%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL690^1 : 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 : 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 08:12:02 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 57 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 205 ( 23 equ; 0 cnn)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 545 ( 74 ~; 76 |; 10 &; 358 @)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 53 ( 53 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 7 con; 0-3 aty)
% Number of variables : 146 ( 47 ^; 99 !; 0 ?; 146 :)
% Comments :
%------------------------------------------------------------------------------
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_52,type,
cs4_valid: ( $i > $o ) > $o ).
thf(decl_53,type,
esk1_2: ( $i > $o ) > $i > $i ).
thf(decl_55,type,
esk3_2: ( $i > $o ) > $i > $i ).
thf(decl_59,type,
epred1_0: $i > $o ).
thf(decl_60,type,
epred2_0: $i > $o ).
thf(decl_61,type,
esk7_0: $i ).
thf(decl_62,type,
esk8_0: $i ).
thf(decl_63,type,
esk9_3: $i > $i > $i > $i ).
thf(decl_64,type,
esk10_0: $i ).
thf(decl_65,type,
esk11_0: $i ).
thf(decl_66,type,
esk12_0: $i ).
thf(decl_67,type,
esk13_0: $i ).
thf(mimpl,axiom,
( mimpl
= ( ^ [X7: $i > $o,X8: $i > $o] : ( mor @ ( mnot @ X7 ) @ X8 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uH52ad6GL8/E---3.1_525993.p',mimpl) ).
thf(mnot,axiom,
( mnot
= ( ^ [X2: $i > $o,X3: $i] :
~ ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uH52ad6GL8/E---3.1_525993.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uH52ad6GL8/E---3.1_525993.p',mor) ).
thf(cs4_atom,axiom,
( cs4_atom
= ( ^ [X11: $i > $o] : ( mbox @ reli @ X11 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uH52ad6GL8/E---3.1_525993.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.uH52ad6GL8/E---3.1_525993.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.uH52ad6GL8/E---3.1_525993.p',cs4_impl) ).
thf(cs4_box,axiom,
( cs4_box
= ( ^ [X19: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ X19 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uH52ad6GL8/E---3.1_525993.p',cs4_box) ).
thf(cs4_valid_def,axiom,
( cs4_valid
= ( ^ [X19: $i > $o] : ( mvalid @ X19 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uH52ad6GL8/E---3.1_525993.p',cs4_valid_def) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X11: $i > $o] :
! [X15: $i] : ( X11 @ X15 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uH52ad6GL8/E---3.1_525993.p',mvalid) ).
thf(cs4_k,conjecture,
! [X19: $i > $o,X20: $i > $o] : ( cs4_valid @ ( cs4_impl @ ( cs4_box @ ( cs4_impl @ ( cs4_atom @ X19 ) @ ( cs4_atom @ X20 ) ) ) @ ( cs4_impl @ ( cs4_box @ ( cs4_atom @ X19 ) ) @ ( cs4_box @ ( cs4_atom @ X20 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uH52ad6GL8/E---3.1_525993.p',cs4_k) ).
thf(trans_axiom_i,axiom,
! [X19: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ X19 ) @ ( mbox @ reli @ ( mbox @ reli @ X19 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uH52ad6GL8/E---3.1_525993.p',trans_axiom_i) ).
thf(refl_axiom_i,axiom,
! [X19: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ X19 ) @ X19 ) ),
file('/export/starexec/sandbox2/tmp/tmp.uH52ad6GL8/E---3.1_525993.p',refl_axiom_i) ).
thf(c_0_12,plain,
( mimpl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimpl]) ).
thf(c_0_13,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_14,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_15,plain,
( cs4_atom
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X29: $i] :
( ( reli @ Z1 @ X29 )
=> ( Z0 @ X29 ) ) ) ),
inference(fof_simplification,[status(thm)],[cs4_atom]) ).
thf(c_0_16,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_17,plain,
( cs4_impl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
! [X30: $i] :
( ( reli @ Z2 @ X30 )
=> ( ~ ( Z0 @ X30 )
| ( Z1 @ X30 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[cs4_impl]) ).
thf(c_0_18,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_12,c_0_13]),c_0_14]) ).
thf(c_0_19,plain,
( cs4_box
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X34: $i] :
( ( reli @ Z1 @ X34 )
=> ! [X33: $i] :
( ( relr @ X34 @ X33 )
=> ( Z0 @ X33 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[cs4_box]) ).
thf(c_0_20,plain,
( cs4_valid
= ( ^ [Z0: $i > $o] :
! [X35: $i] : ( Z0 @ X35 ) ) ),
inference(fof_simplification,[status(thm)],[cs4_valid_def]) ).
thf(c_0_21,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X15: $i] : ( Z0 @ X15 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_22,negated_conjecture,
~ ! [X19: $i > $o,X20: $i > $o] : ( cs4_valid @ ( cs4_impl @ ( cs4_box @ ( cs4_impl @ ( cs4_atom @ X19 ) @ ( cs4_atom @ X20 ) ) ) @ ( cs4_impl @ ( cs4_box @ ( cs4_atom @ X19 ) ) @ ( cs4_box @ ( cs4_atom @ X20 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cs4_k]) ).
thf(c_0_23,plain,
( cs4_atom
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X29: $i] :
( ( reli @ Z1 @ X29 )
=> ( Z0 @ X29 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_24,plain,
( cs4_impl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
! [X30: $i] :
( ( reli @ Z2 @ X30 )
=> ( ~ ( Z0 @ X30 )
| ( Z1 @ X30 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_17,c_0_18]),c_0_16]) ).
thf(c_0_25,plain,
( cs4_box
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X34: $i] :
( ( reli @ Z1 @ X34 )
=> ! [X33: $i] :
( ( relr @ X34 @ X33 )
=> ( Z0 @ X33 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_19,c_0_16]) ).
thf(c_0_26,plain,
( cs4_valid
= ( ^ [Z0: $i > $o] :
! [X35: $i] : ( Z0 @ X35 ) ) ),
inference(apply_def,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_27,negated_conjecture,
~ ! [X19: $i > $o,X20: $i > $o,X66: $i,X65: $i] :
( ( reli @ X66 @ X65 )
=> ( ~ ! [X56: $i] :
( ( reli @ X65 @ X56 )
=> ! [X57: $i] :
( ( relr @ X56 @ X57 )
=> ! [X55: $i] :
( ( reli @ X57 @ X55 )
=> ( ~ ! [X53: $i] :
( ( reli @ X55 @ X53 )
=> ( X19 @ X53 ) )
| ! [X54: $i] :
( ( reli @ X55 @ X54 )
=> ( X20 @ X54 ) ) ) ) ) )
| ! [X64: $i] :
( ( reli @ X65 @ X64 )
=> ( ~ ! [X59: $i] :
( ( reli @ X64 @ X59 )
=> ! [X60: $i] :
( ( relr @ X59 @ X60 )
=> ! [X58: $i] :
( ( reli @ X60 @ X58 )
=> ( X19 @ X58 ) ) ) )
| ! [X62: $i] :
( ( reli @ X64 @ X62 )
=> ! [X63: $i] :
( ( relr @ X62 @ X63 )
=> ! [X61: $i] :
( ( reli @ X63 @ X61 )
=> ( X20 @ X61 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25]),c_0_26]) ).
thf(c_0_28,negated_conjecture,
! [X93: $i,X94: $i,X95: $i,X97: $i,X99: $i,X100: $i,X101: $i] :
( ( reli @ esk7_0 @ esk8_0 )
& ( ( reli @ X95 @ ( esk9_3 @ X93 @ X94 @ X95 ) )
| ~ ( reli @ X95 @ X97 )
| ( epred2_0 @ X97 )
| ~ ( reli @ X94 @ X95 )
| ~ ( relr @ X93 @ X94 )
| ~ ( reli @ esk8_0 @ X93 ) )
& ( ~ ( epred1_0 @ ( esk9_3 @ X93 @ X94 @ X95 ) )
| ~ ( reli @ X95 @ X97 )
| ( epred2_0 @ X97 )
| ~ ( reli @ X94 @ X95 )
| ~ ( relr @ X93 @ X94 )
| ~ ( reli @ esk8_0 @ X93 ) )
& ( reli @ esk8_0 @ esk10_0 )
& ( ~ ( reli @ esk10_0 @ X99 )
| ~ ( relr @ X99 @ X100 )
| ~ ( reli @ X100 @ X101 )
| ( epred1_0 @ X101 ) )
& ( reli @ esk10_0 @ esk11_0 )
& ( relr @ esk11_0 @ esk12_0 )
& ( reli @ esk12_0 @ esk13_0 )
& ~ ( epred2_0 @ esk13_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])])])]) ).
thf(c_0_29,negated_conjecture,
! [X1: $i,X13: $i,X12: $i,X3: $i] :
( ( reli @ X1 @ ( esk9_3 @ X3 @ X12 @ X1 ) )
| ( epred2_0 @ X13 )
| ~ ( reli @ X1 @ X13 )
| ~ ( reli @ X12 @ X1 )
| ~ ( relr @ X3 @ X12 )
| ~ ( reli @ esk8_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_30,negated_conjecture,
reli @ esk12_0 @ esk13_0,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_31,negated_conjecture,
~ ( epred2_0 @ esk13_0 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_32,negated_conjecture,
! [X1: $i,X3: $i,X12: $i] :
( ( epred1_0 @ X12 )
| ~ ( reli @ esk10_0 @ X1 )
| ~ ( relr @ X1 @ X3 )
| ~ ( reli @ X3 @ X12 ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_33,negated_conjecture,
! [X1: $i,X3: $i] :
( ( reli @ esk12_0 @ ( esk9_3 @ X1 @ X3 @ esk12_0 ) )
| ~ ( reli @ esk8_0 @ X1 )
| ~ ( reli @ X3 @ esk12_0 )
| ~ ( relr @ X1 @ X3 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
thf(c_0_34,plain,
! [X19: $i > $o,X43: $i] :
( ~ ! [X40: $i] :
( ( reli @ X43 @ X40 )
=> ( X19 @ X40 ) )
| ! [X42: $i] :
( ( reli @ X43 @ X42 )
=> ! [X41: $i] :
( ( reli @ X42 @ X41 )
=> ( X19 @ X41 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[trans_axiom_i,c_0_18]),c_0_16]),c_0_21]) ).
thf(c_0_35,negated_conjecture,
! [X1: $i,X12: $i,X3: $i] :
( ( epred1_0 @ ( esk9_3 @ X1 @ X3 @ esk12_0 ) )
| ~ ( reli @ esk10_0 @ X12 )
| ~ ( relr @ X12 @ esk12_0 )
| ~ ( reli @ esk8_0 @ X1 )
| ~ ( reli @ X3 @ esk12_0 )
| ~ ( relr @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
thf(c_0_36,negated_conjecture,
relr @ esk11_0 @ esk12_0,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_37,negated_conjecture,
reli @ esk10_0 @ esk11_0,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_38,plain,
! [X19: $i > $o,X37: $i] :
( ~ ! [X36: $i] :
( ( reli @ X37 @ X36 )
=> ( X19 @ X36 ) )
| ( X19 @ X37 ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[refl_axiom_i,c_0_18]),c_0_16]),c_0_21]) ).
thf(c_0_39,plain,
! [X73: $i > $o,X74: $i,X76: $i,X77: $i] :
( ( ( reli @ X74 @ ( esk3_2 @ X73 @ X74 ) )
| ~ ( reli @ X74 @ X76 )
| ~ ( reli @ X76 @ X77 )
| ( X73 @ X77 ) )
& ( ~ ( X73 @ ( esk3_2 @ X73 @ X74 ) )
| ~ ( reli @ X74 @ X76 )
| ~ ( reli @ X76 @ X77 )
| ( X73 @ X77 ) ) ),
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_34])])])])])]) ).
thf(c_0_40,negated_conjecture,
! [X13: $i,X12: $i,X3: $i,X1: $i] :
( ( epred2_0 @ X13 )
| ~ ( epred1_0 @ ( esk9_3 @ X1 @ X3 @ X12 ) )
| ~ ( reli @ X12 @ X13 )
| ~ ( reli @ X3 @ X12 )
| ~ ( relr @ X1 @ X3 )
| ~ ( reli @ esk8_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_41,negated_conjecture,
! [X1: $i,X3: $i] :
( ( epred1_0 @ ( esk9_3 @ X1 @ X3 @ esk12_0 ) )
| ~ ( reli @ esk8_0 @ X1 )
| ~ ( reli @ X3 @ esk12_0 )
| ~ ( relr @ X1 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).
thf(c_0_42,plain,
! [X67: $i > $o,X68: $i] :
( ( ( reli @ X68 @ ( esk1_2 @ X67 @ X68 ) )
| ( X67 @ X68 ) )
& ( ~ ( X67 @ ( esk1_2 @ X67 @ X68 ) )
| ( X67 @ X68 ) ) ),
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_38])])])])]) ).
thf(c_0_43,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_39]) ).
thf(c_0_44,negated_conjecture,
! [X1: $i,X3: $i,X12: $i] :
( ( epred2_0 @ X1 )
| ~ ( reli @ esk8_0 @ X3 )
| ~ ( reli @ esk12_0 @ X1 )
| ~ ( reli @ X12 @ esk12_0 )
| ~ ( relr @ X3 @ X12 ) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
thf(c_0_45,plain,
! [X2: $i > $o,X1: $i] :
( ( X2 @ X1 )
| ~ ( X2 @ ( esk1_2 @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_46,plain,
! [X2: $i > $o,X1: $i] :
( ( reli @ X1 @ ( esk1_2 @ X2 @ X1 ) )
| ( X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_47,negated_conjecture,
! [X2: $i > $o,X1: $i] :
( ( reli @ X1 @ ( esk3_2 @ X2 @ X1 ) )
| ( X2 @ esk11_0 )
| ~ ( reli @ X1 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_43,c_0_37]) ).
thf(c_0_48,negated_conjecture,
reli @ esk8_0 @ esk10_0,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_49,negated_conjecture,
! [X1: $i,X3: $i] :
( ~ ( reli @ esk8_0 @ X1 )
| ~ ( reli @ X3 @ esk12_0 )
| ~ ( relr @ X1 @ X3 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_30]),c_0_31]) ).
thf(c_0_50,plain,
! [X1: $i] : ( reli @ X1 @ X1 ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
thf(c_0_51,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_39]) ).
thf(c_0_52,negated_conjecture,
! [X2: $i > $o] :
( ( reli @ esk8_0 @ ( esk3_2 @ X2 @ esk8_0 ) )
| ( X2 @ esk11_0 ) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
thf(c_0_53,negated_conjecture,
~ ( reli @ esk8_0 @ esk11_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_36]),c_0_50])]) ).
thf(c_0_54,negated_conjecture,
! [X3: $i,X1: $i] :
( ( reli @ esk8_0 @ X1 )
| ~ ( reli @ esk8_0 @ X3 )
| ~ ( reli @ X3 @ X1 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).
thf(c_0_55,negated_conjecture,
! [X1: $i] :
( ( reli @ esk8_0 @ X1 )
| ~ ( reli @ esk10_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_54,c_0_48]) ).
thf(c_0_56,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_37]),c_0_53]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL690^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % 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 09:36:31 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.24 Running higher-order theorem proving
% 0.07/0.24 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.uH52ad6GL8/E---3.1_525993.p
% 0.20/0.29 % Version: 3.5.1-ho
% 0.20/0.29 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.20/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.29 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.20/0.29 % Starting post_as_ho3 with 300s (1) cores
% 0.20/0.29 % Starting post_as_ho11 with 300s (1) cores
% 0.20/0.29 % Starting full_lambda_8 with 300s (1) cores
% 0.20/0.29 % new_ho_10_cnf2 with pid 526006 completed with status 0
% 0.20/0.29 % Result found by new_ho_10_cnf2
% 0.20/0.29 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.20/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.29 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.20/0.29 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.20/0.29 % No SInE strategy applied
% 0.20/0.29 % Search class: HGUNF-FFSS32-SHSSMMBN
% 0.20/0.29 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.29 % Starting SubtermCWHack with 136s (1) cores
% 0.20/0.29 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.20/0.29 % Starting sh5l with 136s (1) cores
% 0.20/0.29 % Starting lpo1_def_fix with 136s (1) cores
% 0.20/0.29 % Starting ehoh_best8_lambda with 136s (1) cores
% 0.20/0.29 % sh5l with pid 526014 completed with status 0
% 0.20/0.29 % Result found by sh5l
% 0.20/0.29 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.20/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.29 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.20/0.29 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.20/0.29 % No SInE strategy applied
% 0.20/0.29 % Search class: HGUNF-FFSS32-SHSSMMBN
% 0.20/0.29 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.29 % Starting SubtermCWHack with 136s (1) cores
% 0.20/0.29 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.20/0.29 % Starting sh5l with 136s (1) cores
% 0.20/0.29 % Preprocessing time : 0.002 s
% 0.20/0.29 % Presaturation interreduction done
% 0.20/0.29
% 0.20/0.29 % Proof found!
% 0.20/0.29 % SZS status Theorem
% 0.20/0.29 % SZS output start CNFRefutation
% See solution above
% 0.20/0.29 % Parsed axioms : 61
% 0.20/0.29 % Removed by relevancy pruning/SinE : 0
% 0.20/0.29 % Initial clauses : 51
% 0.20/0.29 % Removed in clause preprocessing : 31
% 0.20/0.29 % Initial clauses in saturation : 20
% 0.20/0.29 % Processed clauses : 143
% 0.20/0.29 % ...of these trivial : 0
% 0.20/0.29 % ...subsumed : 10
% 0.20/0.29 % ...remaining for further processing : 133
% 0.20/0.29 % Other redundant clauses eliminated : 0
% 0.20/0.29 % Clauses deleted for lack of memory : 0
% 0.20/0.29 % Backward-subsumed : 4
% 0.20/0.29 % Backward-rewritten : 4
% 0.20/0.29 % Generated clauses : 446
% 0.20/0.29 % ...of the previous two non-redundant : 396
% 0.20/0.29 % ...aggressively subsumed : 0
% 0.20/0.29 % Contextual simplify-reflections : 0
% 0.20/0.29 % Paramodulations : 441
% 0.20/0.29 % Factorizations : 0
% 0.20/0.29 % NegExts : 0
% 0.20/0.29 % Equation resolutions : 0
% 0.20/0.29 % Disequality decompositions : 0
% 0.20/0.29 % Total rewrite steps : 62
% 0.20/0.29 % ...of those cached : 46
% 0.20/0.29 % Propositional unsat checks : 0
% 0.20/0.29 % Propositional check models : 0
% 0.20/0.29 % Propositional check unsatisfiable : 0
% 0.20/0.29 % Propositional clauses : 0
% 0.20/0.29 % Propositional clauses after purity: 0
% 0.20/0.29 % Propositional unsat core size : 0
% 0.20/0.29 % Propositional preprocessing time : 0.000
% 0.20/0.29 % Propositional encoding time : 0.000
% 0.20/0.29 % Propositional solver time : 0.000
% 0.20/0.29 % Success case prop preproc time : 0.000
% 0.20/0.29 % Success case prop encoding time : 0.000
% 0.20/0.29 % Success case prop solver time : 0.000
% 0.20/0.29 % Current number of processed clauses : 105
% 0.20/0.29 % Positive orientable unit clauses : 15
% 0.20/0.29 % Positive unorientable unit clauses: 0
% 0.20/0.29 % Negative unit clauses : 4
% 0.20/0.29 % Non-unit-clauses : 86
% 0.20/0.29 % Current number of unprocessed clauses: 283
% 0.20/0.29 % ...number of literals in the above : 946
% 0.20/0.29 % Current number of archived formulas : 0
% 0.20/0.29 % Current number of archived clauses : 28
% 0.20/0.29 % Clause-clause subsumption calls (NU) : 1163
% 0.20/0.29 % Rec. Clause-clause subsumption calls : 698
% 0.20/0.29 % Non-unit clause-clause subsumptions : 9
% 0.20/0.29 % Unit Clause-clause subsumption calls : 46
% 0.20/0.29 % Rewrite failures with RHS unbound : 0
% 0.20/0.29 % BW rewrite match attempts : 28
% 0.20/0.29 % BW rewrite match successes : 3
% 0.20/0.29 % Condensation attempts : 143
% 0.20/0.29 % Condensation successes : 0
% 0.20/0.29 % Termbank termtop insertions : 34687
% 0.20/0.29 % Search garbage collected termcells : 1585
% 0.20/0.29
% 0.20/0.29 % -------------------------------------------------
% 0.20/0.29 % User time : 0.024 s
% 0.20/0.29 % System time : 0.008 s
% 0.20/0.29 % Total time : 0.033 s
% 0.20/0.29 % Maximum resident set size: 3940 pages
% 0.20/0.29
% 0.20/0.29 % -------------------------------------------------
% 0.20/0.29 % User time : 0.112 s
% 0.20/0.29 % System time : 0.026 s
% 0.20/0.29 % Total time : 0.137 s
% 0.20/0.29 % Maximum resident set size: 4608 pages
% 0.20/0.29 % E exiting
%------------------------------------------------------------------------------