TSTP Solution File: SYO443^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SYO443^1 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n016.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 08:46:01 EDT 2024

% Result   : Theorem 0.14s 0.43s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   32
% Syntax   : Number of formulae    :  106 (  37 unt;  18 typ;   0 def)
%            Number of atoms       :  309 (  23 equ;   0 cnn)
%            Maximal formula atoms :   80 (   3 avg)
%            Number of connectives :  776 ( 131   ~; 158   |;  27   &; 454   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   32 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   81 (  81   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   20 (  18 usr;   6 con; 0-3 aty)
%            Number of variables   :  121 (  46   ^  75   !;   0   ?; 121   :)

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

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

thf(decl_26,type,
    mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).

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

thf(decl_29,type,
    mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).

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

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

thf(decl_42,type,
    mtransitive: ( $i > $i > $o ) > $o ).

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

thf(decl_53,type,
    rel_s5: $i > $i > $o ).

thf(decl_54,type,
    mbox_s5: ( $i > $o ) > $i > $o ).

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

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

thf(decl_58,type,
    esk1_0: $i ).

thf(decl_59,type,
    esk2_0: $i ).

thf(decl_60,type,
    esk3_0: $i ).

thf(decl_61,type,
    esk4_0: $i ).

thf(decl_62,type,
    esk5_0: $i ).

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

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

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

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

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

thf(mbox_s5,axiom,
    ( mbox_s5
    = ( ^ [X6: $i > $o,X3: $i] :
        ! [X14: $i] :
          ( ~ ( rel_s5 @ X3 @ X14 )
          | ( X6 @ X14 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).

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

thf(a2,axiom,
    mtransitive @ rel_s5,
    file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a2) ).

thf(prove,conjecture,
    mvalid @ ( mequiv @ ( mbox_s5 @ ( mor @ ( mnot @ p ) @ ( mbox_s5 @ q ) ) ) @ ( mor @ ( mbox_s5 @ ( mnot @ p ) ) @ ( mbox_s5 @ q ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).

thf(a3,axiom,
    msymmetric @ rel_s5,
    file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a3) ).

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

thf(a1,axiom,
    mreflexive @ rel_s5,
    file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a1) ).

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

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

thf(c_0_22,plain,
    ( mequiv
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ~ ( ~ ( ~ ( Z0 @ Z2 )
                | ( Z1 @ Z2 ) )
            | ~ ( ~ ( Z1 @ Z2 )
                | ( Z0 @ Z2 ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).

thf(c_0_23,plain,
    ( mvalid
    = ( ^ [Z0: $i > $o] :
        ! [X3: $i] : ( Z0 @ X3 ) ) ),
    inference(fof_simplification,[status(thm)],[mvalid]) ).

thf(c_0_24,plain,
    ( mbox_s5
    = ( ^ [Z0: $i > $o,Z1: $i] :
        ! [X14: $i] :
          ( ~ ( rel_s5 @ Z1 @ X14 )
          | ( Z0 @ X14 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mbox_s5]) ).

thf(c_0_25,plain,
    ( msymmetric
    = ( ^ [Z0: $i > $i > $o] :
        ! [X15: $i,X16: $i] :
          ( ( Z0 @ X15 @ X16 )
         => ( Z0 @ X16 @ X15 ) ) ) ),
    inference(fof_simplification,[status(thm)],[msymmetric]) ).

thf(c_0_26,plain,
    ! [X23: $i,X24: $i,X25: $i] :
      ( ( ( rel_s5 @ X23 @ X24 )
        & ( rel_s5 @ X24 @ X25 ) )
     => ( rel_s5 @ X23 @ X25 ) ),
    inference(apply_def,[status(thm)],[a2,c_0_21]) ).

thf(c_0_27,negated_conjecture,
    ~ ! [X32: $i] :
        ~ ( ~ ( ~ ! [X29: $i] :
                    ( ~ ( rel_s5 @ X32 @ X29 )
                    | ~ ( p @ X29 )
                    | ! [X28: $i] :
                        ( ~ ( rel_s5 @ X29 @ X28 )
                        | ( q @ X28 ) ) )
              | ! [X30: $i] :
                  ( ~ ( rel_s5 @ X32 @ X30 )
                  | ~ ( p @ X30 ) )
              | ! [X31: $i] :
                  ( ~ ( rel_s5 @ X32 @ X31 )
                  | ( q @ X31 ) ) )
          | ~ ( ~ ( ! [X30: $i] :
                      ( ~ ( rel_s5 @ X32 @ X30 )
                      | ~ ( p @ X30 ) )
                  | ! [X31: $i] :
                      ( ~ ( rel_s5 @ X32 @ X31 )
                      | ( q @ X31 ) ) )
              | ! [X29: $i] :
                  ( ~ ( rel_s5 @ X32 @ X29 )
                  | ~ ( p @ X29 )
                  | ! [X28: $i] :
                      ( ~ ( rel_s5 @ X29 @ X28 )
                      | ( q @ X28 ) ) ) ) ),
    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(assume_negation,[status(cth)],[prove]),c_0_15]),c_0_16]),c_0_22]),c_0_23]),c_0_24])]) ).

thf(c_0_28,plain,
    ! [X26: $i,X27: $i] :
      ( ( rel_s5 @ X26 @ X27 )
     => ( rel_s5 @ X27 @ X26 ) ),
    inference(apply_def,[status(thm)],[a3,c_0_25]) ).

thf(c_0_29,plain,
    ! [X34: $i,X35: $i,X36: $i] :
      ( ~ ( rel_s5 @ X34 @ X35 )
      | ~ ( rel_s5 @ X35 @ X36 )
      | ( rel_s5 @ X34 @ X36 ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])]) ).

thf(c_0_30,negated_conjecture,
    ! [X40: $i,X41: $i,X44: $i,X45: $i] :
      ( ( ~ ( rel_s5 @ esk1_0 @ X44 )
        | ~ ( p @ X44 )
        | ~ ( rel_s5 @ esk1_0 @ X45 )
        | ( q @ X45 )
        | ~ ( rel_s5 @ esk1_0 @ X40 )
        | ~ ( p @ X40 )
        | ~ ( rel_s5 @ X40 @ X41 )
        | ( q @ X41 ) )
      & ( ( rel_s5 @ esk1_0 @ esk4_0 )
        | ~ ( rel_s5 @ esk1_0 @ X40 )
        | ~ ( p @ X40 )
        | ~ ( rel_s5 @ X40 @ X41 )
        | ( q @ X41 ) )
      & ( ( p @ esk4_0 )
        | ~ ( rel_s5 @ esk1_0 @ X40 )
        | ~ ( p @ X40 )
        | ~ ( rel_s5 @ X40 @ X41 )
        | ( q @ X41 ) )
      & ( ( rel_s5 @ esk4_0 @ esk5_0 )
        | ~ ( rel_s5 @ esk1_0 @ X40 )
        | ~ ( p @ X40 )
        | ~ ( rel_s5 @ X40 @ X41 )
        | ( q @ X41 ) )
      & ( ~ ( q @ esk5_0 )
        | ~ ( rel_s5 @ esk1_0 @ X40 )
        | ~ ( p @ X40 )
        | ~ ( rel_s5 @ X40 @ X41 )
        | ( q @ X41 ) )
      & ( ~ ( rel_s5 @ esk1_0 @ X44 )
        | ~ ( p @ X44 )
        | ~ ( rel_s5 @ esk1_0 @ X45 )
        | ( q @ X45 )
        | ( rel_s5 @ esk1_0 @ esk2_0 ) )
      & ( ( rel_s5 @ esk1_0 @ esk4_0 )
        | ( rel_s5 @ esk1_0 @ esk2_0 ) )
      & ( ( p @ esk4_0 )
        | ( rel_s5 @ esk1_0 @ esk2_0 ) )
      & ( ( rel_s5 @ esk4_0 @ esk5_0 )
        | ( rel_s5 @ esk1_0 @ esk2_0 ) )
      & ( ~ ( q @ esk5_0 )
        | ( rel_s5 @ esk1_0 @ esk2_0 ) )
      & ( ~ ( rel_s5 @ esk1_0 @ X44 )
        | ~ ( p @ X44 )
        | ~ ( rel_s5 @ esk1_0 @ X45 )
        | ( q @ X45 )
        | ( p @ esk2_0 ) )
      & ( ( rel_s5 @ esk1_0 @ esk4_0 )
        | ( p @ esk2_0 ) )
      & ( ( p @ esk4_0 )
        | ( p @ esk2_0 ) )
      & ( ( rel_s5 @ esk4_0 @ esk5_0 )
        | ( p @ esk2_0 ) )
      & ( ~ ( q @ esk5_0 )
        | ( p @ esk2_0 ) )
      & ( ~ ( rel_s5 @ esk1_0 @ X44 )
        | ~ ( p @ X44 )
        | ~ ( rel_s5 @ esk1_0 @ X45 )
        | ( q @ X45 )
        | ( rel_s5 @ esk1_0 @ esk3_0 ) )
      & ( ( rel_s5 @ esk1_0 @ esk4_0 )
        | ( rel_s5 @ esk1_0 @ esk3_0 ) )
      & ( ( p @ esk4_0 )
        | ( rel_s5 @ esk1_0 @ esk3_0 ) )
      & ( ( rel_s5 @ esk4_0 @ esk5_0 )
        | ( rel_s5 @ esk1_0 @ esk3_0 ) )
      & ( ~ ( q @ esk5_0 )
        | ( rel_s5 @ esk1_0 @ esk3_0 ) )
      & ( ~ ( rel_s5 @ esk1_0 @ X44 )
        | ~ ( p @ X44 )
        | ~ ( rel_s5 @ esk1_0 @ X45 )
        | ( q @ X45 )
        | ~ ( q @ esk3_0 ) )
      & ( ( rel_s5 @ esk1_0 @ esk4_0 )
        | ~ ( q @ esk3_0 ) )
      & ( ( p @ esk4_0 )
        | ~ ( q @ esk3_0 ) )
      & ( ( rel_s5 @ esk4_0 @ esk5_0 )
        | ~ ( q @ esk3_0 ) )
      & ( ~ ( q @ esk5_0 )
        | ~ ( q @ esk3_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_27])])])])])]) ).

thf(c_0_31,plain,
    ! [X37: $i,X38: $i] :
      ( ~ ( rel_s5 @ X37 @ X38 )
      | ( rel_s5 @ X38 @ X37 ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).

thf(c_0_32,plain,
    ! [X14: $i,X3: $i,X15: $i] :
      ( ( rel_s5 @ X3 @ X15 )
      | ~ ( rel_s5 @ X3 @ X14 )
      | ~ ( rel_s5 @ X14 @ X15 ) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

thf(c_0_33,negated_conjecture,
    ( ( rel_s5 @ esk1_0 @ esk4_0 )
    | ( rel_s5 @ esk1_0 @ esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_34,plain,
    ! [X3: $i,X14: $i] :
      ( ( rel_s5 @ X14 @ X3 )
      | ~ ( rel_s5 @ X3 @ X14 ) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

thf(c_0_35,negated_conjecture,
    ( ( rel_s5 @ esk1_0 @ esk4_0 )
    | ( rel_s5 @ esk1_0 @ esk3_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_36,negated_conjecture,
    ! [X3: $i] :
      ( ( rel_s5 @ esk1_0 @ esk4_0 )
      | ( rel_s5 @ X3 @ esk2_0 )
      | ~ ( rel_s5 @ X3 @ esk1_0 ) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

thf(c_0_37,negated_conjecture,
    ( ( rel_s5 @ esk1_0 @ esk4_0 )
    | ( rel_s5 @ esk3_0 @ esk1_0 ) ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

thf(c_0_38,negated_conjecture,
    ( ( p @ esk4_0 )
    | ( rel_s5 @ esk1_0 @ esk3_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_39,negated_conjecture,
    ( ( p @ esk4_0 )
    | ( rel_s5 @ esk1_0 @ esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_40,negated_conjecture,
    ! [X3: $i,X14: $i] :
      ( ( rel_s5 @ esk1_0 @ esk4_0 )
      | ( q @ X14 )
      | ~ ( rel_s5 @ esk1_0 @ X3 )
      | ~ ( p @ X3 )
      | ~ ( rel_s5 @ X3 @ X14 ) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_41,negated_conjecture,
    ( ( rel_s5 @ esk1_0 @ esk4_0 )
    | ( p @ esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_42,negated_conjecture,
    ( ( rel_s5 @ esk3_0 @ esk2_0 )
    | ( rel_s5 @ esk1_0 @ esk4_0 ) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

thf(c_0_43,negated_conjecture,
    ! [X3: $i,X14: $i] :
      ( ( p @ esk4_0 )
      | ( q @ X14 )
      | ~ ( rel_s5 @ esk1_0 @ X3 )
      | ~ ( p @ X3 )
      | ~ ( rel_s5 @ X3 @ X14 ) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_44,negated_conjecture,
    ( ( p @ esk4_0 )
    | ( p @ esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_45,negated_conjecture,
    ! [X3: $i] :
      ( ( rel_s5 @ X3 @ esk3_0 )
      | ( p @ esk4_0 )
      | ~ ( rel_s5 @ X3 @ esk1_0 ) ),
    inference(spm,[status(thm)],[c_0_32,c_0_38]) ).

thf(c_0_46,negated_conjecture,
    ( ( rel_s5 @ esk2_0 @ esk1_0 )
    | ( p @ esk4_0 ) ),
    inference(spm,[status(thm)],[c_0_34,c_0_39]) ).

thf(c_0_47,negated_conjecture,
    ! [X3: $i] :
      ( ( rel_s5 @ esk1_0 @ esk4_0 )
      | ( q @ X3 )
      | ~ ( rel_s5 @ esk2_0 @ X3 ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_33]),c_0_41]) ).

thf(c_0_48,negated_conjecture,
    ( ( rel_s5 @ esk1_0 @ esk4_0 )
    | ( rel_s5 @ esk2_0 @ esk3_0 ) ),
    inference(spm,[status(thm)],[c_0_34,c_0_42]) ).

thf(c_0_49,negated_conjecture,
    ( ( rel_s5 @ esk1_0 @ esk4_0 )
    | ~ ( q @ esk3_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_50,negated_conjecture,
    ! [X3: $i] :
      ( ( p @ esk4_0 )
      | ( q @ X3 )
      | ~ ( rel_s5 @ esk2_0 @ X3 ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_39]),c_0_44]) ).

thf(c_0_51,negated_conjecture,
    ( ( rel_s5 @ esk2_0 @ esk3_0 )
    | ( p @ esk4_0 ) ),
    inference(spm,[status(thm)],[c_0_45,c_0_46]) ).

thf(c_0_52,negated_conjecture,
    ( ( p @ esk4_0 )
    | ~ ( q @ esk3_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_53,negated_conjecture,
    ( ( rel_s5 @ esk4_0 @ esk5_0 )
    | ( rel_s5 @ esk1_0 @ esk3_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_54,negated_conjecture,
    rel_s5 @ esk1_0 @ esk4_0,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).

thf(c_0_55,negated_conjecture,
    ! [X3: $i,X14: $i] :
      ( ( rel_s5 @ esk4_0 @ esk5_0 )
      | ( q @ X14 )
      | ~ ( rel_s5 @ esk1_0 @ X3 )
      | ~ ( p @ X3 )
      | ~ ( rel_s5 @ X3 @ X14 ) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_56,negated_conjecture,
    p @ esk4_0,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).

thf(c_0_57,negated_conjecture,
    ! [X3: $i] :
      ( ( rel_s5 @ esk4_0 @ esk5_0 )
      | ( rel_s5 @ X3 @ esk3_0 )
      | ~ ( rel_s5 @ X3 @ esk1_0 ) ),
    inference(spm,[status(thm)],[c_0_32,c_0_53]) ).

thf(c_0_58,negated_conjecture,
    rel_s5 @ esk4_0 @ esk1_0,
    inference(spm,[status(thm)],[c_0_34,c_0_54]) ).

thf(c_0_59,negated_conjecture,
    ! [X3: $i] :
      ( ( rel_s5 @ esk4_0 @ esk5_0 )
      | ( q @ X3 )
      | ~ ( rel_s5 @ esk4_0 @ X3 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_54]),c_0_56])]) ).

thf(c_0_60,negated_conjecture,
    ( ( rel_s5 @ esk4_0 @ esk3_0 )
    | ( rel_s5 @ esk4_0 @ esk5_0 ) ),
    inference(spm,[status(thm)],[c_0_57,c_0_58]) ).

thf(c_0_61,negated_conjecture,
    ( ( rel_s5 @ esk4_0 @ esk5_0 )
    | ~ ( q @ esk3_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_62,plain,
    ( mreflexive
    = ( ^ [Z0: $i > $i > $o] :
        ! [X15: $i] : ( Z0 @ X15 @ X15 ) ) ),
    inference(fof_simplification,[status(thm)],[mreflexive]) ).

thf(c_0_63,negated_conjecture,
    rel_s5 @ esk4_0 @ esk5_0,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).

thf(c_0_64,negated_conjecture,
    ! [X14: $i,X15: $i,X3: $i,X16: $i] :
      ( ( q @ X14 )
      | ( q @ X16 )
      | ~ ( rel_s5 @ esk1_0 @ X3 )
      | ~ ( p @ X3 )
      | ~ ( rel_s5 @ esk1_0 @ X14 )
      | ~ ( rel_s5 @ esk1_0 @ X15 )
      | ~ ( p @ X15 )
      | ~ ( rel_s5 @ X15 @ X16 ) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_65,plain,
    ! [X22: $i] : ( rel_s5 @ X22 @ X22 ),
    inference(apply_def,[status(thm)],[a1,c_0_62]) ).

thf(c_0_66,negated_conjecture,
    ! [X3: $i] :
      ( ( rel_s5 @ X3 @ esk1_0 )
      | ~ ( rel_s5 @ X3 @ esk4_0 ) ),
    inference(spm,[status(thm)],[c_0_32,c_0_58]) ).

thf(c_0_67,negated_conjecture,
    rel_s5 @ esk5_0 @ esk4_0,
    inference(spm,[status(thm)],[c_0_34,c_0_63]) ).

thf(c_0_68,negated_conjecture,
    ! [X14: $i,X3: $i,X15: $i] :
      ( ( q @ X3 )
      | ( q @ X14 )
      | ~ ( rel_s5 @ esk1_0 @ X15 )
      | ~ ( rel_s5 @ esk1_0 @ X3 )
      | ~ ( rel_s5 @ X15 @ X14 )
      | ~ ( p @ X15 ) ),
    inference(condense,[status(thm)],[c_0_64]) ).

thf(c_0_69,negated_conjecture,
    ( ( rel_s5 @ esk1_0 @ esk3_0 )
    | ~ ( q @ esk5_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_70,plain,
    ! [X33: $i] : ( rel_s5 @ X33 @ X33 ),
    inference(variable_rename,[status(thm)],[c_0_65]) ).

thf(c_0_71,negated_conjecture,
    rel_s5 @ esk5_0 @ esk1_0,
    inference(spm,[status(thm)],[c_0_66,c_0_67]) ).

thf(c_0_72,negated_conjecture,
    ! [X3: $i,X14: $i] :
      ( ( q @ X3 )
      | ( q @ X14 )
      | ~ ( rel_s5 @ esk1_0 @ X3 )
      | ~ ( rel_s5 @ esk4_0 @ X14 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_54]),c_0_56])]) ).

thf(c_0_73,negated_conjecture,
    ! [X3: $i] :
      ( ( rel_s5 @ X3 @ esk3_0 )
      | ~ ( rel_s5 @ X3 @ esk1_0 )
      | ~ ( q @ esk5_0 ) ),
    inference(spm,[status(thm)],[c_0_32,c_0_69]) ).

thf(c_0_74,plain,
    ! [X3: $i] : ( rel_s5 @ X3 @ X3 ),
    inference(split_conjunct,[status(thm)],[c_0_70]) ).

thf(c_0_75,negated_conjecture,
    ( ~ ( q @ esk5_0 )
    | ~ ( q @ esk3_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_76,negated_conjecture,
    ! [X3: $i] :
      ( ( rel_s5 @ X3 @ esk4_0 )
      | ~ ( rel_s5 @ X3 @ esk1_0 ) ),
    inference(spm,[status(thm)],[c_0_32,c_0_54]) ).

thf(c_0_77,negated_conjecture,
    rel_s5 @ esk1_0 @ esk5_0,
    inference(spm,[status(thm)],[c_0_34,c_0_71]) ).

thf(c_0_78,negated_conjecture,
    ! [X3: $i] :
      ( ( q @ X3 )
      | ~ ( rel_s5 @ esk4_0 @ X3 )
      | ~ ( q @ esk5_0 ) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74])]),c_0_75]) ).

thf(c_0_79,negated_conjecture,
    ! [X3: $i] :
      ( ( rel_s5 @ esk4_0 @ X3 )
      | ~ ( rel_s5 @ X3 @ esk1_0 ) ),
    inference(spm,[status(thm)],[c_0_34,c_0_76]) ).

thf(c_0_80,negated_conjecture,
    ( ( rel_s5 @ esk3_0 @ esk1_0 )
    | ~ ( q @ esk5_0 ) ),
    inference(spm,[status(thm)],[c_0_34,c_0_69]) ).

thf(c_0_81,negated_conjecture,
    ! [X3: $i] :
      ( ( q @ X3 )
      | ~ ( rel_s5 @ esk4_0 @ X3 ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_77]),c_0_78]) ).

thf(c_0_82,negated_conjecture,
    ! [X3: $i] :
      ( ( rel_s5 @ X3 @ esk5_0 )
      | ~ ( rel_s5 @ X3 @ esk1_0 ) ),
    inference(spm,[status(thm)],[c_0_32,c_0_77]) ).

thf(c_0_83,negated_conjecture,
    ( ( rel_s5 @ esk4_0 @ esk3_0 )
    | ~ ( q @ esk5_0 ) ),
    inference(spm,[status(thm)],[c_0_79,c_0_80]) ).

thf(c_0_84,negated_conjecture,
    q @ esk5_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_58])]) ).

thf(c_0_85,negated_conjecture,
    rel_s5 @ esk4_0 @ esk3_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_84])]) ).

thf(c_0_86,negated_conjecture,
    ~ ( q @ esk3_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_84])]) ).

thf(c_0_87,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_85]),c_0_86]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : SYO443^1 : TPTP v8.2.0. Released v4.0.0.
% 0.08/0.10  % Command    : run_E %s %d THM
% 0.09/0.30  % Computer : n016.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit   : 300
% 0.09/0.30  % WCLimit    : 300
% 0.09/0.30  % DateTime   : Mon May 20 09:03:07 EDT 2024
% 0.09/0.30  % CPUTime    : 
% 0.14/0.40  Running higher-order theorem proving
% 0.14/0.40  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
% 0.14/0.43  # Version: 3.1.0-ho
% 0.14/0.43  # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.14/0.43  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.14/0.43  # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.14/0.43  # Starting almost_fo_3_lam with 300s (1) cores
% 0.14/0.43  # Starting post_as_ho1 with 300s (1) cores
% 0.14/0.43  # ho_unfolding_3 with pid 13771 completed with status 0
% 0.14/0.43  # Result found by ho_unfolding_3
% 0.14/0.43  # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.14/0.43  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.14/0.43  # No SInE strategy applied
% 0.14/0.43  # Search class: HGHNF-FFMM00-SHSSMFNN
% 0.14/0.43  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.43  # Starting new_ho_10 with 811s (1) cores
% 0.14/0.43  # Starting ho_unfolding_3 with 151s (1) cores
% 0.14/0.43  # Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.14/0.43  # Starting lpo1_def_fix with 136s (1) cores
% 0.14/0.43  # Starting ehoh_best8_lambda with 136s (1) cores
% 0.14/0.43  # ho_unfolding_3 with pid 13778 completed with status 0
% 0.14/0.43  # Result found by ho_unfolding_3
% 0.14/0.43  # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.14/0.43  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.14/0.43  # No SInE strategy applied
% 0.14/0.43  # Search class: HGHNF-FFMM00-SHSSMFNN
% 0.14/0.43  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.43  # Starting new_ho_10 with 811s (1) cores
% 0.14/0.43  # Starting ho_unfolding_3 with 151s (1) cores
% 0.14/0.43  # Preprocessing time       : 0.001 s
% 0.14/0.43  # Presaturation interreduction done
% 0.14/0.43  
% 0.14/0.43  # Proof found!
% 0.14/0.43  # SZS status Theorem
% 0.14/0.43  # SZS output start CNFRefutation
% See solution above
% 0.14/0.43  # Parsed axioms                        : 74
% 0.14/0.43  # Removed by relevancy pruning/SinE    : 0
% 0.14/0.43  # Initial clauses                      : 65
% 0.14/0.43  # Removed in clause preprocessing      : 37
% 0.14/0.43  # Initial clauses in saturation        : 28
% 0.14/0.43  # Processed clauses                    : 238
% 0.14/0.43  # ...of these trivial                  : 4
% 0.14/0.43  # ...subsumed                          : 80
% 0.14/0.43  # ...remaining for further processing  : 154
% 0.14/0.43  # Other redundant clauses eliminated   : 0
% 0.14/0.43  # Clauses deleted for lack of memory   : 0
% 0.14/0.43  # Backward-subsumed                    : 28
% 0.14/0.43  # Backward-rewritten                   : 65
% 0.14/0.43  # Generated clauses                    : 477
% 0.14/0.43  # ...of the previous two non-redundant : 402
% 0.14/0.43  # ...aggressively subsumed             : 0
% 0.14/0.43  # Contextual simplify-reflections      : 11
% 0.14/0.43  # Paramodulations                      : 477
% 0.14/0.43  # Factorizations                       : 0
% 0.14/0.43  # NegExts                              : 0
% 0.14/0.43  # Equation resolutions                 : 0
% 0.14/0.43  # Disequality decompositions           : 0
% 0.14/0.43  # Total rewrite steps                  : 214
% 0.14/0.43  # ...of those cached                   : 196
% 0.14/0.43  # Propositional unsat checks           : 0
% 0.14/0.43  #    Propositional check models        : 0
% 0.14/0.43  #    Propositional check unsatisfiable : 0
% 0.14/0.43  #    Propositional clauses             : 0
% 0.14/0.43  #    Propositional clauses after purity: 0
% 0.14/0.43  #    Propositional unsat core size     : 0
% 0.14/0.43  #    Propositional preprocessing time  : 0.000
% 0.14/0.43  #    Propositional encoding time       : 0.000
% 0.14/0.43  #    Propositional solver time         : 0.000
% 0.14/0.43  #    Success case prop preproc time    : 0.000
% 0.14/0.43  #    Success case prop encoding time   : 0.000
% 0.14/0.43  #    Success case prop solver time     : 0.000
% 0.14/0.43  # Current number of processed clauses  : 33
% 0.14/0.43  #    Positive orientable unit clauses  : 14
% 0.14/0.43  #    Positive unorientable unit clauses: 0
% 0.14/0.43  #    Negative unit clauses             : 2
% 0.14/0.43  #    Non-unit-clauses                  : 17
% 0.14/0.43  # Current number of unprocessed clauses: 97
% 0.14/0.43  # ...number of literals in the above   : 338
% 0.14/0.43  # Current number of archived formulas  : 0
% 0.14/0.43  # Current number of archived clauses   : 121
% 0.14/0.43  # Clause-clause subsumption calls (NU) : 717
% 0.14/0.43  # Rec. Clause-clause subsumption calls : 551
% 0.14/0.43  # Non-unit clause-clause subsumptions  : 101
% 0.14/0.43  # Unit Clause-clause subsumption calls : 53
% 0.14/0.43  # Rewrite failures with RHS unbound    : 0
% 0.14/0.43  # BW rewrite match attempts            : 11
% 0.14/0.43  # BW rewrite match successes           : 10
% 0.14/0.43  # Condensation attempts                : 238
% 0.14/0.43  # Condensation successes               : 2
% 0.14/0.43  # Termbank termtop insertions          : 9370
% 0.14/0.43  # Search garbage collected termcells   : 705
% 0.14/0.43  
% 0.14/0.43  # -------------------------------------------------
% 0.14/0.43  # User time                : 0.017 s
% 0.14/0.43  # System time              : 0.003 s
% 0.14/0.43  # Total time               : 0.020 s
% 0.14/0.43  # Maximum resident set size: 1976 pages
% 0.14/0.43  
% 0.14/0.43  # -------------------------------------------------
% 0.14/0.43  # User time                : 0.080 s
% 0.14/0.43  # System time              : 0.010 s
% 0.14/0.43  # Total time               : 0.090 s
% 0.14/0.43  # Maximum resident set size: 1804 pages
% 0.14/0.43  % E---3.1 exiting
% 0.14/0.43  % E exiting
%------------------------------------------------------------------------------