%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV446^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 1.08s 0.46s
% Output : CNFRefutation 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 17
% Syntax : Number of formulae : 76 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 258 ( 34 equ; 0 cnn)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 699 ( 86 ~; 93 |; 11 &; 469 @)
% ( 0 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 71 ( 71 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 28 usr; 8 con; 0-3 aty)
% Number of variables : 201 ( 72 ^; 129 !; 0 ?; 201 :)
% 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_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_0: $i ).
thf(decl_76,type,
esk11_0: $i ).
thf(decl_77,type,
esk12_0: $i ).
thf(decl_78,type,
esk13_3: $i > $i > $i > $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/sandbox/tmp/tmp.UN0H7s6HY7/E---3.1_972872.p',mimpl) ).
thf(mnot,axiom,
( mnot
= ( ^ [X2: $i > $o,X3: $i] :
~ ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UN0H7s6HY7/E---3.1_972872.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UN0H7s6HY7/E---3.1_972872.p',mor) ).
thf(cs4_atom,axiom,
( cs4_atom
= ( ^ [X11: $i > $o] : ( mbox @ reli @ X11 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UN0H7s6HY7/E---3.1_972872.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/sandbox/tmp/tmp.UN0H7s6HY7/E---3.1_972872.p',mbox) ).
thf(cs4_impl,axiom,
( cs4_impl
= ( ^ [X19: $i > $o,X20: $i > $o] : ( mbox @ reli @ ( mimpl @ X19 @ X20 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UN0H7s6HY7/E---3.1_972872.p',cs4_impl) ).
thf(cs4_box,axiom,
( cs4_box
= ( ^ [X19: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ X19 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UN0H7s6HY7/E---3.1_972872.p',cs4_box) ).
thf(bl_princ,axiom,
( bl_princ
= ( ^ [X11: $i > $o] : ( cs4_atom @ X11 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UN0H7s6HY7/E---3.1_972872.p',bl_princ) ).
thf(bl_atom,axiom,
( bl_atom
= ( ^ [X11: $i > $o] : ( cs4_atom @ X11 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UN0H7s6HY7/E---3.1_972872.p',bl_atom) ).
thf(bl_impl,axiom,
( bl_impl
= ( ^ [X19: $i > $o,X20: $i > $o] : ( cs4_impl @ X19 @ X20 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UN0H7s6HY7/E---3.1_972872.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/sandbox/tmp/tmp.UN0H7s6HY7/E---3.1_972872.p',bl_says) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X11: $i > $o] :
! [X15: $i] : ( X11 @ X15 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UN0H7s6HY7/E---3.1_972872.p',mvalid) ).
thf(bl_conceit,conjecture,
! [X23: individuals,X19: $i > $o] : ( bl_valid @ ( bl_says @ X23 @ ( bl_impl @ ( bl_says @ X23 @ ( bl_atom @ X19 ) ) @ ( bl_atom @ X19 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UN0H7s6HY7/E---3.1_972872.p',bl_conceit) ).
thf(bl_valid_def,axiom,
( bl_valid
= ( ^ [Z0: $i > $o] :
! [X47: $i] : ( Z0 @ X47 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UN0H7s6HY7/E---3.1_972872.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/sandbox/tmp/tmp.UN0H7s6HY7/E---3.1_972872.p',trans_axiom_i) ).
thf(refl_axiom_r,axiom,
! [X19: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ relr @ X19 ) @ X19 ) ),
file('/export/starexec/sandbox/tmp/tmp.UN0H7s6HY7/E---3.1_972872.p',refl_axiom_r) ).
thf(refl_axiom_i,axiom,
! [X19: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ X19 ) @ X19 ) ),
file('/export/starexec/sandbox/tmp/tmp.UN0H7s6HY7/E---3.1_972872.p',refl_axiom_i) ).
thf(c_0_17,plain,
( mimpl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimpl]) ).
thf(c_0_18,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_19,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_20,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_21,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_22,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_23,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_17,c_0_18]),c_0_19]) ).
thf(c_0_24,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_25,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_26,plain,
( cs4_atom
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X31: $i] :
( ( reli @ Z1 @ X31 )
=> ( Z0 @ X31 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_27,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_28,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_29,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_22,c_0_23]),c_0_21]) ).
thf(c_0_30,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_31,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_24,c_0_21]) ).
thf(c_0_32,plain,
( bl_princ
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X39: $i] :
( ( reli @ Z1 @ X39 )
=> ( Z0 @ X39 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_33,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X15: $i] : ( Z0 @ X15 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_34,negated_conjecture,
~ ! [X23: individuals,X19: $i > $o] : ( bl_valid @ ( bl_says @ X23 @ ( bl_impl @ ( bl_says @ X23 @ ( bl_atom @ X19 ) ) @ ( bl_atom @ X19 ) ) ) ),
inference(assume_negation,[status(cth)],[bl_conceit]) ).
thf(c_0_35,plain,
( bl_atom
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X38: $i] :
( ( reli @ Z1 @ X38 )
=> ( Z0 @ X38 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_27,c_0_26]) ).
thf(c_0_36,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_28,c_0_29]) ).
thf(c_0_37,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_30,c_0_29]),c_0_31]),c_0_32]) ).
thf(c_0_38,axiom,
( bl_valid
= ( ^ [Z0: $i > $o] :
! [X47: $i] : ( Z0 @ X47 ) ) ),
inference(apply_def,[status(thm)],[bl_valid_def,c_0_33]) ).
thf(c_0_39,negated_conjecture,
~ ! [X23: individuals,X19: $i > $o,X80: $i,X76: $i] :
( ( reli @ X80 @ X76 )
=> ! [X77: $i] :
( ( relr @ X76 @ X77 )
=> ! [X78: $i] :
( ( reli @ X77 @ X78 )
=> ( ~ ! [X79: $i] :
( ( reli @ X78 @ X79 )
=> ( princ_inj @ X23 @ X79 ) )
| ! [X75: $i] :
( ( reli @ X78 @ X75 )
=> ( ~ ! [X70: $i] :
( ( reli @ X75 @ 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 ) ) ) ) ) )
| ! [X74: $i] :
( ( reli @ X75 @ 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_34,c_0_35]),c_0_36]),c_0_37]),c_0_38]) ).
thf(c_0_40,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_23]),c_0_21]),c_0_33]) ).
thf(c_0_41,negated_conjecture,
! [X113: $i,X115: $i,X116: $i,X117: $i,X119: $i] :
( ( reli @ esk8_0 @ esk9_0 )
& ( relr @ esk9_0 @ esk10_0 )
& ( reli @ esk10_0 @ esk11_0 )
& ( ~ ( reli @ esk11_0 @ X113 )
| ( princ_inj @ esk7_0 @ X113 ) )
& ( reli @ esk11_0 @ esk12_0 )
& ( ( reli @ X117 @ ( esk13_3 @ X115 @ X116 @ X117 ) )
| ~ ( reli @ X117 @ X119 )
| ( epred1_0 @ X119 )
| ~ ( reli @ X116 @ X117 )
| ~ ( relr @ X115 @ X116 )
| ~ ( reli @ esk12_0 @ X115 ) )
& ( ~ ( princ_inj @ esk7_0 @ ( esk13_3 @ X115 @ X116 @ X117 ) )
| ~ ( reli @ X117 @ X119 )
| ( epred1_0 @ X119 )
| ~ ( reli @ X116 @ X117 )
| ~ ( relr @ X115 @ X116 )
| ~ ( reli @ esk12_0 @ X115 ) )
& ( reli @ esk12_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_39])])])])])]) ).
thf(c_0_42,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_23]),c_0_21]),c_0_33]) ).
thf(c_0_43,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_40])])])])])]) ).
thf(c_0_44,negated_conjecture,
! [X1: $i,X13: $i,X12: $i,X3: $i] :
( ( reli @ X1 @ ( esk13_3 @ X3 @ X12 @ X1 ) )
| ( epred1_0 @ X13 )
| ~ ( reli @ X1 @ X13 )
| ~ ( reli @ X12 @ X1 )
| ~ ( relr @ X3 @ X12 )
| ~ ( reli @ esk12_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_45,negated_conjecture,
reli @ esk12_0 @ esk14_0,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_46,negated_conjecture,
~ ( epred1_0 @ esk14_0 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_47,plain,
! [X84: $i > $o,X85: $i] :
( ( ( relr @ X85 @ ( esk2_2 @ X84 @ X85 ) )
| ( X84 @ X85 ) )
& ( ~ ( X84 @ ( esk2_2 @ X84 @ X85 ) )
| ( X84 @ X85 ) ) ),
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_42])])])])]) ).
thf(c_0_48,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_23]),c_0_21]),c_0_33]) ).
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_43]) ).
thf(c_0_50,negated_conjecture,
! [X1: $i,X3: $i] :
( ( reli @ esk12_0 @ ( esk13_3 @ X1 @ X3 @ esk12_0 ) )
| ~ ( reli @ esk12_0 @ X1 )
| ~ ( reli @ X3 @ esk12_0 )
| ~ ( relr @ X1 @ X3 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
thf(c_0_51,plain,
! [X2: $i > $o,X1: $i] :
( ( X2 @ X1 )
| ~ ( X2 @ ( esk2_2 @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_52,plain,
! [X2: $i > $o,X1: $i] :
( ( relr @ X1 @ ( esk2_2 @ X2 @ X1 ) )
| ( X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_53,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_48])])])])]) ).
thf(c_0_54,negated_conjecture,
! [X2: $i > $o,X1: $i,X12: $i,X3: $i] :
( ( X2 @ ( esk13_3 @ X1 @ X3 @ esk12_0 ) )
| ( reli @ X12 @ ( esk3_2 @ X2 @ X12 ) )
| ~ ( reli @ X12 @ esk12_0 )
| ~ ( reli @ esk12_0 @ X1 )
| ~ ( reli @ X3 @ esk12_0 )
| ~ ( relr @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
thf(c_0_55,plain,
! [X1: $i] : ( relr @ 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 @ ( esk1_2 @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_57,plain,
! [X2: $i > $o,X1: $i] :
( ( reli @ X1 @ ( esk1_2 @ X2 @ X1 ) )
| ( X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_58,negated_conjecture,
! [X1: $i,X2: $i > $o,X3: $i] :
( ( reli @ X1 @ ( esk3_2 @ X2 @ X1 ) )
| ( X2 @ ( esk13_3 @ X3 @ X3 @ esk12_0 ) )
| ~ ( reli @ X1 @ esk12_0 )
| ~ ( reli @ esk12_0 @ X3 )
| ~ ( reli @ X3 @ esk12_0 ) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
thf(c_0_59,plain,
! [X1: $i] : ( reli @ X1 @ X1 ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
thf(c_0_60,negated_conjecture,
! [X2: $i > $o,X1: $i] :
( ( X2 @ ( esk13_3 @ esk12_0 @ esk12_0 @ esk12_0 ) )
| ( reli @ X1 @ ( esk3_2 @ X2 @ X1 ) )
| ~ ( reli @ X1 @ esk12_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_59])]) ).
thf(c_0_61,negated_conjecture,
reli @ esk11_0 @ esk12_0,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_62,negated_conjecture,
! [X13: $i,X12: $i,X3: $i,X1: $i] :
( ( epred1_0 @ X13 )
| ~ ( princ_inj @ esk7_0 @ ( esk13_3 @ X1 @ X3 @ X12 ) )
| ~ ( reli @ X12 @ X13 )
| ~ ( reli @ X3 @ X12 )
| ~ ( relr @ X1 @ X3 )
| ~ ( reli @ esk12_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_63,negated_conjecture,
! [X2: $i > $o] :
( ( reli @ esk11_0 @ ( esk3_2 @ X2 @ esk11_0 ) )
| ( X2 @ ( esk13_3 @ esk12_0 @ esk12_0 @ esk12_0 ) ) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
thf(c_0_64,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_43]) ).
thf(c_0_65,negated_conjecture,
! [X1: $i] :
( ( princ_inj @ esk7_0 @ X1 )
| ~ ( reli @ esk11_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_66,negated_conjecture,
! [X1: $i] :
( ( reli @ esk11_0 @ ( esk3_2 @ ( princ_inj @ esk7_0 ) @ esk11_0 ) )
| ( epred1_0 @ X1 )
| ~ ( reli @ esk12_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_59]),c_0_55])]) ).
thf(c_0_67,negated_conjecture,
! [X1: $i,X3: $i,X12: $i] :
( ( princ_inj @ esk7_0 @ X1 )
| ~ ( reli @ esk11_0 @ ( esk3_2 @ ( princ_inj @ esk7_0 ) @ X3 ) )
| ~ ( reli @ X12 @ X1 )
| ~ ( reli @ X3 @ X12 ) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
thf(c_0_68,negated_conjecture,
reli @ esk11_0 @ ( esk3_2 @ ( princ_inj @ esk7_0 ) @ esk11_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_45]),c_0_46]) ).
thf(c_0_69,negated_conjecture,
! [X3: $i,X1: $i] :
( ( princ_inj @ esk7_0 @ X1 )
| ~ ( reli @ esk11_0 @ X3 )
| ~ ( reli @ X3 @ X1 ) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
thf(c_0_70,negated_conjecture,
! [X1: $i] :
( ( princ_inj @ esk7_0 @ X1 )
| ~ ( reli @ esk12_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_69,c_0_61]) ).
thf(c_0_71,negated_conjecture,
! [X1: $i,X3: $i,X13: $i,X12: $i] :
( ( epred1_0 @ X1 )
| ~ ( reli @ esk12_0 @ ( esk13_3 @ X3 @ X12 @ X13 ) )
| ~ ( reli @ esk12_0 @ X3 )
| ~ ( reli @ X13 @ X1 )
| ~ ( reli @ X12 @ X13 )
| ~ ( relr @ X3 @ X12 ) ),
inference(spm,[status(thm)],[c_0_62,c_0_70]) ).
thf(c_0_72,negated_conjecture,
! [X1: $i,X3: $i,X12: $i] :
( ( epred1_0 @ X1 )
| ~ ( reli @ esk12_0 @ X3 )
| ~ ( reli @ esk12_0 @ X1 )
| ~ ( reli @ X12 @ esk12_0 )
| ~ ( relr @ X3 @ X12 ) ),
inference(spm,[status(thm)],[c_0_71,c_0_50]) ).
thf(c_0_73,negated_conjecture,
! [X1: $i,X3: $i] :
( ~ ( reli @ esk12_0 @ X1 )
| ~ ( reli @ X3 @ esk12_0 )
| ~ ( relr @ X1 @ X3 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_45]),c_0_46]) ).
thf(c_0_74,negated_conjecture,
! [X1: $i] :
( ~ ( reli @ esk12_0 @ X1 )
| ~ ( reli @ X1 @ esk12_0 ) ),
inference(spm,[status(thm)],[c_0_73,c_0_55]) ).
thf(c_0_75,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_59]),c_0_59])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV446^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n019.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 16:04:47 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.24 Running higher-order theorem proving
% 0.07/0.26 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/tmp/tmp.UN0H7s6HY7/E---3.1_972872.p
% 1.08/0.46 % Version: 3.5.1-ho
% 1.08/0.46 % Preprocessing class: HSMSSMSSMLSNHSN.
% 1.08/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.08/0.46 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 1.08/0.46 % Starting post_as_ho3 with 300s (1) cores
% 1.08/0.46 % Starting post_as_ho11 with 300s (1) cores
% 1.08/0.46 % Starting full_lambda_8 with 300s (1) cores
% 1.08/0.46 % new_ho_10_cnf2 with pid 972885 completed with status 0
% 1.08/0.46 % Result found by new_ho_10_cnf2
% 1.08/0.46 % Preprocessing class: HSMSSMSSMLSNHSN.
% 1.08/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.08/0.46 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 1.08/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.08/0.46 % No SInE strategy applied
% 1.08/0.46 % Search class: HGUNF-FFSS32-SHSSMMBN
% 1.08/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.08/0.46 % Starting SubtermCWHack with 136s (1) cores
% 1.08/0.46 % Starting new_ho_10_cnf2 with 151s (1) cores
% 1.08/0.46 % Starting sh5l with 136s (1) cores
% 1.08/0.46 % Starting lpo1_def_fix with 136s (1) cores
% 1.08/0.46 % Starting ehoh_best8_lambda with 136s (1) cores
% 1.08/0.46 % sh5l with pid 972893 completed with status 0
% 1.08/0.46 % Result found by sh5l
% 1.08/0.46 % Preprocessing class: HSMSSMSSMLSNHSN.
% 1.08/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.08/0.46 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 1.08/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.08/0.46 % No SInE strategy applied
% 1.08/0.46 % Search class: HGUNF-FFSS32-SHSSMMBN
% 1.08/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.08/0.46 % Starting SubtermCWHack with 136s (1) cores
% 1.08/0.46 % Starting new_ho_10_cnf2 with 151s (1) cores
% 1.08/0.46 % Starting sh5l with 136s (1) cores
% 1.08/0.46 % Preprocessing time : 0.002 s
% 1.08/0.46 % Presaturation interreduction done
% 1.08/0.46
% 1.08/0.46 % Proof found!
% 1.08/0.46 % SZS status Theorem
% 1.08/0.46 % SZS output start CNFRefutation
% See solution above
% 1.08/0.46 % Parsed axioms : 84
% 1.08/0.46 % Removed by relevancy pruning/SinE : 0
% 1.08/0.46 % Initial clauses : 64
% 1.08/0.46 % Removed in clause preprocessing : 43
% 1.08/0.46 % Initial clauses in saturation : 21
% 1.08/0.46 % Processed clauses : 672
% 1.08/0.46 % ...of these trivial : 8
% 1.08/0.46 % ...subsumed : 197
% 1.08/0.46 % ...remaining for further processing : 467
% 1.08/0.46 % Other redundant clauses eliminated : 4
% 1.08/0.46 % Clauses deleted for lack of memory : 0
% 1.08/0.46 % Backward-subsumed : 25
% 1.08/0.46 % Backward-rewritten : 35
% 1.08/0.46 % Generated clauses : 4257
% 1.08/0.46 % ...of the previous two non-redundant : 3664
% 1.08/0.46 % ...aggressively subsumed : 0
% 1.08/0.46 % Contextual simplify-reflections : 0
% 1.08/0.46 % Paramodulations : 4248
% 1.08/0.46 % Factorizations : 0
% 1.08/0.46 % NegExts : 0
% 1.08/0.46 % Equation resolutions : 4
% 1.08/0.46 % Disequality decompositions : 0
% 1.08/0.46 % Total rewrite steps : 675
% 1.08/0.46 % ...of those cached : 634
% 1.08/0.46 % Propositional unsat checks : 0
% 1.08/0.46 % Propositional check models : 0
% 1.08/0.46 % Propositional check unsatisfiable : 0
% 1.08/0.46 % Propositional clauses : 0
% 1.08/0.46 % Propositional clauses after purity: 0
% 1.08/0.46 % Propositional unsat core size : 0
% 1.08/0.46 % Propositional preprocessing time : 0.000
% 1.08/0.46 % Propositional encoding time : 0.000
% 1.08/0.46 % Propositional solver time : 0.000
% 1.08/0.46 % Success case prop preproc time : 0.000
% 1.08/0.46 % Success case prop encoding time : 0.000
% 1.08/0.46 % Success case prop solver time : 0.000
% 1.08/0.46 % Current number of processed clauses : 386
% 1.08/0.46 % Positive orientable unit clauses : 44
% 1.08/0.46 % Positive unorientable unit clauses: 0
% 1.08/0.46 % Negative unit clauses : 2
% 1.08/0.46 % Non-unit-clauses : 340
% 1.08/0.46 % Current number of unprocessed clauses: 2923
% 1.08/0.46 % ...number of literals in the above : 10993
% 1.08/0.46 % Current number of archived formulas : 0
% 1.08/0.46 % Current number of archived clauses : 81
% 1.08/0.46 % Clause-clause subsumption calls (NU) : 19195
% 1.08/0.46 % Rec. Clause-clause subsumption calls : 12334
% 1.08/0.46 % Non-unit clause-clause subsumptions : 220
% 1.08/0.46 % Unit Clause-clause subsumption calls : 208
% 1.08/0.46 % Rewrite failures with RHS unbound : 0
% 1.08/0.46 % BW rewrite match attempts : 42
% 1.08/0.46 % BW rewrite match successes : 13
% 1.08/0.46 % Condensation attempts : 672
% 1.08/0.46 % Condensation successes : 0
% 1.08/0.46 % Termbank termtop insertions : 242969
% 1.08/0.46 % Search garbage collected termcells : 1654
% 1.08/0.46
% 1.08/0.46 % -------------------------------------------------
% 1.08/0.46 % User time : 0.171 s
% 1.08/0.46 % System time : 0.006 s
% 1.08/0.46 % Total time : 0.178 s
% 1.08/0.46 % Maximum resident set size: 3952 pages
% 1.08/0.46
% 1.08/0.46 % -------------------------------------------------
% 1.08/0.46 % User time : 0.833 s
% 1.08/0.46 % System time : 0.037 s
% 1.08/0.46 % Total time : 0.870 s
% 1.08/0.46 % Maximum resident set size: 4864 pages
% 1.08/0.46 % E exiting
%------------------------------------------------------------------------------