%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV445^1 : 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 : n005.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 08:39:45 AM UTC 2026
% Result : Theorem 0.24s 0.32s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 16
% Syntax : Number of formulae : 77 ( 48 unt; 0 typ; 0 def)
% Number of atoms : 356 ( 34 equ; 0 cnn)
% Maximal formula atoms : 48 ( 4 avg)
% Number of connectives : 1148 ( 176 ~; 184 |; 12 &; 735 @)
% ( 0 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 62 ( 62 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 28 usr; 8 con; 0-6 aty)
% Number of variables : 244 ( 72 ^; 172 !; 0 ?; 244 :)
% 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_54,type,
bl_atom: ( $i > $o ) > $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_66,type,
esk2_2: ( $i > $o ) > $i > $i ).
thf(decl_71,type,
esk7_0: individuals ).
thf(decl_72,type,
epred1_0: $i > $o ).
thf(decl_73,type,
esk8_0: $i ).
thf(decl_74,type,
esk9_0: $i ).
thf(decl_75,type,
esk10_3: $i > $i > $i > $i ).
thf(decl_76,type,
esk11_6: $i > $i > $i > $i > $i > $i > $i ).
thf(decl_77,type,
esk12_0: $i ).
thf(decl_78,type,
esk13_0: $i ).
thf(decl_79,type,
esk14_0: $i ).
thf(decl_80,type,
esk15_0: $i ).
thf(mimpl,axiom,
( mimpl
= ( ^ [X7: $i > $o,X8: $i > $o] : ( mor @ ( mnot @ X7 ) @ X8 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.tWuKjAVPu7/E---3.1_1852443.p',mimpl) ).
thf(mnot,axiom,
( mnot
= ( ^ [X2: $i > $o,X3: $i] :
~ ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.tWuKjAVPu7/E---3.1_1852443.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.tWuKjAVPu7/E---3.1_1852443.p',mor) ).
thf(cs4_atom,axiom,
( cs4_atom
= ( ^ [X11: $i > $o] : ( mbox @ reli @ X11 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.tWuKjAVPu7/E---3.1_1852443.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.tWuKjAVPu7/E---3.1_1852443.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.tWuKjAVPu7/E---3.1_1852443.p',cs4_impl) ).
thf(cs4_box,axiom,
( cs4_box
= ( ^ [X19: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ X19 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.tWuKjAVPu7/E---3.1_1852443.p',cs4_box) ).
thf(bl_princ,axiom,
( bl_princ
= ( ^ [X11: $i > $o] : ( cs4_atom @ X11 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.tWuKjAVPu7/E---3.1_1852443.p',bl_princ) ).
thf(bl_atom,axiom,
( bl_atom
= ( ^ [X11: $i > $o] : ( cs4_atom @ X11 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.tWuKjAVPu7/E---3.1_1852443.p',bl_atom) ).
thf(bl_impl,axiom,
( bl_impl
= ( ^ [X19: $i > $o,X20: $i > $o] : ( cs4_impl @ X19 @ X20 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.tWuKjAVPu7/E---3.1_1852443.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.tWuKjAVPu7/E---3.1_1852443.p',bl_says) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X11: $i > $o] :
! [X15: $i] : ( X11 @ X15 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.tWuKjAVPu7/E---3.1_1852443.p',mvalid) ).
thf(bl_c4,conjecture,
! [X23: individuals,X19: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_says @ X23 @ ( bl_says @ X23 @ ( bl_atom @ X19 ) ) ) @ ( bl_says @ X23 @ ( bl_atom @ X19 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.tWuKjAVPu7/E---3.1_1852443.p',bl_c4) ).
thf(bl_valid_def,axiom,
( bl_valid
= ( ^ [Z0: $i > $o] :
! [X47: $i] : ( Z0 @ X47 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.tWuKjAVPu7/E---3.1_1852443.p',bl_valid_def) ).
thf(refl_axiom_i,axiom,
! [X19: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ X19 ) @ X19 ) ),
file('/export/starexec/sandbox2/tmp/tmp.tWuKjAVPu7/E---3.1_1852443.p',refl_axiom_i) ).
thf(refl_axiom_r,axiom,
! [X19: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ relr @ X19 ) @ X19 ) ),
file('/export/starexec/sandbox2/tmp/tmp.tWuKjAVPu7/E---3.1_1852443.p',refl_axiom_r) ).
thf(c_0_16,plain,
( mimpl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimpl]) ).
thf(c_0_17,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_18,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_19,plain,
( cs4_atom
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X31: $i] :
( ( reli @ Z1 @ X31 )
=> ( Z0 @ X31 ) ) ) ),
inference(fof_simplification,[status(thm)],[cs4_atom]) ).
thf(c_0_20,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_21,plain,
( cs4_impl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
! [X32: $i] :
( ( reli @ Z2 @ X32 )
=> ( ~ ( Z0 @ X32 )
| ( Z1 @ X32 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[cs4_impl]) ).
thf(c_0_22,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_16,c_0_17]),c_0_18]) ).
thf(c_0_23,plain,
( cs4_box
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X36: $i] :
( ( reli @ Z1 @ X36 )
=> ! [X35: $i] :
( ( relr @ X36 @ X35 )
=> ( Z0 @ X35 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[cs4_box]) ).
thf(c_0_24,plain,
( bl_princ
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X39: $i] :
( ( reli @ Z1 @ X39 )
=> ( Z0 @ X39 ) ) ) ),
inference(fof_simplification,[status(thm)],[bl_princ]) ).
thf(c_0_25,plain,
( cs4_atom
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X31: $i] :
( ( reli @ Z1 @ X31 )
=> ( Z0 @ X31 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_26,plain,
( bl_atom
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X38: $i] :
( ( reli @ Z1 @ X38 )
=> ( Z0 @ X38 ) ) ) ),
inference(fof_simplification,[status(thm)],[bl_atom]) ).
thf(c_0_27,plain,
( bl_impl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
! [X40: $i] :
( ( reli @ Z2 @ X40 )
=> ( ~ ( Z0 @ X40 )
| ( Z1 @ X40 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[bl_impl]) ).
thf(c_0_28,plain,
( cs4_impl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
! [X32: $i] :
( ( reli @ Z2 @ X32 )
=> ( ~ ( Z0 @ X32 )
| ( Z1 @ X32 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_21,c_0_22]),c_0_20]) ).
thf(c_0_29,plain,
( bl_says
= ( ^ [Z0: individuals,Z1: $i > $o,Z2: $i] :
! [X45: $i] :
( ( reli @ Z2 @ X45 )
=> ! [X46: $i] :
( ( relr @ X45 @ X46 )
=> ! [X44: $i] :
( ( reli @ X46 @ X44 )
=> ( ~ ! [X43: $i] :
( ( reli @ X44 @ X43 )
=> ( princ_inj @ Z0 @ X43 ) )
| ( Z1 @ X44 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[bl_says]) ).
thf(c_0_30,plain,
( cs4_box
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X36: $i] :
( ( reli @ Z1 @ X36 )
=> ! [X35: $i] :
( ( relr @ X36 @ X35 )
=> ( Z0 @ X35 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_23,c_0_20]) ).
thf(c_0_31,plain,
( bl_princ
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X39: $i] :
( ( reli @ Z1 @ X39 )
=> ( Z0 @ X39 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_32,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X15: $i] : ( Z0 @ X15 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_33,negated_conjecture,
~ ! [X23: individuals,X19: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_says @ X23 @ ( bl_says @ X23 @ ( bl_atom @ X19 ) ) ) @ ( bl_says @ X23 @ ( bl_atom @ X19 ) ) ) ),
inference(assume_negation,[status(cth)],[bl_c4]) ).
thf(c_0_34,plain,
( bl_atom
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X38: $i] :
( ( reli @ Z1 @ X38 )
=> ( Z0 @ X38 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_26,c_0_25]) ).
thf(c_0_35,plain,
( bl_impl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
! [X40: $i] :
( ( reli @ Z2 @ X40 )
=> ( ~ ( Z0 @ X40 )
| ( Z1 @ X40 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_36,plain,
( bl_says
= ( ^ [Z0: individuals,Z1: $i > $o,Z2: $i] :
! [X45: $i] :
( ( reli @ Z2 @ X45 )
=> ! [X46: $i] :
( ( relr @ X45 @ X46 )
=> ! [X44: $i] :
( ( reli @ X46 @ X44 )
=> ( ~ ! [X43: $i] :
( ( reli @ X44 @ X43 )
=> ( princ_inj @ Z0 @ X43 ) )
| ( Z1 @ X44 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_29,c_0_28]),c_0_30]),c_0_31]) ).
thf(c_0_37,axiom,
( bl_valid
= ( ^ [Z0: $i > $o] :
! [X47: $i] : ( Z0 @ X47 ) ) ),
inference(apply_def,[status(thm)],[bl_valid_def,c_0_32]) ).
thf(c_0_38,negated_conjecture,
~ ! [X23: individuals,X19: $i > $o,X84: $i,X83: $i] :
( ( reli @ X84 @ X83 )
=> ( ~ ! [X74: $i] :
( ( reli @ X83 @ X74 )
=> ! [X75: $i] :
( ( relr @ X74 @ X75 )
=> ! [X76: $i] :
( ( reli @ X75 @ X76 )
=> ( ~ ! [X77: $i] :
( ( reli @ X76 @ X77 )
=> ( princ_inj @ X23 @ X77 ) )
| ! [X70: $i] :
( ( reli @ X76 @ X70 )
=> ! [X71: $i] :
( ( relr @ X70 @ X71 )
=> ! [X72: $i] :
( ( reli @ X71 @ X72 )
=> ( ~ ! [X73: $i] :
( ( reli @ X72 @ X73 )
=> ( princ_inj @ X23 @ X73 ) )
| ! [X69: $i] :
( ( reli @ X72 @ X69 )
=> ( X19 @ X69 ) ) ) ) ) ) ) ) ) )
| ! [X79: $i] :
( ( reli @ X83 @ X79 )
=> ! [X80: $i] :
( ( relr @ X79 @ X80 )
=> ! [X81: $i] :
( ( reli @ X80 @ X81 )
=> ( ~ ! [X82: $i] :
( ( reli @ X81 @ X82 )
=> ( princ_inj @ X23 @ X82 ) )
| ! [X78: $i] :
( ( reli @ X81 @ X78 )
=> ( X19 @ X78 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_36]),c_0_37]) ).
thf(c_0_39,negated_conjecture,
! [X115: $i,X116: $i,X117: $i,X119: $i,X120: $i,X121: $i,X123: $i,X127: $i] :
( ( reli @ esk8_0 @ esk9_0 )
& ( ( reli @ X121 @ ( esk11_6 @ X115 @ X116 @ X117 @ X119 @ X120 @ X121 ) )
| ~ ( reli @ X121 @ X123 )
| ( epred1_0 @ X123 )
| ~ ( reli @ X120 @ X121 )
| ~ ( relr @ X119 @ X120 )
| ~ ( reli @ X117 @ X119 )
| ( reli @ X117 @ ( esk10_3 @ X115 @ X116 @ X117 ) )
| ~ ( reli @ X116 @ X117 )
| ~ ( relr @ X115 @ X116 )
| ~ ( reli @ esk9_0 @ X115 ) )
& ( ~ ( princ_inj @ esk7_0 @ ( esk11_6 @ X115 @ X116 @ X117 @ X119 @ X120 @ X121 ) )
| ~ ( reli @ X121 @ X123 )
| ( epred1_0 @ X123 )
| ~ ( reli @ X120 @ X121 )
| ~ ( relr @ X119 @ X120 )
| ~ ( reli @ X117 @ X119 )
| ( reli @ X117 @ ( esk10_3 @ X115 @ X116 @ X117 ) )
| ~ ( reli @ X116 @ X117 )
| ~ ( relr @ X115 @ X116 )
| ~ ( reli @ esk9_0 @ X115 ) )
& ( ( reli @ X121 @ ( esk11_6 @ X115 @ X116 @ X117 @ X119 @ X120 @ X121 ) )
| ~ ( reli @ X121 @ X123 )
| ( epred1_0 @ X123 )
| ~ ( reli @ X120 @ X121 )
| ~ ( relr @ X119 @ X120 )
| ~ ( reli @ X117 @ X119 )
| ~ ( princ_inj @ esk7_0 @ ( esk10_3 @ X115 @ X116 @ X117 ) )
| ~ ( reli @ X116 @ X117 )
| ~ ( relr @ X115 @ X116 )
| ~ ( reli @ esk9_0 @ X115 ) )
& ( ~ ( princ_inj @ esk7_0 @ ( esk11_6 @ X115 @ X116 @ X117 @ X119 @ X120 @ X121 ) )
| ~ ( reli @ X121 @ X123 )
| ( epred1_0 @ X123 )
| ~ ( reli @ X120 @ X121 )
| ~ ( relr @ X119 @ X120 )
| ~ ( reli @ X117 @ X119 )
| ~ ( princ_inj @ esk7_0 @ ( esk10_3 @ X115 @ X116 @ X117 ) )
| ~ ( reli @ X116 @ X117 )
| ~ ( relr @ X115 @ X116 )
| ~ ( reli @ esk9_0 @ X115 ) )
& ( reli @ esk9_0 @ esk12_0 )
& ( relr @ esk12_0 @ esk13_0 )
& ( reli @ esk13_0 @ esk14_0 )
& ( ~ ( reli @ esk14_0 @ X127 )
| ( princ_inj @ esk7_0 @ X127 ) )
& ( reli @ esk14_0 @ esk15_0 )
& ~ ( epred1_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_38])])])])])]) ).
thf(c_0_40,negated_conjecture,
! [X1: $i,X15: $i,X32: $i,X31: $i,X13: $i,X12: $i,X3: $i] :
( ( reli @ X1 @ ( esk11_6 @ X3 @ X12 @ X13 @ X15 @ X31 @ X1 ) )
| ( epred1_0 @ X32 )
| ( reli @ X13 @ ( esk10_3 @ X3 @ X12 @ X13 ) )
| ~ ( reli @ X1 @ X32 )
| ~ ( reli @ X31 @ X1 )
| ~ ( relr @ X15 @ X31 )
| ~ ( reli @ X13 @ X15 )
| ~ ( reli @ X12 @ X13 )
| ~ ( relr @ X3 @ X12 )
| ~ ( reli @ esk9_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_41,negated_conjecture,
reli @ esk14_0 @ esk15_0,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_42,negated_conjecture,
~ ( epred1_0 @ esk15_0 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_43,negated_conjecture,
! [X1: $i] :
( ( princ_inj @ esk7_0 @ X1 )
| ~ ( reli @ esk14_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_44,negated_conjecture,
! [X1: $i,X13: $i,X12: $i,X15: $i,X3: $i] :
( ( reli @ esk14_0 @ ( esk11_6 @ X1 @ X3 @ X12 @ X13 @ X15 @ esk14_0 ) )
| ( reli @ X12 @ ( esk10_3 @ X1 @ X3 @ X12 ) )
| ~ ( reli @ esk9_0 @ X1 )
| ~ ( reli @ X15 @ esk14_0 )
| ~ ( reli @ X12 @ X13 )
| ~ ( reli @ X3 @ X12 )
| ~ ( relr @ X13 @ X15 )
| ~ ( relr @ X1 @ X3 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
thf(c_0_45,plain,
! [X19: $i > $o,X49: $i] :
( ~ ! [X48: $i] :
( ( reli @ X49 @ X48 )
=> ( X19 @ X48 ) )
| ( X19 @ X49 ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[refl_axiom_i,c_0_22]),c_0_20]),c_0_32]) ).
thf(c_0_46,negated_conjecture,
! [X15: $i,X32: $i,X31: $i,X13: $i,X12: $i,X3: $i,X1: $i] :
( ( epred1_0 @ X32 )
| ( reli @ X12 @ ( esk10_3 @ X1 @ X3 @ X12 ) )
| ~ ( princ_inj @ esk7_0 @ ( esk11_6 @ X1 @ X3 @ X12 @ X13 @ X15 @ X31 ) )
| ~ ( reli @ X31 @ X32 )
| ~ ( reli @ X15 @ X31 )
| ~ ( relr @ X13 @ X15 )
| ~ ( reli @ X12 @ X13 )
| ~ ( reli @ X3 @ X12 )
| ~ ( relr @ X1 @ X3 )
| ~ ( reli @ esk9_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_47,negated_conjecture,
! [X1: $i,X13: $i,X12: $i,X15: $i,X3: $i] :
( ( princ_inj @ esk7_0 @ ( esk11_6 @ X1 @ X3 @ X12 @ X13 @ X15 @ esk14_0 ) )
| ( reli @ X12 @ ( esk10_3 @ X1 @ X3 @ X12 ) )
| ~ ( reli @ esk9_0 @ X1 )
| ~ ( reli @ X15 @ esk14_0 )
| ~ ( reli @ X12 @ X13 )
| ~ ( reli @ X3 @ X12 )
| ~ ( relr @ X13 @ X15 )
| ~ ( relr @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
thf(c_0_48,plain,
! [X85: $i > $o,X86: $i] :
( ( ( reli @ X86 @ ( esk1_2 @ X85 @ X86 ) )
| ( X85 @ X86 ) )
& ( ~ ( X85 @ ( esk1_2 @ X85 @ X86 ) )
| ( X85 @ X86 ) ) ),
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_45])])])])]) ).
thf(c_0_49,plain,
! [X19: $i > $o,X51: $i] :
( ~ ! [X50: $i] :
( ( relr @ X51 @ X50 )
=> ( X19 @ X50 ) )
| ( X19 @ X51 ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[refl_axiom_r,c_0_22]),c_0_20]),c_0_32]) ).
thf(c_0_50,negated_conjecture,
! [X1: $i,X3: $i,X15: $i,X13: $i,X31: $i,X12: $i] :
( ( reli @ X1 @ ( esk10_3 @ X3 @ X12 @ X1 ) )
| ( epred1_0 @ X13 )
| ~ ( reli @ esk9_0 @ X3 )
| ~ ( reli @ esk14_0 @ X13 )
| ~ ( reli @ X15 @ esk14_0 )
| ~ ( reli @ X1 @ X31 )
| ~ ( reli @ X12 @ X1 )
| ~ ( relr @ X31 @ X15 )
| ~ ( relr @ X3 @ X12 ) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
thf(c_0_51,plain,
! [X2: $i > $o,X1: $i] :
( ( X2 @ X1 )
| ~ ( X2 @ ( esk1_2 @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
thf(c_0_52,plain,
! [X2: $i > $o,X1: $i] :
( ( reli @ X1 @ ( esk1_2 @ X2 @ X1 ) )
| ( X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
thf(c_0_53,plain,
! [X88: $i > $o,X89: $i] :
( ( ( relr @ X89 @ ( esk2_2 @ X88 @ X89 ) )
| ( X88 @ X89 ) )
& ( ~ ( X88 @ ( esk2_2 @ X88 @ X89 ) )
| ( X88 @ X89 ) ) ),
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_49])])])])]) ).
thf(c_0_54,negated_conjecture,
! [X1: $i,X15: $i,X3: $i,X13: $i,X12: $i] :
( ( reli @ X1 @ ( esk10_3 @ X3 @ X12 @ X1 ) )
| ~ ( reli @ esk9_0 @ X3 )
| ~ ( reli @ X13 @ esk14_0 )
| ~ ( reli @ X1 @ X15 )
| ~ ( reli @ X12 @ X1 )
| ~ ( relr @ X15 @ X13 )
| ~ ( relr @ X3 @ X12 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_41]),c_0_42]) ).
thf(c_0_55,plain,
! [X1: $i] : ( reli @ X1 @ X1 ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
thf(c_0_56,plain,
! [X2: $i > $o,X1: $i] :
( ( X2 @ X1 )
| ~ ( X2 @ ( esk2_2 @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_57,plain,
! [X2: $i > $o,X1: $i] :
( ( relr @ X1 @ ( esk2_2 @ X2 @ X1 ) )
| ( X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_58,negated_conjecture,
! [X1: $i,X15: $i,X32: $i,X31: $i,X13: $i,X12: $i,X3: $i] :
( ( reli @ X1 @ ( esk11_6 @ X3 @ X12 @ X13 @ X15 @ X31 @ X1 ) )
| ( epred1_0 @ X32 )
| ~ ( reli @ X1 @ X32 )
| ~ ( reli @ X31 @ X1 )
| ~ ( relr @ X15 @ X31 )
| ~ ( reli @ X13 @ X15 )
| ~ ( princ_inj @ esk7_0 @ ( esk10_3 @ X3 @ X12 @ X13 ) )
| ~ ( reli @ X12 @ X13 )
| ~ ( relr @ X3 @ X12 )
| ~ ( reli @ esk9_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_59,negated_conjecture,
! [X1: $i,X3: $i,X13: $i,X12: $i] :
( ( reli @ X1 @ ( esk10_3 @ X3 @ X12 @ X1 ) )
| ~ ( reli @ esk9_0 @ X3 )
| ~ ( relr @ X13 @ esk14_0 )
| ~ ( reli @ X1 @ X13 )
| ~ ( reli @ X12 @ X1 )
| ~ ( relr @ X3 @ X12 ) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
thf(c_0_60,plain,
! [X1: $i] : ( relr @ X1 @ X1 ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
thf(c_0_61,negated_conjecture,
! [X1: $i,X13: $i,X12: $i,X15: $i,X3: $i] :
( ( reli @ esk14_0 @ ( esk11_6 @ X1 @ X3 @ X12 @ X13 @ X15 @ esk14_0 ) )
| ~ ( princ_inj @ esk7_0 @ ( esk10_3 @ X1 @ X3 @ X12 ) )
| ~ ( reli @ esk9_0 @ X1 )
| ~ ( reli @ X15 @ esk14_0 )
| ~ ( reli @ X12 @ X13 )
| ~ ( reli @ X3 @ X12 )
| ~ ( relr @ X13 @ X15 )
| ~ ( relr @ X1 @ X3 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_41]),c_0_42]) ).
thf(c_0_62,negated_conjecture,
! [X1: $i,X3: $i,X12: $i] :
( ( reli @ X1 @ ( esk10_3 @ X3 @ X12 @ X1 ) )
| ~ ( reli @ esk9_0 @ X3 )
| ~ ( reli @ X1 @ esk14_0 )
| ~ ( reli @ X12 @ X1 )
| ~ ( relr @ X3 @ X12 ) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
thf(c_0_63,negated_conjecture,
! [X15: $i,X32: $i,X31: $i,X13: $i,X12: $i,X3: $i,X1: $i] :
( ( epred1_0 @ X32 )
| ~ ( princ_inj @ esk7_0 @ ( esk11_6 @ X1 @ X3 @ X12 @ X13 @ X15 @ X31 ) )
| ~ ( reli @ X31 @ X32 )
| ~ ( reli @ X15 @ X31 )
| ~ ( relr @ X13 @ X15 )
| ~ ( reli @ X12 @ X13 )
| ~ ( princ_inj @ esk7_0 @ ( esk10_3 @ X1 @ X3 @ X12 ) )
| ~ ( reli @ X3 @ X12 )
| ~ ( relr @ X1 @ X3 )
| ~ ( reli @ esk9_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_64,negated_conjecture,
! [X1: $i,X13: $i,X12: $i,X15: $i,X3: $i] :
( ( princ_inj @ esk7_0 @ ( esk11_6 @ X1 @ X3 @ X12 @ X13 @ X15 @ esk14_0 ) )
| ~ ( princ_inj @ esk7_0 @ ( esk10_3 @ X1 @ X3 @ X12 ) )
| ~ ( reli @ esk9_0 @ X1 )
| ~ ( reli @ X15 @ esk14_0 )
| ~ ( reli @ X12 @ X13 )
| ~ ( reli @ X3 @ X12 )
| ~ ( relr @ X13 @ X15 )
| ~ ( relr @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_43,c_0_61]) ).
thf(c_0_65,negated_conjecture,
! [X1: $i,X3: $i] :
( ( reli @ esk14_0 @ ( esk10_3 @ X1 @ X3 @ esk14_0 ) )
| ~ ( reli @ esk9_0 @ X1 )
| ~ ( reli @ X3 @ esk14_0 )
| ~ ( relr @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_62,c_0_55]) ).
thf(c_0_66,negated_conjecture,
! [X1: $i,X3: $i,X15: $i,X31: $i,X13: $i,X12: $i] :
( ( epred1_0 @ X1 )
| ~ ( princ_inj @ esk7_0 @ ( esk10_3 @ X3 @ X12 @ X13 ) )
| ~ ( reli @ esk9_0 @ X3 )
| ~ ( reli @ esk14_0 @ X1 )
| ~ ( reli @ X15 @ esk14_0 )
| ~ ( reli @ X13 @ X31 )
| ~ ( reli @ X12 @ X13 )
| ~ ( relr @ X31 @ X15 )
| ~ ( relr @ X3 @ X12 ) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
thf(c_0_67,negated_conjecture,
! [X1: $i,X3: $i] :
( ( princ_inj @ esk7_0 @ ( esk10_3 @ X1 @ X3 @ esk14_0 ) )
| ~ ( reli @ esk9_0 @ X1 )
| ~ ( reli @ X3 @ esk14_0 )
| ~ ( relr @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_43,c_0_65]) ).
thf(c_0_68,negated_conjecture,
! [X1: $i,X3: $i,X13: $i,X12: $i,X15: $i] :
( ( epred1_0 @ X1 )
| ~ ( reli @ esk9_0 @ X3 )
| ~ ( reli @ esk14_0 @ X1 )
| ~ ( reli @ X12 @ esk14_0 )
| ~ ( reli @ esk14_0 @ X13 )
| ~ ( reli @ X15 @ esk14_0 )
| ~ ( relr @ X13 @ X12 )
| ~ ( relr @ X3 @ X15 ) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
thf(c_0_69,negated_conjecture,
reli @ esk9_0 @ esk12_0,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_70,negated_conjecture,
! [X1: $i,X13: $i,X12: $i,X3: $i] :
( ( epred1_0 @ X1 )
| ~ ( reli @ esk14_0 @ X1 )
| ~ ( reli @ X3 @ esk14_0 )
| ~ ( reli @ esk14_0 @ X12 )
| ~ ( reli @ X13 @ esk14_0 )
| ~ ( relr @ esk12_0 @ X13 )
| ~ ( relr @ X12 @ X3 ) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
thf(c_0_71,negated_conjecture,
! [X12: $i,X3: $i,X1: $i] :
( ~ ( reli @ X1 @ esk14_0 )
| ~ ( reli @ esk14_0 @ X3 )
| ~ ( reli @ X12 @ esk14_0 )
| ~ ( relr @ esk12_0 @ X12 )
| ~ ( relr @ X3 @ X1 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_41]),c_0_42]) ).
thf(c_0_72,negated_conjecture,
! [X3: $i,X1: $i] :
( ~ ( reli @ esk14_0 @ X1 )
| ~ ( reli @ X3 @ esk14_0 )
| ~ ( relr @ esk12_0 @ X3 )
| ~ ( relr @ X1 @ esk14_0 ) ),
inference(spm,[status(thm)],[c_0_71,c_0_55]) ).
thf(c_0_73,negated_conjecture,
relr @ esk12_0 @ esk13_0,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_74,negated_conjecture,
reli @ esk13_0 @ esk14_0,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_75,negated_conjecture,
! [X1: $i] :
( ~ ( reli @ esk14_0 @ X1 )
| ~ ( relr @ X1 @ esk14_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74])]) ).
thf(c_0_76,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_60]),c_0_55])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV445^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.19 % Computer : n005.cluster.edu
% 0.13/0.19 % Model : x86_64 x86_64
% 0.13/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.19 % Memory : 8046.5625MB
% 0.13/0.19 % OS : Linux 6.8.0-71-generic
% 0.13/0.19 % CPULimit : 300
% 0.13/0.19 % WCLimit : 300
% 0.13/0.19 % DateTime : Tue Sep 29 16:04:31 UTC 2026
% 0.13/0.20 % CPUTime :
% 0.13/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.24 Running higher-order theorem proving
% 0.13/0.26 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.tWuKjAVPu7/E---3.1_1852443.p
% 0.24/0.32 % Version: 3.5.1-ho
% 0.24/0.32 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.24/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.32 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.24/0.32 % Starting post_as_ho3 with 300s (1) cores
% 0.24/0.32 % Starting post_as_ho11 with 300s (1) cores
% 0.24/0.32 % Starting full_lambda_8 with 300s (1) cores
% 0.24/0.32 % new_ho_10_cnf2 with pid 1852456 completed with status 0
% 0.24/0.32 % Result found by new_ho_10_cnf2
% 0.24/0.32 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.24/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.32 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.24/0.32 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.32 % No SInE strategy applied
% 0.24/0.32 % Search class: HGUNF-FFMS32-SHSSMSBN
% 0.24/0.32 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.32 % Starting SubtermCWHack with 151s (1) cores
% 0.24/0.32 % Starting new_ho_10_cnf2 with 901s (1) cores
% 0.24/0.32 % Starting sh5l with 151s (1) cores
% 0.24/0.32 % Starting lpo1_def_fix with 151s (1) cores
% 0.24/0.32 % Starting lpo1_lambda_fix with 146s (1) cores
% 0.24/0.32 % lpo1_lambda_fix with pid 1852465 completed with status 0
% 0.24/0.32 % Result found by lpo1_lambda_fix
% 0.24/0.32 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.24/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.32 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.24/0.32 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.32 % No SInE strategy applied
% 0.24/0.32 % Search class: HGUNF-FFMS32-SHSSMSBN
% 0.24/0.32 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.32 % Starting SubtermCWHack with 151s (1) cores
% 0.24/0.32 % Starting new_ho_10_cnf2 with 901s (1) cores
% 0.24/0.32 % Starting sh5l with 151s (1) cores
% 0.24/0.32 % Starting lpo1_def_fix with 151s (1) cores
% 0.24/0.32 % Starting lpo1_lambda_fix with 146s (1) cores
% 0.24/0.32 % Preprocessing time : 0.002 s
% 0.24/0.32 % Presaturation interreduction done
% 0.24/0.32
% 0.24/0.32 % Proof found!
% 0.24/0.32 % SZS status Theorem
% 0.24/0.32 % SZS output start CNFRefutation
% See solution above
% 0.24/0.32 % Parsed axioms : 84
% 0.24/0.32 % Removed by relevancy pruning/SinE : 0
% 0.24/0.32 % Initial clauses : 66
% 0.24/0.32 % Removed in clause preprocessing : 43
% 0.24/0.32 % Initial clauses in saturation : 23
% 0.24/0.32 % Processed clauses : 129
% 0.24/0.32 % ...of these trivial : 0
% 0.24/0.32 % ...subsumed : 5
% 0.24/0.32 % ...remaining for further processing : 124
% 0.24/0.32 % Other redundant clauses eliminated : 2
% 0.24/0.32 % Clauses deleted for lack of memory : 0
% 0.24/0.32 % Backward-subsumed : 23
% 0.24/0.32 % Backward-rewritten : 4
% 0.24/0.32 % Generated clauses : 338
% 0.24/0.32 % ...of the previous two non-redundant : 292
% 0.24/0.32 % ...aggressively subsumed : 0
% 0.24/0.32 % Contextual simplify-reflections : 0
% 0.24/0.32 % Paramodulations : 305
% 0.24/0.32 % Factorizations : 0
% 0.24/0.32 % NegExts : 0
% 0.24/0.32 % Equation resolutions : 2
% 0.24/0.32 % Disequality decompositions : 0
% 0.24/0.32 % Total rewrite steps : 33
% 0.24/0.32 % ...of those cached : 22
% 0.24/0.32 % Propositional unsat checks : 0
% 0.24/0.32 % Propositional check models : 0
% 0.24/0.32 % Propositional check unsatisfiable : 0
% 0.24/0.32 % Propositional clauses : 0
% 0.24/0.32 % Propositional clauses after purity: 0
% 0.24/0.32 % Propositional unsat core size : 0
% 0.24/0.32 % Propositional preprocessing time : 0.000
% 0.24/0.32 % Propositional encoding time : 0.000
% 0.24/0.32 % Propositional solver time : 0.000
% 0.24/0.32 % Success case prop preproc time : 0.000
% 0.24/0.32 % Success case prop encoding time : 0.000
% 0.24/0.32 % Success case prop solver time : 0.000
% 0.24/0.32 % Current number of processed clauses : 74
% 0.24/0.32 % Positive orientable unit clauses : 16
% 0.24/0.32 % Positive unorientable unit clauses: 0
% 0.24/0.32 % Negative unit clauses : 3
% 0.24/0.32 % Non-unit-clauses : 55
% 0.24/0.32 % Current number of unprocessed clauses: 202
% 0.24/0.32 % ...number of literals in the above : 1191
% 0.24/0.32 % Current number of archived formulas : 0
% 0.24/0.32 % Current number of archived clauses : 50
% 0.24/0.32 % Clause-clause subsumption calls (NU) : 2481
% 0.24/0.32 % Rec. Clause-clause subsumption calls : 497
% 0.24/0.32 % Non-unit clause-clause subsumptions : 26
% 0.24/0.32 % Unit Clause-clause subsumption calls : 80
% 0.24/0.32 % Rewrite failures with RHS unbound : 0
% 0.24/0.32 % BW rewrite match attempts : 16
% 0.24/0.32 % BW rewrite match successes : 3
% 0.24/0.32 % Condensation attempts : 0
% 0.24/0.32 % Condensation successes : 0
% 0.24/0.32 % Termbank termtop insertions : 19176
% 0.24/0.32 % Search garbage collected termcells : 1858
% 0.24/0.32
% 0.24/0.32 % -------------------------------------------------
% 0.24/0.32 % User time : 0.029 s
% 0.24/0.32 % System time : 0.005 s
% 0.24/0.32 % Total time : 0.034 s
% 0.24/0.32 % Maximum resident set size: 3952 pages
% 0.24/0.32
% 0.24/0.32 % -------------------------------------------------
% 0.24/0.32 % User time : 0.148 s
% 0.24/0.32 % System time : 0.016 s
% 0.24/0.32 % Total time : 0.164 s
% 0.24/0.32 % Maximum resident set size: 4608 pages
% 0.24/0.32 % E exiting
%------------------------------------------------------------------------------