%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV444^1 : 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 : n020.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 0.22s 0.31s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 20
% Syntax : Number of formulae : 86 ( 53 unt; 0 typ; 0 def)
% Number of atoms : 296 ( 42 equ; 0 cnn)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 740 ( 89 ~; 96 |; 10 &; 502 @)
% ( 0 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 79 ( 79 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 31 usr; 9 con; 0-3 aty)
% Number of variables : 224 ( 85 ^; 139 !; 0 ?; 224 :)
% 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_36,type,
mall: ( individuals > $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_50,type,
cs4_all: ( individuals > $i > $o ) > $i > $o ).
thf(decl_51,type,
cs4_box: ( $i > $o ) > $i > $o ).
thf(decl_52,type,
cs4_valid: ( $i > $o ) > $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_64,type,
loca: individuals ).
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,
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_0: $i ).
thf(decl_77,type,
esk12_0: $i ).
thf(decl_78,type,
esk13_0: $i ).
thf(decl_79,type,
esk14_0: $i ).
thf(mimpl,axiom,
( mimpl
= ( ^ [X7: $i > $o,X8: $i > $o] : ( mor @ ( mnot @ X7 ) @ X8 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.NMIjBZpqLK/E---3.1_1227718.p',mimpl) ).
thf(mnot,axiom,
( mnot
= ( ^ [X2: $i > $o,X3: $i] :
~ ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.NMIjBZpqLK/E---3.1_1227718.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.NMIjBZpqLK/E---3.1_1227718.p',mor) ).
thf(cs4_atom,axiom,
( cs4_atom
= ( ^ [X11: $i > $o] : ( mbox @ reli @ X11 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.NMIjBZpqLK/E---3.1_1227718.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.NMIjBZpqLK/E---3.1_1227718.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.NMIjBZpqLK/E---3.1_1227718.p',cs4_impl) ).
thf(cs4_box,axiom,
( cs4_box
= ( ^ [X19: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ X19 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.NMIjBZpqLK/E---3.1_1227718.p',cs4_box) ).
thf(bl_princ,axiom,
( bl_princ
= ( ^ [X11: $i > $o] : ( cs4_atom @ X11 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.NMIjBZpqLK/E---3.1_1227718.p',bl_princ) ).
thf(bl_atom,axiom,
( bl_atom
= ( ^ [X11: $i > $o] : ( cs4_atom @ X11 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.NMIjBZpqLK/E---3.1_1227718.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.NMIjBZpqLK/E---3.1_1227718.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.NMIjBZpqLK/E---3.1_1227718.p',bl_says) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X11: $i > $o] :
! [X15: $i] : ( X11 @ X15 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.NMIjBZpqLK/E---3.1_1227718.p',mvalid) ).
thf(bl_strength,conjecture,
! [X23: individuals,X19: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_says @ loca @ ( bl_atom @ X19 ) ) @ ( bl_says @ X23 @ ( bl_atom @ X19 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.NMIjBZpqLK/E---3.1_1227718.p',bl_strength) ).
thf(bl_valid_def,axiom,
( bl_valid
= ( ^ [Z0: $i > $o] :
! [X47: $i] : ( Z0 @ X47 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.NMIjBZpqLK/E---3.1_1227718.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.NMIjBZpqLK/E---3.1_1227718.p',trans_axiom_i) ).
thf(refl_axiom_i,axiom,
! [X19: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ X19 ) @ X19 ) ),
file('/export/starexec/sandbox2/tmp/tmp.NMIjBZpqLK/E---3.1_1227718.p',refl_axiom_i) ).
thf(cs4_all,axiom,
( cs4_all
= ( ^ [X21: individuals > $i > $o] : ( mbox @ reli @ ( mall @ X21 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.NMIjBZpqLK/E---3.1_1227718.p',cs4_all) ).
thf(mall,axiom,
( mall
= ( ^ [X14: individuals > $i > $o,X15: $i] :
! [X16: individuals] : ( X14 @ X16 @ X15 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.NMIjBZpqLK/E---3.1_1227718.p',mall) ).
thf(cs4_valid_def,axiom,
( cs4_valid
= ( ^ [X19: $i > $o] : ( mvalid @ X19 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.NMIjBZpqLK/E---3.1_1227718.p',cs4_valid_def) ).
thf(loca_strength,axiom,
( cs4_valid
@ ( cs4_all
@ ^ [X23: individuals] : ( cs4_impl @ ( princ_inj @ X23 ) @ ( princ_inj @ loca ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.NMIjBZpqLK/E---3.1_1227718.p',loca_strength) ).
thf(c_0_20,plain,
( mimpl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimpl]) ).
thf(c_0_21,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_22,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_23,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_24,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_25,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_26,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_20,c_0_21]),c_0_22]) ).
thf(c_0_27,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_28,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_29,plain,
( cs4_atom
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X31: $i] :
( ( reli @ Z1 @ X31 )
=> ( Z0 @ X31 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_30,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_31,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_32,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_25,c_0_26]),c_0_24]) ).
thf(c_0_33,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_34,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_27,c_0_24]) ).
thf(c_0_35,plain,
( bl_princ
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X39: $i] :
( ( reli @ Z1 @ X39 )
=> ( Z0 @ X39 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_36,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X15: $i] : ( Z0 @ X15 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_37,negated_conjecture,
~ ! [X23: individuals,X19: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_says @ loca @ ( bl_atom @ X19 ) ) @ ( bl_says @ X23 @ ( bl_atom @ X19 ) ) ) ),
inference(assume_negation,[status(cth)],[bl_strength]) ).
thf(c_0_38,plain,
( bl_atom
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X38: $i] :
( ( reli @ Z1 @ X38 )
=> ( Z0 @ X38 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_30,c_0_29]) ).
thf(c_0_39,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_31,c_0_32]) ).
thf(c_0_40,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_33,c_0_32]),c_0_34]),c_0_35]) ).
thf(c_0_41,axiom,
( bl_valid
= ( ^ [Z0: $i > $o] :
! [X47: $i] : ( Z0 @ X47 ) ) ),
inference(apply_def,[status(thm)],[bl_valid_def,c_0_36]) ).
thf(c_0_42,negated_conjecture,
~ ! [X23: individuals,X19: $i > $o,X80: $i,X79: $i] :
( ( reli @ X80 @ X79 )
=> ( ~ ! [X70: $i] :
( ( reli @ X79 @ X70 )
=> ! [X71: $i] :
( ( relr @ X70 @ X71 )
=> ! [X72: $i] :
( ( reli @ X71 @ X72 )
=> ( ~ ! [X73: $i] :
( ( reli @ X72 @ X73 )
=> ( princ_inj @ loca @ X73 ) )
| ! [X69: $i] :
( ( reli @ X72 @ X69 )
=> ( X19 @ X69 ) ) ) ) ) )
| ! [X75: $i] :
( ( reli @ X79 @ X75 )
=> ! [X76: $i] :
( ( relr @ X75 @ X76 )
=> ! [X77: $i] :
( ( reli @ X76 @ X77 )
=> ( ~ ! [X78: $i] :
( ( reli @ X77 @ X78 )
=> ( princ_inj @ X23 @ X78 ) )
| ! [X74: $i] :
( ( reli @ X77 @ X74 )
=> ( X19 @ X74 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_40]),c_0_41]) ).
thf(c_0_43,plain,
! [X19: $i > $o,X55: $i] :
( ~ ! [X52: $i] :
( ( reli @ X55 @ X52 )
=> ( X19 @ X52 ) )
| ! [X54: $i] :
( ( reli @ X55 @ X54 )
=> ! [X53: $i] :
( ( reli @ X54 @ X53 )
=> ( X19 @ X53 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[trans_axiom_i,c_0_26]),c_0_24]),c_0_36]) ).
thf(c_0_44,negated_conjecture,
! [X111: $i,X112: $i,X113: $i,X115: $i,X119: $i] :
( ( reli @ esk8_0 @ esk9_0 )
& ( ( reli @ X113 @ ( esk10_3 @ X111 @ X112 @ X113 ) )
| ~ ( reli @ X113 @ X115 )
| ( epred1_0 @ X115 )
| ~ ( reli @ X112 @ X113 )
| ~ ( relr @ X111 @ X112 )
| ~ ( reli @ esk9_0 @ X111 ) )
& ( ~ ( princ_inj @ loca @ ( esk10_3 @ X111 @ X112 @ X113 ) )
| ~ ( reli @ X113 @ X115 )
| ( epred1_0 @ X115 )
| ~ ( reli @ X112 @ X113 )
| ~ ( relr @ X111 @ X112 )
| ~ ( reli @ esk9_0 @ X111 ) )
& ( reli @ esk9_0 @ esk11_0 )
& ( relr @ esk11_0 @ esk12_0 )
& ( reli @ esk12_0 @ esk13_0 )
& ( ~ ( reli @ esk13_0 @ X119 )
| ( princ_inj @ esk7_0 @ X119 ) )
& ( reli @ esk13_0 @ esk14_0 )
& ~ ( epred1_0 @ esk14_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_42])])])])])]) ).
thf(c_0_45,plain,
! [X87: $i > $o,X88: $i,X90: $i,X91: $i] :
( ( ( reli @ X88 @ ( esk3_2 @ X87 @ X88 ) )
| ~ ( reli @ X88 @ X90 )
| ~ ( reli @ X90 @ X91 )
| ( X87 @ X91 ) )
& ( ~ ( X87 @ ( esk3_2 @ X87 @ X88 ) )
| ~ ( reli @ X88 @ X90 )
| ~ ( reli @ X90 @ X91 )
| ( X87 @ X91 ) ) ),
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_43])])])])])]) ).
thf(c_0_46,negated_conjecture,
! [X1: $i,X13: $i,X12: $i,X3: $i] :
( ( reli @ X1 @ ( esk10_3 @ X3 @ X12 @ X1 ) )
| ( epred1_0 @ X13 )
| ~ ( reli @ X1 @ X13 )
| ~ ( reli @ X12 @ X1 )
| ~ ( relr @ X3 @ X12 )
| ~ ( reli @ esk9_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
thf(c_0_47,negated_conjecture,
reli @ esk13_0 @ esk14_0,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
thf(c_0_48,negated_conjecture,
~ ( epred1_0 @ esk14_0 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
thf(c_0_49,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_45]) ).
thf(c_0_50,negated_conjecture,
! [X1: $i,X3: $i] :
( ( reli @ esk13_0 @ ( esk10_3 @ X1 @ X3 @ esk13_0 ) )
| ~ ( reli @ esk9_0 @ X1 )
| ~ ( reli @ X3 @ esk13_0 )
| ~ ( relr @ X1 @ X3 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
thf(c_0_51,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_26]),c_0_24]),c_0_36]) ).
thf(c_0_52,plain,
( cs4_all
= ( ^ [Z0: individuals > $i > $o,Z1: $i] :
! [X34: $i] :
( ( reli @ Z1 @ X34 )
=> ! [X33: individuals] : ( Z0 @ X33 @ X34 ) ) ) ),
inference(fof_simplification,[status(thm)],[cs4_all]) ).
thf(c_0_53,plain,
( mall
= ( ^ [Z0: individuals > $i > $o,Z1: $i] :
! [X16: individuals] : ( Z0 @ X16 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mall]) ).
thf(c_0_54,plain,
( cs4_valid
= ( ^ [Z0: $i > $o] :
! [X37: $i] : ( Z0 @ X37 ) ) ),
inference(fof_simplification,[status(thm)],[cs4_valid_def]) ).
thf(c_0_55,negated_conjecture,
! [X2: $i > $o,X1: $i,X12: $i,X3: $i] :
( ( X2 @ ( esk10_3 @ X1 @ X3 @ esk13_0 ) )
| ( reli @ X12 @ ( esk3_2 @ X2 @ X12 ) )
| ~ ( reli @ X12 @ esk13_0 )
| ~ ( reli @ esk9_0 @ X1 )
| ~ ( reli @ X3 @ esk13_0 )
| ~ ( relr @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
thf(c_0_56,negated_conjecture,
reli @ esk9_0 @ esk11_0,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
thf(c_0_57,plain,
! [X81: $i > $o,X82: $i] :
( ( ( reli @ X82 @ ( esk1_2 @ X81 @ X82 ) )
| ( X81 @ X82 ) )
& ( ~ ( X81 @ ( esk1_2 @ X81 @ X82 ) )
| ( X81 @ X82 ) ) ),
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_51])])])])]) ).
thf(c_0_58,plain,
( cs4_all
= ( ^ [Z0: individuals > $i > $o,Z1: $i] :
! [X34: $i] :
( ( reli @ Z1 @ X34 )
=> ! [X33: individuals] : ( Z0 @ X33 @ X34 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_52,c_0_24]),c_0_53]) ).
thf(c_0_59,plain,
( cs4_valid
= ( ^ [Z0: $i > $o] :
! [X37: $i] : ( Z0 @ X37 ) ) ),
inference(apply_def,[status(thm)],[c_0_54,c_0_36]) ).
thf(c_0_60,negated_conjecture,
! [X3: $i,X2: $i > $o,X1: $i] :
( ( X2 @ ( esk10_3 @ esk11_0 @ X1 @ esk13_0 ) )
| ( reli @ X3 @ ( esk3_2 @ X2 @ X3 ) )
| ~ ( reli @ X3 @ esk13_0 )
| ~ ( reli @ X1 @ esk13_0 )
| ~ ( relr @ esk11_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
thf(c_0_61,negated_conjecture,
relr @ esk11_0 @ esk12_0,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
thf(c_0_62,negated_conjecture,
reli @ esk12_0 @ esk13_0,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
thf(c_0_63,plain,
! [X2: $i > $o,X1: $i] :
( ( X2 @ X1 )
| ~ ( X2 @ ( esk1_2 @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
thf(c_0_64,plain,
! [X2: $i > $o,X1: $i] :
( ( reli @ X1 @ ( esk1_2 @ X2 @ X1 ) )
| ( X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
thf(c_0_65,plain,
! [X68: $i,X66: $i] :
( ( reli @ X68 @ X66 )
=> ! [X67: individuals,X65: $i] :
( ( reli @ X66 @ X65 )
=> ( ~ ( princ_inj @ X67 @ X65 )
| ( princ_inj @ loca @ X65 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[loca_strength]),c_0_32]),c_0_58]),c_0_59])]) ).
thf(c_0_66,negated_conjecture,
! [X2: $i > $o,X1: $i] :
( ( X2 @ ( esk10_3 @ esk11_0 @ esk12_0 @ esk13_0 ) )
| ( reli @ X1 @ ( esk3_2 @ X2 @ X1 ) )
| ~ ( reli @ X1 @ esk13_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62])]) ).
thf(c_0_67,plain,
! [X1: $i] : ( reli @ X1 @ X1 ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
thf(c_0_68,plain,
! [X103: $i,X104: $i,X105: individuals,X106: $i] :
( ~ ( reli @ X103 @ X104 )
| ~ ( reli @ X104 @ X106 )
| ~ ( princ_inj @ X105 @ X106 )
| ( princ_inj @ loca @ X106 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_65])])])]) ).
thf(c_0_69,negated_conjecture,
! [X13: $i,X12: $i,X3: $i,X1: $i] :
( ( epred1_0 @ X13 )
| ~ ( princ_inj @ loca @ ( esk10_3 @ X1 @ X3 @ X12 ) )
| ~ ( reli @ X12 @ X13 )
| ~ ( reli @ X3 @ X12 )
| ~ ( relr @ X1 @ X3 )
| ~ ( reli @ esk9_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
thf(c_0_70,negated_conjecture,
! [X2: $i > $o] :
( ( reli @ esk13_0 @ ( esk3_2 @ X2 @ esk13_0 ) )
| ( X2 @ ( esk10_3 @ esk11_0 @ esk12_0 @ esk13_0 ) ) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
thf(c_0_71,plain,
! [X1: $i,X3: $i,X16: individuals,X12: $i] :
( ( princ_inj @ loca @ X12 )
| ~ ( reli @ X1 @ X3 )
| ~ ( reli @ X3 @ X12 )
| ~ ( princ_inj @ X16 @ X12 ) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
thf(c_0_72,negated_conjecture,
! [X1: $i] :
( ( reli @ esk13_0 @ ( esk3_2 @ ( princ_inj @ loca ) @ esk13_0 ) )
| ( epred1_0 @ X1 )
| ~ ( reli @ esk13_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_56]),c_0_62]),c_0_61])]) ).
thf(c_0_73,plain,
! [X16: individuals,X3: $i,X1: $i] :
( ( princ_inj @ loca @ X1 )
| ~ ( reli @ X3 @ X1 )
| ~ ( princ_inj @ X16 @ X1 ) ),
inference(spm,[status(thm)],[c_0_71,c_0_67]) ).
thf(c_0_74,negated_conjecture,
reli @ esk13_0 @ ( esk3_2 @ ( princ_inj @ loca ) @ esk13_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_47]),c_0_48]) ).
thf(c_0_75,negated_conjecture,
! [X16: individuals] :
( ( princ_inj @ loca @ ( esk3_2 @ ( princ_inj @ loca ) @ esk13_0 ) )
| ~ ( princ_inj @ X16 @ ( esk3_2 @ ( princ_inj @ loca ) @ esk13_0 ) ) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
thf(c_0_76,negated_conjecture,
! [X1: $i] :
( ( princ_inj @ esk7_0 @ X1 )
| ~ ( reli @ esk13_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
thf(c_0_77,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_45]) ).
thf(c_0_78,negated_conjecture,
princ_inj @ loca @ ( esk3_2 @ ( princ_inj @ loca ) @ esk13_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_74])]) ).
thf(c_0_79,negated_conjecture,
! [X3: $i,X1: $i] :
( ( princ_inj @ loca @ X1 )
| ~ ( reli @ esk13_0 @ X3 )
| ~ ( reli @ X3 @ X1 ) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
thf(c_0_80,negated_conjecture,
! [X1: $i] :
( ( princ_inj @ loca @ X1 )
| ~ ( reli @ esk13_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_79,c_0_67]) ).
thf(c_0_81,negated_conjecture,
! [X1: $i,X3: $i,X13: $i,X12: $i] :
( ( epred1_0 @ X1 )
| ~ ( reli @ esk13_0 @ ( esk10_3 @ X3 @ X12 @ X13 ) )
| ~ ( reli @ esk9_0 @ X3 )
| ~ ( reli @ X13 @ X1 )
| ~ ( reli @ X12 @ X13 )
| ~ ( relr @ X3 @ X12 ) ),
inference(spm,[status(thm)],[c_0_69,c_0_80]) ).
thf(c_0_82,negated_conjecture,
! [X1: $i,X3: $i,X12: $i] :
( ( epred1_0 @ X1 )
| ~ ( reli @ esk9_0 @ X3 )
| ~ ( reli @ esk13_0 @ X1 )
| ~ ( reli @ X12 @ esk13_0 )
| ~ ( relr @ X3 @ X12 ) ),
inference(spm,[status(thm)],[c_0_81,c_0_50]) ).
thf(c_0_83,negated_conjecture,
! [X1: $i,X3: $i] :
( ( epred1_0 @ X1 )
| ~ ( reli @ esk13_0 @ X1 )
| ~ ( reli @ X3 @ esk13_0 )
| ~ ( relr @ esk11_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_82,c_0_56]) ).
thf(c_0_84,negated_conjecture,
! [X1: $i] :
( ( epred1_0 @ X1 )
| ~ ( reli @ esk13_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_61]),c_0_62])]) ).
thf(c_0_85,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_84]),c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV444^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n020.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:05:34 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 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.NMIjBZpqLK/E---3.1_1227718.p
% 0.22/0.31 % Version: 3.5.1-ho
% 0.22/0.31 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.22/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.31 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.22/0.31 % Starting post_as_ho3 with 300s (1) cores
% 0.22/0.31 % Starting post_as_ho11 with 300s (1) cores
% 0.22/0.31 % Starting full_lambda_8 with 300s (1) cores
% 0.22/0.31 % new_ho_10_cnf2 with pid 1227731 completed with status 0
% 0.22/0.31 % Result found by new_ho_10_cnf2
% 0.22/0.31 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.22/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.31 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.22/0.31 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.31 % No SInE strategy applied
% 0.22/0.31 % Search class: HGUNF-FFSS32-SHSSMMBN
% 0.22/0.31 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.31 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.31 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.22/0.31 % Starting sh5l with 136s (1) cores
% 0.22/0.31 % Starting lpo1_def_fix with 136s (1) cores
% 0.22/0.31 % Starting ehoh_best8_lambda with 136s (1) cores
% 0.22/0.31 % lpo1_def_fix with pid 1227741 completed with status 0
% 0.22/0.31 % Result found by lpo1_def_fix
% 0.22/0.31 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.22/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.31 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.22/0.31 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.31 % No SInE strategy applied
% 0.22/0.31 % Search class: HGUNF-FFSS32-SHSSMMBN
% 0.22/0.31 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.31 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.31 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.22/0.31 % Starting sh5l with 136s (1) cores
% 0.22/0.31 % Starting lpo1_def_fix with 136s (1) cores
% 0.22/0.31 % Preprocessing time : 0.002 s
% 0.22/0.31 % Presaturation interreduction done
% 0.22/0.31
% 0.22/0.31 % Proof found!
% 0.22/0.31 % SZS status Theorem
% 0.22/0.31 % SZS output start CNFRefutation
% See solution above
% 0.22/0.31 % Parsed axioms : 84
% 0.22/0.31 % Removed by relevancy pruning/SinE : 0
% 0.22/0.31 % Initial clauses : 64
% 0.22/0.31 % Removed in clause preprocessing : 43
% 0.22/0.31 % Initial clauses in saturation : 21
% 0.22/0.31 % Processed clauses : 207
% 0.22/0.31 % ...of these trivial : 1
% 0.22/0.31 % ...subsumed : 29
% 0.22/0.31 % ...remaining for further processing : 177
% 0.22/0.31 % Other redundant clauses eliminated : 11
% 0.22/0.31 % Clauses deleted for lack of memory : 0
% 0.22/0.31 % Backward-subsumed : 20
% 0.22/0.31 % Backward-rewritten : 17
% 0.22/0.31 % Generated clauses : 702
% 0.22/0.31 % ...of the previous two non-redundant : 622
% 0.22/0.31 % ...aggressively subsumed : 0
% 0.22/0.31 % Contextual simplify-reflections : 0
% 0.22/0.31 % Paramodulations : 652
% 0.22/0.31 % Factorizations : 0
% 0.22/0.31 % NegExts : 0
% 0.22/0.31 % Equation resolutions : 11
% 0.22/0.31 % Disequality decompositions : 0
% 0.22/0.31 % Total rewrite steps : 132
% 0.22/0.31 % ...of those cached : 107
% 0.22/0.31 % Propositional unsat checks : 0
% 0.22/0.31 % Propositional check models : 0
% 0.22/0.31 % Propositional check unsatisfiable : 0
% 0.22/0.31 % Propositional clauses : 0
% 0.22/0.31 % Propositional clauses after purity: 0
% 0.22/0.31 % Propositional unsat core size : 0
% 0.22/0.31 % Propositional preprocessing time : 0.000
% 0.22/0.31 % Propositional encoding time : 0.000
% 0.22/0.31 % Propositional solver time : 0.000
% 0.22/0.31 % Success case prop preproc time : 0.000
% 0.22/0.31 % Success case prop encoding time : 0.000
% 0.22/0.31 % Success case prop solver time : 0.000
% 0.22/0.31 % Current number of processed clauses : 119
% 0.22/0.31 % Positive orientable unit clauses : 27
% 0.22/0.31 % Positive unorientable unit clauses: 0
% 0.22/0.31 % Negative unit clauses : 2
% 0.22/0.31 % Non-unit-clauses : 90
% 0.22/0.31 % Current number of unprocessed clauses: 427
% 0.22/0.31 % ...number of literals in the above : 1420
% 0.22/0.31 % Current number of archived formulas : 0
% 0.22/0.31 % Current number of archived clauses : 58
% 0.22/0.31 % Clause-clause subsumption calls (NU) : 2508
% 0.22/0.31 % Rec. Clause-clause subsumption calls : 1637
% 0.22/0.31 % Non-unit clause-clause subsumptions : 48
% 0.22/0.31 % Unit Clause-clause subsumption calls : 48
% 0.22/0.31 % Rewrite failures with RHS unbound : 0
% 0.22/0.31 % BW rewrite match attempts : 38
% 0.22/0.31 % BW rewrite match successes : 9
% 0.22/0.31 % Condensation attempts : 0
% 0.22/0.31 % Condensation successes : 0
% 0.22/0.31 % Termbank termtop insertions : 21898
% 0.22/0.31 % Search garbage collected termcells : 1650
% 0.22/0.31
% 0.22/0.31 % -------------------------------------------------
% 0.22/0.31 % User time : 0.040 s
% 0.22/0.31 % System time : 0.003 s
% 0.22/0.31 % Total time : 0.043 s
% 0.22/0.31 % Maximum resident set size: 3952 pages
% 0.22/0.31
% 0.22/0.31 % -------------------------------------------------
% 0.22/0.31 % User time : 0.156 s
% 0.22/0.31 % System time : 0.016 s
% 0.22/0.31 % Total time : 0.172 s
% 0.22/0.31 % Maximum resident set size: 4864 pages
% 0.22/0.31 % E exiting
%------------------------------------------------------------------------------