%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV441^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 : Wed Sep 30 08:39:44 AM UTC 2026
% Result : Theorem 1.93s 0.55s
% Output : CNFRefutation 1.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 71 ( 44 unt; 0 typ; 0 def)
% Number of atoms : 277 ( 31 equ; 0 cnn)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 760 ( 106 ~; 115 |; 12 &; 486 @)
% ( 0 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 28 usr; 8 con; 0-3 aty)
% Number of variables : 195 ( 67 ^; 128 !; 0 ?; 195 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
individuals: $tType ).
thf(decl_29,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_30,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_32,type,
mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_34,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_38,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_42,type,
reli: $i > $i > $o ).
thf(decl_43,type,
relr: $i > $i > $o ).
thf(decl_44,type,
cs4_atom: ( $i > $o ) > $i > $o ).
thf(decl_47,type,
cs4_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_51,type,
cs4_box: ( $i > $o ) > $i > $o ).
thf(decl_53,type,
princ_inj: individuals > $i > $o ).
thf(decl_55,type,
bl_princ: ( $i > $o ) > $i > $o ).
thf(decl_58,type,
bl_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_62,type,
bl_says: individuals > ( $i > $o ) > $i > $o ).
thf(decl_63,type,
bl_valid: ( $i > $o ) > $o ).
thf(decl_65,type,
esk1_2: ( $i > $o ) > $i > $i ).
thf(decl_67,type,
esk3_2: ( $i > $o ) > $i > $i ).
thf(decl_71,type,
esk7_0: individuals ).
thf(decl_72,type,
epred1_0: $i > $o ).
thf(decl_73,type,
epred2_0: $i > $o ).
thf(decl_74,type,
esk8_0: $i ).
thf(decl_75,type,
esk9_0: $i ).
thf(decl_76,type,
esk10_3: $i > $i > $i > $i ).
thf(decl_77,type,
esk11_0: $i ).
thf(decl_78,type,
esk12_3: $i > $i > $i > $i ).
thf(decl_79,type,
esk13_0: $i ).
thf(decl_80,type,
esk14_0: $i ).
thf(decl_81,type,
esk15_0: $i ).
thf(mimpl,axiom,
( mimpl
= ( ^ [X7: $i > $o,X8: $i > $o] : ( mor @ ( mnot @ X7 ) @ X8 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.FsaYcaTQkU/E---3.1_912343.p',mimpl) ).
thf(mnot,axiom,
( mnot
= ( ^ [X2: $i > $o,X3: $i] :
~ ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.FsaYcaTQkU/E---3.1_912343.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.FsaYcaTQkU/E---3.1_912343.p',mor) ).
thf(cs4_atom,axiom,
( cs4_atom
= ( ^ [X11: $i > $o] : ( mbox @ reli @ X11 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.FsaYcaTQkU/E---3.1_912343.p',cs4_atom) ).
thf(mbox,axiom,
( mbox
= ( ^ [X10: $i > $i > $o,X11: $i > $o,X1: $i] :
! [X12: $i] :
( ( X10 @ X1 @ X12 )
=> ( X11 @ X12 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.FsaYcaTQkU/E---3.1_912343.p',mbox) ).
thf(cs4_impl,axiom,
( cs4_impl
= ( ^ [X19: $i > $o,X20: $i > $o] : ( mbox @ reli @ ( mimpl @ X19 @ X20 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.FsaYcaTQkU/E---3.1_912343.p',cs4_impl) ).
thf(cs4_box,axiom,
( cs4_box
= ( ^ [X19: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ X19 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.FsaYcaTQkU/E---3.1_912343.p',cs4_box) ).
thf(bl_princ,axiom,
( bl_princ
= ( ^ [X11: $i > $o] : ( cs4_atom @ X11 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.FsaYcaTQkU/E---3.1_912343.p',bl_princ) ).
thf(bl_impl,axiom,
( bl_impl
= ( ^ [X19: $i > $o,X20: $i > $o] : ( cs4_impl @ X19 @ X20 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.FsaYcaTQkU/E---3.1_912343.p',bl_impl) ).
thf(bl_says,axiom,
( bl_says
= ( ^ [X23: individuals,X19: $i > $o] : ( cs4_box @ ( cs4_impl @ ( bl_princ @ ( princ_inj @ X23 ) ) @ X19 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.FsaYcaTQkU/E---3.1_912343.p',bl_says) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X11: $i > $o] :
! [X15: $i] : ( X11 @ X15 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.FsaYcaTQkU/E---3.1_912343.p',mvalid) ).
thf(bl_k,conjecture,
! [X23: individuals,X19: $i > $o,X20: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_says @ X23 @ ( bl_impl @ X19 @ X20 ) ) @ ( bl_impl @ ( bl_says @ X23 @ X19 ) @ ( bl_says @ X23 @ X20 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.FsaYcaTQkU/E---3.1_912343.p',bl_k) ).
thf(bl_valid_def,axiom,
( bl_valid
= ( ^ [Z0: $i > $o] :
! [X48: $i] : ( Z0 @ X48 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.FsaYcaTQkU/E---3.1_912343.p',bl_valid_def) ).
thf(trans_axiom_i,axiom,
! [X19: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ X19 ) @ ( mbox @ reli @ ( mbox @ reli @ X19 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.FsaYcaTQkU/E---3.1_912343.p',trans_axiom_i) ).
thf(refl_axiom_i,axiom,
! [X19: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ X19 ) @ X19 ) ),
file('/export/starexec/sandbox2/tmp/tmp.FsaYcaTQkU/E---3.1_912343.p',refl_axiom_i) ).
thf(c_0_15,plain,
( mimpl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimpl]) ).
thf(c_0_16,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_17,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_18,plain,
( cs4_atom
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X32: $i] :
( ( reli @ Z1 @ X32 )
=> ( Z0 @ X32 ) ) ) ),
inference(fof_simplification,[status(thm)],[cs4_atom]) ).
thf(c_0_19,plain,
( mbox
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
! [X12: $i] :
( ( Z0 @ Z2 @ X12 )
=> ( Z1 @ X12 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox]) ).
thf(c_0_20,plain,
( cs4_impl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
! [X33: $i] :
( ( reli @ Z2 @ X33 )
=> ( ~ ( Z0 @ X33 )
| ( Z1 @ X33 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[cs4_impl]) ).
thf(c_0_21,plain,
( mimpl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
thf(c_0_22,plain,
( cs4_box
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X37: $i] :
( ( reli @ Z1 @ X37 )
=> ! [X36: $i] :
( ( relr @ X37 @ X36 )
=> ( Z0 @ X36 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[cs4_box]) ).
thf(c_0_23,plain,
( bl_princ
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X40: $i] :
( ( reli @ Z1 @ X40 )
=> ( Z0 @ X40 ) ) ) ),
inference(fof_simplification,[status(thm)],[bl_princ]) ).
thf(c_0_24,plain,
( cs4_atom
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X32: $i] :
( ( reli @ Z1 @ X32 )
=> ( Z0 @ X32 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_25,plain,
( bl_impl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
! [X41: $i] :
( ( reli @ Z2 @ X41 )
=> ( ~ ( Z0 @ X41 )
| ( Z1 @ X41 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[bl_impl]) ).
thf(c_0_26,plain,
( cs4_impl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
! [X33: $i] :
( ( reli @ Z2 @ X33 )
=> ( ~ ( Z0 @ X33 )
| ( Z1 @ X33 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_20,c_0_21]),c_0_19]) ).
thf(c_0_27,plain,
( bl_says
= ( ^ [Z0: individuals,Z1: $i > $o,Z2: $i] :
! [X46: $i] :
( ( reli @ Z2 @ X46 )
=> ! [X47: $i] :
( ( relr @ X46 @ X47 )
=> ! [X45: $i] :
( ( reli @ X47 @ X45 )
=> ( ~ ! [X44: $i] :
( ( reli @ X45 @ X44 )
=> ( princ_inj @ Z0 @ X44 ) )
| ( Z1 @ X45 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[bl_says]) ).
thf(c_0_28,plain,
( cs4_box
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X37: $i] :
( ( reli @ Z1 @ X37 )
=> ! [X36: $i] :
( ( relr @ X37 @ X36 )
=> ( Z0 @ X36 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_22,c_0_19]) ).
thf(c_0_29,plain,
( bl_princ
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X40: $i] :
( ( reli @ Z1 @ X40 )
=> ( Z0 @ X40 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_30,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X15: $i] : ( Z0 @ X15 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_31,negated_conjecture,
~ ! [X23: individuals,X19: $i > $o,X20: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_says @ X23 @ ( bl_impl @ X19 @ X20 ) ) @ ( bl_impl @ ( bl_says @ X23 @ X19 ) @ ( bl_says @ X23 @ X20 ) ) ) ),
inference(assume_negation,[status(cth)],[bl_k]) ).
thf(c_0_32,plain,
( bl_impl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
! [X41: $i] :
( ( reli @ Z2 @ X41 )
=> ( ~ ( Z0 @ X41 )
| ( Z1 @ X41 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_33,plain,
( bl_says
= ( ^ [Z0: individuals,Z1: $i > $o,Z2: $i] :
! [X46: $i] :
( ( reli @ Z2 @ X46 )
=> ! [X47: $i] :
( ( relr @ X46 @ X47 )
=> ! [X45: $i] :
( ( reli @ X47 @ X45 )
=> ( ~ ! [X44: $i] :
( ( reli @ X45 @ X44 )
=> ( princ_inj @ Z0 @ X44 ) )
| ( Z1 @ X45 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_27,c_0_26]),c_0_28]),c_0_29]) ).
thf(c_0_34,axiom,
( bl_valid
= ( ^ [Z0: $i > $o] :
! [X48: $i] : ( Z0 @ X48 ) ) ),
inference(apply_def,[status(thm)],[bl_valid_def,c_0_30]) ).
thf(c_0_35,negated_conjecture,
~ ! [X23: individuals,X19: $i > $o,X20: $i > $o,X85: $i,X84: $i] :
( ( reli @ X85 @ X84 )
=> ( ~ ! [X71: $i] :
( ( reli @ X84 @ X71 )
=> ! [X72: $i] :
( ( relr @ X71 @ X72 )
=> ! [X73: $i] :
( ( reli @ X72 @ X73 )
=> ( ~ ! [X74: $i] :
( ( reli @ X73 @ X74 )
=> ( princ_inj @ X23 @ X74 ) )
| ! [X70: $i] :
( ( reli @ X73 @ X70 )
=> ( ~ ( X19 @ X70 )
| ( X20 @ X70 ) ) ) ) ) ) )
| ! [X83: $i] :
( ( reli @ X84 @ X83 )
=> ( ~ ! [X75: $i] :
( ( reli @ X83 @ X75 )
=> ! [X76: $i] :
( ( relr @ X75 @ X76 )
=> ! [X77: $i] :
( ( reli @ X76 @ X77 )
=> ( ~ ! [X78: $i] :
( ( reli @ X77 @ X78 )
=> ( princ_inj @ X23 @ X78 ) )
| ( X19 @ X77 ) ) ) ) )
| ! [X79: $i] :
( ( reli @ X83 @ X79 )
=> ! [X80: $i] :
( ( relr @ X79 @ X80 )
=> ! [X81: $i] :
( ( reli @ X80 @ X81 )
=> ( ~ ! [X82: $i] :
( ( reli @ X81 @ X82 )
=> ( princ_inj @ X23 @ X82 ) )
| ( X20 @ X81 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_34]) ).
thf(c_0_36,plain,
! [X19: $i > $o,X56: $i] :
( ~ ! [X53: $i] :
( ( reli @ X56 @ X53 )
=> ( X19 @ X53 ) )
| ! [X55: $i] :
( ( reli @ X56 @ X55 )
=> ! [X54: $i] :
( ( reli @ X55 @ X54 )
=> ( X19 @ X54 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[trans_axiom_i,c_0_21]),c_0_19]),c_0_30]) ).
thf(c_0_37,negated_conjecture,
! [X117: $i,X118: $i,X119: $i,X121: $i,X123: $i,X124: $i,X125: $i,X130: $i] :
( ( reli @ esk8_0 @ esk9_0 )
& ( ( reli @ X119 @ ( esk10_3 @ X117 @ X118 @ X119 ) )
| ~ ( reli @ X119 @ X121 )
| ~ ( epred1_0 @ X121 )
| ( epred2_0 @ X121 )
| ~ ( reli @ X118 @ X119 )
| ~ ( relr @ X117 @ X118 )
| ~ ( reli @ esk9_0 @ X117 ) )
& ( ~ ( princ_inj @ esk7_0 @ ( esk10_3 @ X117 @ X118 @ X119 ) )
| ~ ( reli @ X119 @ X121 )
| ~ ( epred1_0 @ X121 )
| ( epred2_0 @ X121 )
| ~ ( reli @ X118 @ X119 )
| ~ ( relr @ X117 @ X118 )
| ~ ( reli @ esk9_0 @ X117 ) )
& ( reli @ esk9_0 @ esk11_0 )
& ( ( reli @ X125 @ ( esk12_3 @ X123 @ X124 @ X125 ) )
| ( epred1_0 @ X125 )
| ~ ( reli @ X124 @ X125 )
| ~ ( relr @ X123 @ X124 )
| ~ ( reli @ esk11_0 @ X123 ) )
& ( ~ ( princ_inj @ esk7_0 @ ( esk12_3 @ X123 @ X124 @ X125 ) )
| ( epred1_0 @ X125 )
| ~ ( reli @ X124 @ X125 )
| ~ ( relr @ X123 @ X124 )
| ~ ( reli @ esk11_0 @ X123 ) )
& ( reli @ esk11_0 @ esk13_0 )
& ( relr @ esk13_0 @ esk14_0 )
& ( reli @ esk14_0 @ esk15_0 )
& ( ~ ( reli @ esk15_0 @ X130 )
| ( princ_inj @ esk7_0 @ X130 ) )
& ~ ( epred2_0 @ esk15_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_35])])])])])]) ).
thf(c_0_38,plain,
! [X92: $i > $o,X93: $i,X95: $i,X96: $i] :
( ( ( reli @ X93 @ ( esk3_2 @ X92 @ X93 ) )
| ~ ( reli @ X93 @ X95 )
| ~ ( reli @ X95 @ X96 )
| ( X92 @ X96 ) )
& ( ~ ( X92 @ ( esk3_2 @ X92 @ X93 ) )
| ~ ( reli @ X93 @ X95 )
| ~ ( reli @ X95 @ X96 )
| ( X92 @ X96 ) ) ),
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_36])])])])])]) ).
thf(c_0_39,plain,
! [X19: $i > $o,X50: $i] :
( ~ ! [X49: $i] :
( ( reli @ X50 @ X49 )
=> ( X19 @ X49 ) )
| ( X19 @ X50 ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[refl_axiom_i,c_0_21]),c_0_19]),c_0_30]) ).
thf(c_0_40,negated_conjecture,
! [X12: $i,X3: $i,X1: $i] :
( ( epred1_0 @ X12 )
| ~ ( princ_inj @ esk7_0 @ ( esk12_3 @ X1 @ X3 @ X12 ) )
| ~ ( reli @ X3 @ X12 )
| ~ ( relr @ X1 @ X3 )
| ~ ( reli @ esk11_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_41,negated_conjecture,
! [X1: $i] :
( ( princ_inj @ esk7_0 @ X1 )
| ~ ( reli @ esk15_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_42,plain,
! [X1: $i,X2: $i > $o,X3: $i,X12: $i] :
( ( reli @ X1 @ ( esk3_2 @ X2 @ X1 ) )
| ( X2 @ X12 )
| ~ ( reli @ X1 @ X3 )
| ~ ( reli @ X3 @ X12 ) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_43,negated_conjecture,
reli @ esk11_0 @ esk13_0,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_44,plain,
! [X86: $i > $o,X87: $i] :
( ( ( reli @ X87 @ ( esk1_2 @ X86 @ X87 ) )
| ( X86 @ X87 ) )
& ( ~ ( X86 @ ( esk1_2 @ X86 @ X87 ) )
| ( X86 @ X87 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])])])]) ).
thf(c_0_45,negated_conjecture,
! [X1: $i,X3: $i,X12: $i] :
( ( epred1_0 @ X1 )
| ~ ( reli @ esk15_0 @ ( esk12_3 @ X3 @ X12 @ X1 ) )
| ~ ( reli @ esk11_0 @ X3 )
| ~ ( reli @ X12 @ X1 )
| ~ ( relr @ X3 @ X12 ) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
thf(c_0_46,negated_conjecture,
! [X1: $i,X12: $i,X3: $i] :
( ( reli @ X1 @ ( esk12_3 @ X3 @ X12 @ X1 ) )
| ( epred1_0 @ X1 )
| ~ ( reli @ X12 @ X1 )
| ~ ( relr @ X3 @ X12 )
| ~ ( reli @ esk11_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_47,negated_conjecture,
! [X2: $i > $o,X1: $i] :
( ( reli @ X1 @ ( esk3_2 @ X2 @ X1 ) )
| ( X2 @ esk13_0 )
| ~ ( reli @ X1 @ esk11_0 ) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
thf(c_0_48,negated_conjecture,
reli @ esk9_0 @ esk11_0,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_49,plain,
! [X2: $i > $o,X1: $i] :
( ( X2 @ X1 )
| ~ ( X2 @ ( esk1_2 @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
thf(c_0_50,plain,
! [X2: $i > $o,X1: $i] :
( ( reli @ X1 @ ( esk1_2 @ X2 @ X1 ) )
| ( X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
thf(c_0_51,negated_conjecture,
! [X1: $i,X3: $i] :
( ( epred1_0 @ esk15_0 )
| ~ ( reli @ esk11_0 @ X1 )
| ~ ( reli @ X3 @ esk15_0 )
| ~ ( relr @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
thf(c_0_52,plain,
! [X1: $i,X2: $i > $o,X3: $i,X12: $i] :
( ( X2 @ X12 )
| ~ ( X2 @ ( esk3_2 @ X2 @ X1 ) )
| ~ ( reli @ X1 @ X3 )
| ~ ( reli @ X3 @ X12 ) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_53,negated_conjecture,
! [X2: $i > $o] :
( ( reli @ esk9_0 @ ( esk3_2 @ X2 @ esk9_0 ) )
| ( X2 @ esk13_0 ) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
thf(c_0_54,negated_conjecture,
! [X13: $i,X12: $i,X3: $i,X1: $i] :
( ( epred2_0 @ X13 )
| ~ ( princ_inj @ esk7_0 @ ( esk10_3 @ X1 @ X3 @ X12 ) )
| ~ ( reli @ X12 @ X13 )
| ~ ( epred1_0 @ X13 )
| ~ ( reli @ X3 @ X12 )
| ~ ( relr @ X1 @ X3 )
| ~ ( reli @ esk9_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_55,negated_conjecture,
! [X1: $i,X13: $i,X12: $i,X3: $i] :
( ( reli @ X1 @ ( esk10_3 @ X3 @ X12 @ X1 ) )
| ( epred2_0 @ X13 )
| ~ ( reli @ X1 @ X13 )
| ~ ( epred1_0 @ X13 )
| ~ ( reli @ X12 @ X1 )
| ~ ( relr @ X3 @ X12 )
| ~ ( reli @ esk9_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_56,plain,
! [X1: $i] : ( reli @ X1 @ X1 ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
thf(c_0_57,negated_conjecture,
! [X1: $i] :
( ( epred1_0 @ esk15_0 )
| ~ ( reli @ X1 @ esk15_0 )
| ~ ( relr @ esk13_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_51,c_0_43]) ).
thf(c_0_58,negated_conjecture,
relr @ esk13_0 @ esk14_0,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_59,negated_conjecture,
reli @ esk14_0 @ esk15_0,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_60,negated_conjecture,
! [X3: $i,X1: $i] :
( ( reli @ esk9_0 @ esk13_0 )
| ( reli @ esk9_0 @ X1 )
| ~ ( reli @ esk9_0 @ X3 )
| ~ ( reli @ X3 @ X1 ) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
thf(c_0_61,negated_conjecture,
! [X13: $i,X12: $i,X3: $i,X1: $i] :
( ( epred2_0 @ X1 )
| ~ ( reli @ esk15_0 @ ( esk10_3 @ X3 @ X12 @ X13 ) )
| ~ ( reli @ esk9_0 @ X3 )
| ~ ( reli @ X13 @ X1 )
| ~ ( reli @ X12 @ X13 )
| ~ ( relr @ X3 @ X12 )
| ~ ( epred1_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_54,c_0_41]) ).
thf(c_0_62,negated_conjecture,
! [X12: $i,X3: $i,X1: $i] :
( ( reli @ X1 @ ( esk10_3 @ X3 @ X12 @ X1 ) )
| ( epred2_0 @ X1 )
| ~ ( reli @ esk9_0 @ X3 )
| ~ ( reli @ X12 @ X1 )
| ~ ( relr @ X3 @ X12 )
| ~ ( epred1_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
thf(c_0_63,negated_conjecture,
epred1_0 @ esk15_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59])]) ).
thf(c_0_64,negated_conjecture,
~ ( epred2_0 @ esk15_0 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_65,negated_conjecture,
! [X1: $i] :
( ( reli @ esk9_0 @ esk13_0 )
| ( reli @ esk9_0 @ X1 )
| ~ ( reli @ esk11_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_60,c_0_48]) ).
thf(c_0_66,negated_conjecture,
! [X12: $i,X3: $i,X1: $i] :
( ( epred2_0 @ X1 )
| ~ ( reli @ esk9_0 @ X3 )
| ~ ( reli @ esk15_0 @ X1 )
| ~ ( reli @ X12 @ esk15_0 )
| ~ ( relr @ X3 @ X12 )
| ~ ( epred1_0 @ X1 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63])]),c_0_64]) ).
thf(c_0_67,negated_conjecture,
reli @ esk9_0 @ esk13_0,
inference(spm,[status(thm)],[c_0_65,c_0_43]) ).
thf(c_0_68,negated_conjecture,
! [X3: $i,X1: $i] :
( ( epred2_0 @ X1 )
| ~ ( reli @ esk15_0 @ X1 )
| ~ ( reli @ X3 @ esk15_0 )
| ~ ( relr @ esk13_0 @ X3 )
| ~ ( epred1_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
thf(c_0_69,negated_conjecture,
! [X1: $i] :
( ( epred2_0 @ X1 )
| ~ ( reli @ esk15_0 @ X1 )
| ~ ( epred1_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_58]),c_0_59])]) ).
thf(c_0_70,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_69]),c_0_56]),c_0_63])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV441^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n006.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 16:03:54 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.FsaYcaTQkU/E---3.1_912343.p
% 1.93/0.55 % Version: 3.5.1-ho
% 1.93/0.55 % Preprocessing class: HSMSSMSSMLSNHSN.
% 1.93/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.93/0.55 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 1.93/0.55 % Starting post_as_ho3 with 300s (1) cores
% 1.93/0.55 % Starting post_as_ho11 with 300s (1) cores
% 1.93/0.55 % Starting full_lambda_8 with 300s (1) cores
% 1.93/0.55 % new_ho_10_cnf2 with pid 912378 completed with status 0
% 1.93/0.55 % Result found by new_ho_10_cnf2
% 1.93/0.55 % Preprocessing class: HSMSSMSSMLSNHSN.
% 1.93/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.93/0.55 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 1.93/0.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.93/0.55 % No SInE strategy applied
% 1.93/0.55 % Search class: HGUNF-FFMS32-SHSSMSBN
% 1.93/0.55 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 1.93/0.55 % Starting SubtermCWHack with 151s (1) cores
% 1.93/0.55 % Starting new_ho_10_cnf2 with 901s (1) cores
% 1.93/0.55 % Starting sh5l with 151s (1) cores
% 1.93/0.55 % Starting lpo1_def_fix with 151s (1) cores
% 1.93/0.55 % Starting lpo1_lambda_fix with 146s (1) cores
% 1.93/0.55 % lpo1_def_fix with pid 912389 completed with status 0
% 1.93/0.55 % Result found by lpo1_def_fix
% 1.93/0.55 % Preprocessing class: HSMSSMSSMLSNHSN.
% 1.93/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.93/0.55 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 1.93/0.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.93/0.55 % No SInE strategy applied
% 1.93/0.55 % Search class: HGUNF-FFMS32-SHSSMSBN
% 1.93/0.55 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 1.93/0.55 % Starting SubtermCWHack with 151s (1) cores
% 1.93/0.55 % Starting new_ho_10_cnf2 with 901s (1) cores
% 1.93/0.55 % Starting sh5l with 151s (1) cores
% 1.93/0.55 % Starting lpo1_def_fix with 151s (1) cores
% 1.93/0.55 % Preprocessing time : 0.001 s
% 1.93/0.55 % Presaturation interreduction done
% 1.93/0.55
% 1.93/0.55 % Proof found!
% 1.93/0.55 % SZS status Theorem
% 1.93/0.55 % SZS output start CNFRefutation
% See solution above
% 1.93/0.55 % Parsed axioms : 84
% 1.93/0.55 % Removed by relevancy pruning/SinE : 0
% 1.93/0.55 % Initial clauses : 66
% 1.93/0.55 % Removed in clause preprocessing : 43
% 1.93/0.55 % Initial clauses in saturation : 23
% 1.93/0.55 % Processed clauses : 1005
% 1.93/0.55 % ...of these trivial : 17
% 1.93/0.55 % ...subsumed : 197
% 1.93/0.55 % ...remaining for further processing : 791
% 1.93/0.55 % Other redundant clauses eliminated : 22
% 1.93/0.55 % Clauses deleted for lack of memory : 0
% 1.93/0.55 % Backward-subsumed : 65
% 1.93/0.55 % Backward-rewritten : 141
% 1.93/0.55 % Generated clauses : 7430
% 1.93/0.55 % ...of the previous two non-redundant : 7264
% 1.93/0.55 % ...aggressively subsumed : 0
% 1.93/0.55 % Contextual simplify-reflections : 0
% 1.93/0.55 % Paramodulations : 7364
% 1.93/0.55 % Factorizations : 0
% 1.93/0.55 % NegExts : 0
% 1.93/0.55 % Equation resolutions : 22
% 1.93/0.55 % Disequality decompositions : 0
% 1.93/0.55 % Total rewrite steps : 554
% 1.93/0.55 % ...of those cached : 490
% 1.93/0.55 % Propositional unsat checks : 0
% 1.93/0.55 % Propositional check models : 0
% 1.93/0.55 % Propositional check unsatisfiable : 0
% 1.93/0.55 % Propositional clauses : 0
% 1.93/0.55 % Propositional clauses after purity: 0
% 1.93/0.55 % Propositional unsat core size : 0
% 1.93/0.55 % Propositional preprocessing time : 0.000
% 1.93/0.55 % Propositional encoding time : 0.000
% 1.93/0.55 % Propositional solver time : 0.000
% 1.93/0.55 % Success case prop preproc time : 0.000
% 1.93/0.55 % Success case prop encoding time : 0.000
% 1.93/0.55 % Success case prop solver time : 0.000
% 1.93/0.55 % Current number of processed clauses : 562
% 1.93/0.55 % Positive orientable unit clauses : 34
% 1.93/0.55 % Positive unorientable unit clauses: 0
% 1.93/0.55 % Negative unit clauses : 2
% 1.93/0.55 % Non-unit-clauses : 526
% 1.93/0.55 % Current number of unprocessed clauses: 5713
% 1.93/0.55 % ...number of literals in the above : 23367
% 1.93/0.55 % Current number of archived formulas : 0
% 1.93/0.55 % Current number of archived clauses : 229
% 1.93/0.55 % Clause-clause subsumption calls (NU) : 46913
% 1.93/0.55 % Rec. Clause-clause subsumption calls : 21355
% 1.93/0.55 % Non-unit clause-clause subsumptions : 253
% 1.93/0.55 % Unit Clause-clause subsumption calls : 683
% 1.93/0.55 % Rewrite failures with RHS unbound : 0
% 1.93/0.55 % BW rewrite match attempts : 47
% 1.93/0.55 % BW rewrite match successes : 34
% 1.93/0.55 % Condensation attempts : 0
% 1.93/0.55 % Condensation successes : 0
% 1.93/0.55 % Termbank termtop insertions : 294583
% 1.93/0.55 % Search garbage collected termcells : 1895
% 1.93/0.55
% 1.93/0.55 % -------------------------------------------------
% 1.93/0.55 % User time : 0.268 s
% 1.93/0.55 % System time : 0.010 s
% 1.93/0.55 % Total time : 0.278 s
% 1.93/0.55 % Maximum resident set size: 3900 pages
% 1.93/0.55
% 1.93/0.55 % -------------------------------------------------
% 1.93/0.55 % User time : 1.195 s
% 1.93/0.55 % System time : 0.051 s
% 1.93/0.55 % Total time : 1.246 s
% 1.93/0.55 % Maximum resident set size: 4864 pages
% 1.93/0.55 % E exiting
%------------------------------------------------------------------------------