,
    esk4_3: $i > mu > $i > $i ).

thf(decl_64,type,
    esk5_0: $i ).

thf(decl_65,type,
    esk6_0: mu ).

thf(decl_66,type,
    esk7_0: $i ).

thf(decl_67,type,
    esk8_0: $i ).

thf(decl_68,type,
    esk9_0: mu ).

thf(decl_69,type,
    esk10_0: $i ).

thf(mand,axiom,
    ( mand
    = ( ^ [X4: $i > $o,X5: $i > $o] : ( mnot @ ( mor @ ( mnot @ X4 ) @ ( mnot @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mand) ).

thf(mnot,axiom,
    ( mnot
    = ( ^ [X4: $i > $o,X3: $i] :
          ~ ( X4 @ X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mnot) ).

thf(mor,axiom,
    ( mor
    = ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
          ( ( X4 @ X3 )
          | ( X5 @ X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mor) ).

thf(mimplies,axiom,
    ( mimplies
    = ( ^ [X4: $i > $o,X5: $i > $o] : ( mor @ ( mnot @ X4 ) @ X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mimplies) ).

thf(mtransitive,axiom,
    ( mtransitive
    = ( ^ [X6: $i > $i > $o] :
        ! [X16: $i,X17: $i,X18: $i] :
          ( ( ( X6 @ X16 @ X17 )
            & ( X6 @ X17 @ X18 ) )
         => ( X6 @ X16 @ X18 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mtransitive) ).

thf(mforall_ind,axiom,
    ( mforall_ind
    = ( ^ [X11: mu > $i > $o,X3: $i] :
        ! [X12: mu] :
          ( ( exists_in_world @ X12 @ X3 )
         => ( X11 @ X12 @ X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mforall_ind) ).

thf(mvalid,axiom,
    ( mvalid
    = ( ^ [X4: $i > $o] :
        ! [X3: $i] : ( X4 @ X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mvalid) ).

thf(mbox_s4,axiom,
    ( mbox_s4
    = ( ^ [X4: $i > $o,X3: $i] :
        ! [X7: $i] :
          ( ~ ( rel_s4 @ X3 @ X7 )
          | ( X4 @ X7 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).

thf(a2,axiom,
    mtransitive @ rel_s4,
    file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',a2) ).

thf(x2118,conjecture,
    ( mvalid
    @ ( mbox_s4
      @ ( mimplies
        @ ( mbox_s4
          @ ( mforall_ind
            @ ^ [X20: mu] : ( mor @ ( mand @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( big_q @ X20 ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ p ) ) ) @ ( mbox_s4 @ ( big_r @ X20 ) ) ) ) ) )
        @ ( mor
          @ ( mbox_s4
            @ ( mforall_ind
              @ ^ [X21: mu] : ( mbox_s4 @ ( big_q @ X21 ) ) ) )
          @ ( mbox_s4
            @ ( mforall_ind
              @ ^ [X22: mu] : ( mbox_s4 @ ( big_r @ X22 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2118) ).

thf(mreflexive,axiom,
    ( mreflexive
    = ( ^ [X6: $i > $i > $o] :
        ! [X16: $i] : ( X6 @ X16 @ X16 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mreflexive) ).

thf(a1,axiom,
    mreflexive @ rel_s4,
    file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',a1) ).

thf(cumulative_ax,axiom,
    ! [X19: mu,X7: $i,X3: $i] :
      ( ( ( exists_in_world @ X19 @ X7 )
        & ( rel_s4 @ X7 @ X3 ) )
     => ( exists_in_world @ X19 @ X3 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL015^1.ax',cumulative_ax) ).

thf(nonempty_ax,axiom,
    ! [X7: $i] :
    ? [X10: mu] : ( exists_in_world @ X10 @ X7 ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',nonempty_ax) ).

thf(c_0_14,plain,
    ( mand
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ~ ( ~ ( Z0 @ Z2 )
            | ~ ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mand]) ).

thf(c_0_15,plain,
    ( mnot
    = ( ^ [Z0: $i > $o,Z1: $i] :
          ~ ( Z0 @ Z1 ) ) ),
    inference(fof_simplification,[status(thm)],[mnot]) ).

thf(c_0_16,plain,
    ( mor
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mor]) ).

thf(c_0_17,plain,
    ( mimplies
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ~ ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mimplies]) ).

thf(c_0_18,plain,
    ( mtransitive
    = ( ^ [Z0: $i > $i > $o] :
        ! [X16: $i,X17: $i,X18: $i] :
          ( ( ( Z0 @ X16 @ X17 )
            & ( Z0 @ X17 @ X18 ) )
         => ( Z0 @ X16 @ X18 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mtransitive]) ).

thf(c_0_19,plain,
    ( mand
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ~ ( ~ ( Z0 @ Z2 )
            | ~ ( Z1 @ Z2 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).

thf(c_0_20,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_17,c_0_15]),c_0_16]) ).

thf(c_0_21,plain,
    ( mforall_ind
    = ( ^ [Z0: mu > $i > $o,Z1: $i] :
        ! [X12: mu] :
          ( ( exists_in_world @ X12 @ Z1 )
         => ( Z0 @ X12 @ Z1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mforall_ind]) ).

thf(c_0_22,plain,
    ( mvalid
    = ( ^ [Z0: $i > $o] :
        ! [X3: $i] : ( Z0 @ X3 ) ) ),
    inference(fof_simplification,[status(thm)],[mvalid]) ).

thf(c_0_23,plain,
    ( mbox_s4
    = ( ^ [Z0: $i > $o,Z1: $i] :
        ! [X7: $i] :
          ( ~ ( rel_s4 @ Z1 @ X7 )
          | ( Z0 @ X7 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mbox_s4]) ).

thf(c_0_24,plain,
    ! [X33: $i,X34: $i,X35: $i] :
      ( ( ( rel_s4 @ X33 @ X34 )
        & ( rel_s4 @ X34 @ X35 ) )
     => ( rel_s4 @ X33 @ X35 ) ),
    inference(apply_def,[status(thm)],[a2,c_0_18]) ).

thf(c_0_25,negated_conjecture,
    ~ ! [X50: $i,X49: $i] :
        ( ~ ( rel_s4 @ X50 @ X49 )
        | ~ ! [X42: $i] :
              ( ~ ( rel_s4 @ X49 @ X42 )
              | ! [X41: mu] :
                  ( ( exists_in_world @ X41 @ X42 )
                 => ( ~ ( ~ ! [X36: $i] :
                              ( ~ ( rel_s4 @ X42 @ X36 )
                              | ( p @ X36 ) )
                        | ~ ! [X37: $i] :
                              ( ~ ( rel_s4 @ X42 @ X37 )
                              | ( big_q @ X41 @ X37 ) ) )
                    | ~ ( ~ ! [X39: $i] :
                              ( ~ ( rel_s4 @ X42 @ X39 )
                              | ~ ! [X38: $i] :
                                    ( ~ ( rel_s4 @ X39 @ X38 )
                                    | ( p @ X38 ) ) )
                        | ~ ! [X40: $i] :
                              ( ~ ( rel_s4 @ X42 @ X40 )
                              | ( big_r @ X41 @ X40 ) ) ) ) ) )
        | ! [X45: $i] :
            ( ~ ( rel_s4 @ X49 @ X45 )
            | ! [X44: mu] :
                ( ( exists_in_world @ X44 @ X45 )
               => ! [X43: $i] :
                    ( ~ ( rel_s4 @ X45 @ X43 )
                    | ( big_q @ X44 @ X43 ) ) ) )
        | ! [X48: $i] :
            ( ~ ( rel_s4 @ X49 @ X48 )
            | ! [X47: mu] :
                ( ( exists_in_world @ X47 @ X48 )
               => ! [X46: $i] :
                    ( ~ ( rel_s4 @ X48 @ X46 )
                    | ( big_r @ X47 @ X46 ) ) ) ) ),
    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(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[x2118])]),c_0_15]),c_0_16]),c_0_19]),c_0_20]),c_0_21]),c_0_22]),c_0_23])]) ).

thf(c_0_26,plain,
    ! [X54: $i,X55: $i,X56: $i] :
      ( ~ ( rel_s4 @ X54 @ X55 )
      | ~ ( rel_s4 @ X55 @ X56 )
      | ( rel_s4 @ X54 @ X56 ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).

thf(c_0_27,negated_conjecture,
    ! [X62: $i,X63: mu,X64: $i,X65: $i,X66: $i,X68: $i] :
      ( ( rel_s4 @ esk2_0 @ esk3_0 )
      & ( ( rel_s4 @ X66 @ ( esk4_3 @ X62 @ X63 @ X66 ) )
        | ~ ( rel_s4 @ X62 @ X66 )
        | ~ ( rel_s4 @ X62 @ X64 )
        | ( p @ X64 )
        | ~ ( exists_in_world @ X63 @ X62 )
        | ~ ( rel_s4 @ esk3_0 @ X62 ) )
      & ( ~ ( p @ ( esk4_3 @ X62 @ X63 @ X66 ) )
        | ~ ( rel_s4 @ X62 @ X66 )
        | ~ ( rel_s4 @ X62 @ X64 )
        | ( p @ X64 )
        | ~ ( exists_in_world @ X63 @ X62 )
        | ~ ( rel_s4 @ esk3_0 @ X62 ) )
      & ( ~ ( rel_s4 @ X62 @ X68 )
        | ( big_r @ X63 @ X68 )
        | ~ ( rel_s4 @ X62 @ X64 )
        | ( p @ X64 )
        | ~ ( exists_in_world @ X63 @ X62 )
        | ~ ( rel_s4 @ esk3_0 @ X62 ) )
      & ( ( rel_s4 @ X66 @ ( esk4_3 @ X62 @ X63 @ X66 ) )
        | ~ ( rel_s4 @ X62 @ X66 )
        | ~ ( rel_s4 @ X62 @ X65 )
        | ( big_q @ X63 @ X65 )
        | ~ ( exists_in_world @ X63 @ X62 )
        | ~ ( rel_s4 @ esk3_0 @ X62 ) )
      & ( ~ ( p @ ( esk4_3 @ X62 @ X63 @ X66 ) )
        | ~ ( rel_s4 @ X62 @ X66 )
        | ~ ( rel_s4 @ X62 @ X65 )
        | ( big_q @ X63 @ X65 )
        | ~ ( exists_in_world @ X63 @ X62 )
        | ~ ( rel_s4 @ esk3_0 @ X62 ) )
      & ( ~ ( rel_s4 @ X62 @ X68 )
        | ( big_r @ X63 @ X68 )
        | ~ ( rel_s4 @ X62 @ X65 )
        | ( big_q @ X63 @ X65 )
        | ~ ( exists_in_world @ X63 @ X62 )
        | ~ ( rel_s4 @ esk3_0 @ X62 ) )
      & ( rel_s4 @ esk3_0 @ esk5_0 )
      & ( exists_in_world @ esk6_0 @ esk5_0 )
      & ( rel_s4 @ esk5_0 @ esk7_0 )
      & ~ ( big_q @ esk6_0 @ esk7_0 )
      & ( rel_s4 @ esk3_0 @ esk8_0 )
      & ( exists_in_world @ esk9_0 @ esk8_0 )
      & ( rel_s4 @ esk8_0 @ esk10_0 )
      & ~ ( big_r @ esk9_0 @ esk10_0 ) ),
    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_25])])])])])]) ).

thf(c_0_28,plain,
    ( mreflexive
    = ( ^ [Z0: $i > $i > $o] :
        ! [X16: $i] : ( Z0 @ X16 @ X16 ) ) ),
    inference(fof_simplification,[status(thm)],[mreflexive]) ).

thf(c_0_29,plain,
    ! [X7: $i,X3: $i,X16: $i] :
      ( ( rel_s4 @ X3 @ X16 )
      | ~ ( rel_s4 @ X3 @ X7 )
      | ~ ( rel_s4 @ X7 @ X16 ) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

thf(c_0_30,negated_conjecture,
    rel_s4 @ esk5_0 @ esk7_0,
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

thf(c_0_31,plain,
    ! [X32: $i] : ( rel_s4 @ X32 @ X32 ),
    inference(apply_def,[status(thm)],[a1,c_0_28]) ).

thf(c_0_32,negated_conjecture,
    ! [X16: $i,X3: $i,X10: mu,X7: $i] :
      ( ( rel_s4 @ X3 @ ( esk4_3 @ X7 @ X10 @ X3 ) )
      | ( big_q @ X10 @ X16 )
      | ~ ( rel_s4 @ X7 @ X3 )
      | ~ ( rel_s4 @ X7 @ X16 )
      | ~ ( exists_in_world @ X10 @ X7 )
      | ~ ( rel_s4 @ esk3_0 @ X7 ) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

thf(c_0_33,negated_conjecture,
    ! [X3: $i] :
      ( ( rel_s4 @ X3 @ esk7_0 )
      | ~ ( rel_s4 @ X3 @ esk5_0 ) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

thf(c_0_34,negated_conjecture,
    rel_s4 @ esk3_0 @ esk5_0,
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

thf(c_0_35,plain,
    ! [X53: $i] : ( rel_s4 @ X53 @ X53 ),
    inference(variable_rename,[status(thm)],[c_0_31]) ).

thf(c_0_36,negated_conjecture,
    ! [X3: $i,X7: $i,X10: mu] :
      ( ( rel_s4 @ X3 @ ( esk4_3 @ esk7_0 @ X10 @ X3 ) )
      | ( big_q @ X10 @ X7 )
      | ~ ( rel_s4 @ esk7_0 @ X7 )
      | ~ ( rel_s4 @ esk7_0 @ X3 )
      | ~ ( exists_in_world @ X10 @ esk7_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).

thf(c_0_37,plain,
    ! [X3: $i] : ( rel_s4 @ X3 @ X3 ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

thf(c_0_38,plain,
    ! [X57: mu,X58: $i,X59: $i] :
      ( ~ ( exists_in_world @ X57 @ X58 )
      | ~ ( rel_s4 @ X58 @ X59 )
      | ( exists_in_world @ X57 @ X59 ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cumulative_ax])])]) ).

thf(c_0_39,negated_conjecture,
    ! [X3: $i,X10: mu] :
      ( ( rel_s4 @ X3 @ ( esk4_3 @ esk7_0 @ X10 @ X3 ) )
      | ( big_q @ X10 @ esk7_0 )
      | ~ ( rel_s4 @ esk7_0 @ X3 )
      | ~ ( exists_in_world @ X10 @ esk7_0 ) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

thf(c_0_40,plain,
    ! [X3: $i,X10: mu,X7: $i] :
      ( ( exists_in_world @ X10 @ X7 )
      | ~ ( exists_in_world @ X10 @ X3 )
      | ~ ( rel_s4 @ X3 @ X7 ) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

thf(c_0_41,negated_conjecture,
    ! [X10: mu] :
      ( ( rel_s4 @ esk7_0 @ ( esk4_3 @ esk7_0 @ X10 @ esk7_0 ) )
      | ( big_q @ X10 @ esk7_0 )
      | ~ ( exists_in_world @ X10 @ esk7_0 ) ),
    inference(spm,[status(thm)],[c_0_39,c_0_37]) ).

thf(c_0_42,negated_conjecture,
    ! [X10: mu] :
      ( ( exists_in_world @ X10 @ esk7_0 )
      | ~ ( exists_in_world @ X10 @ esk5_0 ) ),
    inference(spm,[status(thm)],[c_0_40,c_0_30]) ).

thf(c_0_43,negated_conjecture,
    ! [X10: mu] :
      ( ( rel_s4 @ esk7_0 @ ( esk4_3 @ esk7_0 @ X10 @ esk7_0 ) )
      | ( big_q @ X10 @ esk7_0 )
      | ~ ( exists_in_world @ X10 @ esk5_0 ) ),
    inference(spm,[status(thm)],[c_0_41,c_0_42]) ).

thf(c_0_44,negated_conjecture,
    exists_in_world @ esk6_0 @ esk5_0,
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

thf(c_0_45,negated_conjecture,
    ~ ( big_q @ esk6_0 @ esk7_0 ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

thf(c_0_46,negated_conjecture,
    rel_s4 @ esk7_0 @ ( esk4_3 @ esk7_0 @ esk6_0 @ esk7_0 ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).

thf(c_0_47,negated_conjecture,
    ! [X3: $i] :
      ( ( rel_s4 @ X3 @ ( esk4_3 @ esk7_0 @ esk6_0 @ esk7_0 ) )
      | ~ ( rel_s4 @ X3 @ esk7_0 ) ),
    inference(spm,[status(thm)],[c_0_29,c_0_46]) ).

thf(c_0_48,negated_conjecture,
    ! [X16: $i,X3: $i,X10: mu,X7: $i] :
      ( ( rel_s4 @ X3 @ ( esk4_3 @ X7 @ X10 @ X3 ) )
      | ( p @ X16 )
      | ~ ( rel_s4 @ X7 @ X3 )
      | ~ ( rel_s4 @ X7 @ X16 )
      | ~ ( exists_in_world @ X10 @ X7 )
      | ~ ( rel_s4 @ esk3_0 @ X7 ) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

thf(c_0_49,negated_conjecture,
    ! [X3: $i,X7: $i] :
      ( ( rel_s4 @ X3 @ ( esk4_3 @ esk7_0 @ esk6_0 @ esk7_0 ) )
      | ~ ( rel_s4 @ X7 @ esk7_0 )
      | ~ ( rel_s4 @ X3 @ X7 ) ),
    inference(spm,[status(thm)],[c_0_29,c_0_47]) ).

thf(c_0_50,negated_conjecture,
    ! [X3: $i,X7: $i,X10: mu] :
      ( ( rel_s4 @ X3 @ ( esk4_3 @ esk3_0 @ X10 @ X3 ) )
      | ( p @ X7 )
      | ~ ( rel_s4 @ esk3_0 @ X7 )
      | ~ ( rel_s4 @ esk3_0 @ X3 )
      | ~ ( exists_in_world @ X10 @ esk3_0 ) ),
    inference(spm,[status(thm)],[c_0_48,c_0_37]) ).

thf(c_0_51,negated_conjecture,
    ! [X3: $i] :
      ( ( rel_s4 @ X3 @ ( esk4_3 @ esk7_0 @ esk6_0 @ esk7_0 ) )
      | ~ ( rel_s4 @ X3 @ esk5_0 ) ),
    inference(spm,[status(thm)],[c_0_49,c_0_30]) ).

thf(c_0_52,negated_conjecture,
    rel_s4 @ esk3_0 @ esk8_0,
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

thf(c_0_53,negated_conjecture,
    ! [X3: $i,X10: mu] :
      ( ( p @ ( esk4_3 @ esk7_0 @ esk6_0 @ esk7_0 ) )
      | ( rel_s4 @ X3 @ ( esk4_3 @ esk3_0 @ X10 @ X3 ) )
      | ~ ( rel_s4 @ esk3_0 @ X3 )
      | ~ ( exists_in_world @ X10 @ esk3_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_34])]) ).

thf(c_0_54,negated_conjecture,
    ! [X3: $i] :
      ( ( rel_s4 @ X3 @ esk8_0 )
      | ~ ( rel_s4 @ X3 @ esk3_0 ) ),
    inference(spm,[status(thm)],[c_0_29,c_0_52]) ).

thf(c_0_55,plain,
    ! [X51: $i] : ( exists_in_world @ ( esk1_1 @ X51 ) @ X51 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[nonempty_ax])]) ).

thf(c_0_56,negated_conjecture,
    ! [X16: $i,X7: $i,X10: mu,X3: $i] :
      ( ( big_r @ X10 @ X7 )
      | ( p @ X16 )
      | ~ ( rel_s4 @ X3 @ X7 )
      | ~ ( rel_s4 @ X3 @ X16 )
      | ~ ( exists_in_world @ X10 @ X3 )
      | ~ ( rel_s4 @ esk3_0 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

thf(c_0_57,negated_conjecture,
    ! [X10: mu] :
      ( ( rel_s4 @ esk8_0 @ ( esk4_3 @ esk3_0 @ X10 @ esk8_0 ) )
      | ( p @ ( esk4_3 @ esk7_0 @ esk6_0 @ esk7_0 ) )
      | ~ ( exists_in_world @ X10 @ esk3_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_37])]) ).

thf(c_0_58,plain,
    ! [X3: $i] : ( exists_in_world @ ( esk1_1 @ X3 ) @ X3 ),
    inference(split_conjunct,[status(thm)],[c_0_55]) ).

thf(c_0_59,negated_conjecture,
    ! [X3: $i,X7: $i,X10: mu] :
      ( ( big_r @ X10 @ X3 )
      | ( p @ X7 )
      | ~ ( rel_s4 @ esk8_0 @ X7 )
      | ~ ( rel_s4 @ esk8_0 @ X3 )
      | ~ ( exists_in_world @ X10 @ esk8_0 ) ),
    inference(spm,[status(thm)],[c_0_56,c_0_52]) ).

thf(c_0_60,negated_conjecture,
    ( ( rel_s4 @ esk8_0 @ ( esk4_3 @ esk3_0 @ ( esk1_1 @ esk3_0 ) @ esk8_0 ) )
    | ( p @ ( esk4_3 @ esk7_0 @ esk6_0 @ esk7_0 ) ) ),
    inference(spm,[status(thm)],[c_0_57,c_0_58]) ).

thf(c_0_61,negated_conjecture,
    rel_s4 @ esk8_0 @ esk10_0,
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

thf(c_0_62,negated_conjecture,
    ! [X3: $i,X7: $i,X10: mu] :
      ( ( rel_s4 @ X3 @ ( esk4_3 @ esk5_0 @ X10 @ X3 ) )
      | ( p @ X7 )
      | ~ ( rel_s4 @ esk5_0 @ X7 )
      | ~ ( rel_s4 @ esk5_0 @ X3 )
      | ~ ( exists_in_world @ X10 @ esk5_0 ) ),
    inference(spm,[status(thm)],[c_0_48,c_0_34]) ).

thf(c_0_63,negated_conjecture,
    ! [X3: $i,X10: mu] :
      ( ( p @ ( esk4_3 @ esk3_0 @ ( esk1_1 @ esk3_0 ) @ esk8_0 ) )
      | ( p @ ( esk4_3 @ esk7_0 @ esk6_0 @ esk7_0 ) )
      | ( big_r @ X10 @ X3 )
      | ~ ( rel_s4 @ esk8_0 @ X3 )
      | ~ ( exists_in_world @ X10 @ esk8_0 ) ),
    inference(spm,[status(thm)],[c_0_59,c_0_60]) ).

thf(c_0_64,negated_conjecture,
    ! [X3: $i] :
      ( ( rel_s4 @ X3 @ esk10_0 )
      | ~ ( rel_s4 @ X3 @ esk8_0 ) ),
    inference(spm,[status(thm)],[c_0_29,c_0_61]) ).

thf(c_0_65,negated_conjecture,
    ! [X3: $i,X10: mu] :
      ( ( p @ ( esk4_3 @ esk7_0 @ esk6_0 @ esk7_0 ) )
      | ( rel_s4 @ X3 @ ( esk4_3 @ esk5_0 @ X10 @ X3 ) )
      | ~ ( rel_s4 @ esk5_0 @ X3 )
      | ~ ( exists_in_world @ X10 @ esk5_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_47]),c_0_30])]) ).

thf(c_0_66,negated_conjecture,
    ! [X10: mu] :
      ( ( p @ ( esk4_3 @ esk3_0 @ ( esk1_1 @ esk3_0 ) @ esk8_0 ) )
      | ( p @ ( esk4_3 @ esk7_0 @ esk6_0 @ esk7_0 ) )
      | ( big_r @ X10 @ esk10_0 )
      | ~ ( exists_in_world @ X10 @ esk8_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_37])]) ).

thf(c_0_67,negated_conjecture,
    exists_in_world @ esk9_0 @ esk8_0,
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

thf(c_0_68,negated_conjecture,
    ~ ( big_r @ esk9_0 @ esk10_0 ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

thf(c_0_69,negated_conjecture,
    ! [X10: mu] :
      ( ( rel_s4 @ esk7_0 @ ( esk4_3 @ esk5_0 @ X10 @ esk7_0 ) )
      | ( p @ ( esk4_3 @ esk7_0 @ esk6_0 @ esk7_0 ) )
      | ~ ( exists_in_world @ X10 @ esk5_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_33]),c_0_37])]) ).

thf(c_0_70,negated_conjecture,
    ! [X16: $i,X7: $i,X10: mu,X3: $i] :
      ( ( p @ X16 )
      | ~ ( p @ ( esk4_3 @ X3 @ X10 @ X7 ) )
      | ~ ( rel_s4 @ X3 @ X7 )
      | ~ ( rel_s4 @ X3 @ X16 )
      | ~ ( exists_in_world @ X10 @ X3 )
      | ~ ( rel_s4 @ esk3_0 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

thf(c_0_71,negated_conjecture,
    ( ( p @ ( esk4_3 @ esk3_0 @ ( esk1_1 @ esk3_0 ) @ esk8_0 ) )
    | ( p @ ( esk4_3 @ esk7_0 @ esk6_0 @ esk7_0 ) ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]) ).

thf(c_0_72,negated_conjecture,
    ! [X16: $i,X7: $i,X10: mu,X3: $i] :
      ( ( big_q @ X10 @ X16 )
      | ~ ( p @ ( esk4_3 @ X3 @ X10 @ X7 ) )
      | ~ ( rel_s4 @ X3 @ X7 )
      | ~ ( rel_s4 @ X3 @ X16 )
      | ~ ( exists_in_world @ X10 @ X3 )
      | ~ ( rel_s4 @ esk3_0 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

thf(c_0_73,negated_conjecture,
    ( ( rel_s4 @ esk7_0 @ ( esk4_3 @ esk5_0 @ esk6_0 @ esk7_0 ) )
    | ( p @ ( esk4_3 @ esk7_0 @ esk6_0 @ esk7_0 ) ) ),
    inference(spm,[status(thm)],[c_0_69,c_0_44]) ).

thf(c_0_74,negated_conjecture,
    ! [X3: $i] :
      ( ( p @ ( esk4_3 @ esk7_0 @ esk6_0 @ esk7_0 ) )
      | ( p @ X3 )
      | ~ ( rel_s4 @ esk3_0 @ X3 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_37]),c_0_52]),c_0_58])]) ).

thf(c_0_75,negated_conjecture,
    ! [X3: $i] :
      ( ( rel_s4 @ esk7_0 @ ( esk4_3 @ esk5_0 @ esk6_0 @ esk7_0 ) )
      | ( big_q @ esk6_0 @ X3 )
      | ~ ( rel_s4 @ esk3_0 @ esk7_0 )
      | ~ ( exists_in_world @ esk6_0 @ esk7_0 )
      | ~ ( rel_s4 @ esk7_0 @ X3 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_37])]) ).

thf(c_0_76,negated_conjecture,
    p @ ( esk4_3 @ esk7_0 @ esk6_0 @ esk7_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_51]),c_0_34])]) ).

thf(c_0_77,negated_conjecture,
    ! [X3: $i] :
      ( ( rel_s4 @ esk7_0 @ ( esk4_3 @ esk5_0 @ esk6_0 @ esk7_0 ) )
      | ( big_q @ esk6_0 @ X3 )
      | ~ ( exists_in_world @ esk6_0 @ esk7_0 )
      | ~ ( rel_s4 @ esk7_0 @ X3 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_33]),c_0_34])]) ).

thf(c_0_78,negated_conjecture,
    ! [X3: $i] :
      ( ( p @ X3 )
      | ~ ( rel_s4 @ esk3_0 @ esk7_0 )
      | ~ ( exists_in_world @ esk6_0 @ esk7_0 )
      | ~ ( rel_s4 @ esk7_0 @ X3 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_76]),c_0_37])]) ).

thf(c_0_79,negated_conjecture,
    ! [X3: $i] :
      ( ( rel_s4 @ esk7_0 @ ( esk4_3 @ esk5_0 @ esk6_0 @ esk7_0 ) )
      | ( big_q @ esk6_0 @ X3 )
      | ~ ( rel_s4 @ esk7_0 @ X3 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_42]),c_0_44])]) ).

thf(c_0_80,negated_conjecture,
    ! [X3: $i] :
      ( ( p @ X3 )
      | ~ ( exists_in_world @ esk6_0 @ esk7_0 )
      | ~ ( rel_s4 @ esk7_0 @ X3 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_33]),c_0_34])]) ).

thf(c_0_81,negated_conjecture,
    rel_s4 @ esk7_0 @ ( esk4_3 @ esk5_0 @ esk6_0 @ esk7_0 ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_37]),c_0_45]) ).

thf(c_0_82,negated_conjecture,
    ! [X3: $i] :
      ( ( p @ X3 )
      | ~ ( rel_s4 @ esk7_0 @ X3 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_42]),c_0_44])]) ).

thf(c_0_83,negated_conjecture,
    ! [X3: $i] :
      ( ( rel_s4 @ X3 @ ( esk4_3 @ esk5_0 @ esk6_0 @ esk7_0 ) )
      | ~ ( rel_s4 @ X3 @ esk7_0 ) ),
    inference(spm,[status(thm)],[c_0_29,c_0_81]) ).

thf(c_0_84,negated_conjecture,
    p @ ( esk4_3 @ esk5_0 @ esk6_0 @ esk7_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_37])]) ).

thf(c_0_85,negated_conjecture,
    ! [X3: $i] :
      ( ( big_q @ esk6_0 @ X3 )
      | ~ ( rel_s4 @ esk5_0 @ X3 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_84]),c_0_34]),c_0_30]),c_0_44])]) ).

thf(c_0_86,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_85]),c_0_30])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SYN367^7 : TPTP v8.2.0. Released v5.5.0.
% 0.03/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n024.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon May 20 14:28:38 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.20/0.47  Running higher-order theorem proving
% 0.20/0.47  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
% 13.43/2.23  # Version: 3.1.0-ho
% 13.43/2.23  # Preprocessing class: HSMSSMSSMLMNHSN.
% 13.43/2.23  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.43/2.23  # Starting ho_unfolding_3 with 1500s (5) cores
% 13.43/2.23  # Starting ehoh_best2_full_lfho with 300s (1) cores
% 13.43/2.23  # Starting almost_fo_3_lam with 300s (1) cores
% 13.43/2.23  # Starting post_as_ho1 with 300s (1) cores
% 13.43/2.23  # ho_unfolding_3 with pid 6972 completed with status 0
% 13.43/2.23  # Result found by ho_unfolding_3
% 13.43/2.23  # Preprocessing class: HSMSSMSSMLMNHSN.
% 13.43/2.23  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.43/2.23  # Starting ho_unfolding_3 with 1500s (5) cores
% 13.43/2.23  # No SInE strategy applied
% 13.43/2.23  # Search class: HGUNS-FFSM32-SHSSMFNN
% 13.43/2.23  # partial match(2): HGHNS-FFMM32-SHSSMFNN
% 13.43/2.23  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 13.43/2.23  # Starting new_ho_10 with 811s (1) cores
% 13.43/2.23  # Starting ho_unfolding_3 with 151s (1) cores
% 13.43/2.23  # Starting sh4l with 136s (1) cores
% 13.43/2.23  # Starting lpo8_s with 136s (1) cores
% 13.43/2.23  # Starting full_lambda_8 with 136s (1) cores
% 13.43/2.23  # lpo8_s with pid 6982 completed with status 0
% 13.43/2.23  # Result found by lpo8_s
% 13.43/2.23  # Preprocessing class: HSMSSMSSMLMNHSN.
% 13.43/2.23  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.43/2.23  # Starting ho_unfolding_3 with 1500s (5) cores
% 13.43/2.23  # No SInE strategy applied
% 13.43/2.23  # Search class: HGUNS-FFSM32-SHSSMFNN
% 13.43/2.23  # partial match(2): HGHNS-FFMM32-SHSSMFNN
% 13.43/2.23  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 13.43/2.23  # Starting new_ho_10 with 811s (1) cores
% 13.43/2.23  # Starting ho_unfolding_3 with 151s (1) cores
% 13.43/2.23  # Starting sh4l with 136s (1) cores
% 13.43/2.23  # Starting lpo8_s with 136s (1) cores
% 13.43/2.23  # Preprocessing time       : 0.003 s
% 13.43/2.23  # Presaturation interreduction done
% 13.43/2.23  
% 13.43/2.23  # Proof found!
% 13.43/2.23  # SZS status Theorem
% 13.43/2.23  # SZS output start CNFRefutation
% See solution above
% 13.43/2.23  # Parsed axioms                        : 76
% 13.43/2.23  # Removed by relevancy pruning/SinE    : 0
% 13.43/2.23  # Initial clauses                      : 58
% 13.43/2.23  # Removed in clause preprocessing      : 39
% 13.43/2.23  # Initial clauses in saturation        : 19
% 13.43/2.23  # Processed clauses                    : 13494
% 13.43/2.23  # ...of these trivial                  : 24
% 13.43/2.23  # ...subsumed                          : 6909
% 13.43/2.23  # ...remaining for further processing  : 6561
% 13.43/2.23  # Other redundant clauses eliminated   : 0
% 13.43/2.23  # Clauses deleted for lack of memory   : 0
% 13.43/2.23  # Backward-subsumed                    : 568
% 13.43/2.23  # Backward-rewritten                   : 3166
% 13.43/2.23  # Generated clauses                    : 50386
% 13.43/2.23  # ...of the previous two non-redundant : 49970
% 13.43/2.23  # ...aggressively subsumed             : 0
% 13.43/2.23  # Contextual simplify-reflections      : 0
% 13.43/2.23  # Paramodulations                      : 50386
% 13.43/2.23  # Factorizations                       : 0
% 13.43/2.23  # NegExts                              : 0
% 13.43/2.23  # Equation resolutions                 : 0
% 13.43/2.23  # Disequality decompositions           : 0
% 13.43/2.23  # Total rewrite steps                  : 5698
% 13.43/2.23  # ...of those cached                   : 5650
% 13.43/2.23  # Propositional unsat checks           : 0
% 13.43/2.23  #    Propositional check models        : 0
% 13.43/2.23  #    Propositional check unsatisfiable : 0
% 13.43/2.23  #    Propositional clauses             : 0
% 13.43/2.23  #    Propositional clauses after purity: 0
% 13.43/2.23  #    Propositional unsat core size     : 0
% 13.43/2.23  #    Propositional preprocessing time  : 0.000
% 13.43/2.23  #    Propositional encoding time       : 0.000
% 13.43/2.23  #    Propositional solver time         : 0.000
% 13.43/2.23  #    Success case prop preproc time    : 0.000
% 13.43/2.23  #    Success case prop encoding time   : 0.000
% 13.43/2.23  #    Success case prop solver time     : 0.000
% 13.43/2.23  # Current number of processed clauses  : 2808
% 13.43/2.23  #    Positive orientable unit clauses  : 52
% 13.43/2.23  #    Positive unorientable unit clauses: 0
% 13.43/2.23  #    Negative unit clauses             : 2
% 13.43/2.23  #    Non-unit-clauses                  : 2754
% 13.43/2.23  # Current number of unprocessed clauses: 34902
% 13.43/2.23  # ...number of literals in the above   : 154065
% 13.43/2.23  # Current number of archived formulas  : 0
% 13.43/2.23  # Current number of archived clauses   : 3753
% 13.43/2.23  # Clause-clause subsumption calls (NU) : 2631521
% 13.43/2.23  # Rec. Clause-clause subsumption calls : 1326342
% 13.43/2.23  # Non-unit clause-clause subsumptions  : 7409
% 13.43/2.23  # Unit Clause-clause subsumption calls : 12729
% 13.43/2.23  # Rewrite failures with RHS unbound    : 0
% 13.43/2.23  # BW rewrite match attempts            : 84
% 13.43/2.23  # BW rewrite match successes           : 32
% 13.43/2.23  # Condensation attempts                : 13494
% 13.43/2.23  # Condensation successes               : 0
% 13.43/2.23  # Termbank termtop insertions          : 1175334
% 13.43/2.23  # Search garbage collected termcells   : 1131
% 13.43/2.23  
% 13.43/2.23  # -------------------------------------------------
% 13.43/2.23  # User time                : 1.694 s
% 13.43/2.23  # System time              : 0.026 s
% 13.43/2.23  # Total time               : 1.720 s
% 13.43/2.23  # Maximum resident set size: 2076 pages
% 13.43/2.23  
% 13.43/2.23  # -------------------------------------------------
% 13.43/2.23  # User time                : 8.510 s
% 13.43/2.23  # System time              : 0.123 s
% 13.43/2.23  # Total time               : 8.633 s
% 13.43/2.23  # Maximum resident set size: 1808 pages
% 13.43/2.23  % E---3.1 exiting
% 14.06/2.23  % E exiting
%------------------------------------------------------------------------------