%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM689^4 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 08:16:50 AM UTC 2026
% Result : Theorem 0.65s 0.47s
% Output : CNFRefutation 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 54 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 265 ( 45 equ; 0 cnn)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 558 ( 51 ~; 37 |; 8 &; 416 @)
% ( 0 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 7 con; 0-3 aty)
% Number of variables : 118 ( 86 ^; 32 !; 0 ?; 118 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
is_of: $i > ( $i > $o ) > $o ).
thf(decl_24,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_26,type,
in: $i > $i > $o ).
thf(decl_62,type,
imp: $o > $o > $o ).
thf(decl_63,type,
d_not: $o > $o ).
thf(decl_68,type,
l_or: $o > $o > $o ).
thf(decl_73,type,
l_some: $i > ( $i > $o ) > $o ).
thf(decl_78,type,
e_is: $i > $i > $i > $o ).
thf(decl_124,type,
nat: $i ).
thf(decl_125,type,
n_is: $i > $i > $o ).
thf(decl_128,type,
n_some: ( $i > $o ) > $o ).
thf(decl_143,type,
n_pl: $i > $i > $i ).
thf(decl_148,type,
diffprop: $i > $i > $i > $o ).
thf(decl_149,type,
d_29_ii: $i > $i > $o ).
thf(decl_150,type,
iii: $i > $i > $o ).
thf(decl_152,type,
moreis: $i > $i > $o ).
thf(decl_153,type,
lessis: $i > $i > $o ).
thf(decl_156,type,
esk1_0: $i ).
thf(decl_157,type,
esk2_0: $i ).
thf(decl_158,type,
esk3_0: $i ).
thf(decl_159,type,
esk4_0: $i ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rpT9bcJgDp/E---3.1_1602490.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rpT9bcJgDp/E---3.1_1602490.p',def_imp) ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rpT9bcJgDp/E---3.1_1602490.p',def_d_29_ii) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rpT9bcJgDp/E---3.1_1602490.p',def_l_or) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rpT9bcJgDp/E---3.1_1602490.p',def_e_is) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rpT9bcJgDp/E---3.1_1602490.p',def_iii) ).
thf(def_all_of,axiom,
( all_of
= ( ^ [X3: $i > $o,X2: $i > $o] :
! [X4: $i] :
( ( is_of @ X4 @ X3 )
=> ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rpT9bcJgDp/E---3.1_1602490.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rpT9bcJgDp/E---3.1_1602490.p',def_is_of) ).
thf(def_moreis,axiom,
( moreis
= ( ^ [X1: $i,X229: $i] : ( l_or @ ( d_29_ii @ X1 @ X229 ) @ ( n_is @ X1 @ X229 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rpT9bcJgDp/E---3.1_1602490.p',def_moreis) ).
thf(def_n_some,axiom,
( n_some
= ( l_some @ nat ) ),
file('/export/starexec/sandbox/tmp/tmp.rpT9bcJgDp/E---3.1_1602490.p',def_n_some) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rpT9bcJgDp/E---3.1_1602490.p',def_n_is) ).
thf(def_lessis,axiom,
( lessis
= ( ^ [X1: $i,X230: $i] : ( l_or @ ( iii @ X1 @ X230 ) @ ( n_is @ X1 @ X230 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rpT9bcJgDp/E---3.1_1602490.p',def_lessis) ).
thf(satz22c,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X315: $i] : ( in @ X315 @ nat )
@ ^ [X316: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ nat )
@ ^ [X13: $i] :
( ( lessis @ X1 @ X316 )
=> ( ( iii @ X4 @ X13 )
=> ( iii @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X316 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rpT9bcJgDp/E---3.1_1602490.p',satz22c) ).
thf(satz22b,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X313: $i] : ( in @ X313 @ nat )
@ ^ [X314: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ nat )
@ ^ [X13: $i] :
( ( d_29_ii @ X1 @ X314 )
=> ( ( moreis @ X4 @ X13 )
=> ( d_29_ii @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X314 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rpT9bcJgDp/E---3.1_1602490.p',satz22b) ).
thf(satz19f,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X277: $i] : ( in @ X277 @ nat )
@ ^ [X278: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( iii @ X1 @ X278 )
=> ( iii @ ( n_pl @ X4 @ X1 ) @ ( n_pl @ X4 @ X278 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rpT9bcJgDp/E---3.1_1602490.p',satz19f) ).
thf(c_0_15,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_not]) ).
thf(c_0_16,plain,
( imp
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_imp]) ).
thf(c_0_17,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_d_29_ii]) ).
thf(c_0_18,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_l_or]) ).
thf(c_0_19,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_20,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_21,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_22,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_all_of]) ).
thf(c_0_23,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_24,plain,
( moreis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_moreis]) ).
thf(c_0_25,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_17,def_n_some]) ).
thf(c_0_26,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_18,c_0_16]),c_0_19]) ).
thf(c_0_27,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_20]) ).
thf(c_0_28,plain,
( lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_lessis]) ).
thf(c_0_29,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_21,def_n_some]) ).
thf(c_0_30,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_31,plain,
( moreis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]) ).
thf(c_0_32,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X315: $i] : ( in @ X315 @ nat )
@ ^ [X316: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ nat )
@ ^ [X13: $i] :
( ( lessis @ X1 @ X316 )
=> ( ( iii @ X4 @ X13 )
=> ( iii @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X316 @ X13 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[satz22c]) ).
thf(c_0_33,plain,
( lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_28,c_0_29]),c_0_26]),c_0_27]) ).
thf(c_0_34,plain,
! [X516: $i] :
( ( in @ X516 @ nat )
=> ! [X515: $i] :
( ( in @ X515 @ nat )
=> ! [X514: $i] :
( ( in @ X514 @ nat )
=> ! [X513: $i] :
( ( in @ X513 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X516 @ X515 ) )
=> ( ( ( ( l_some @ nat @ ( diffprop @ X514 @ X513 ) )
=> ~ $true )
=> ( X514 = X513 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ X516 @ X514 ) @ ( n_pl @ X515 @ X513 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz22b]),c_0_25]),c_0_30]),c_0_31]) ).
thf(c_0_35,negated_conjecture,
~ ! [X387: $i] :
( ( in @ X387 @ nat )
=> ! [X386: $i] :
( ( in @ X386 @ nat )
=> ! [X385: $i] :
( ( in @ X385 @ nat )
=> ! [X384: $i] :
( ( in @ X384 @ nat )
=> ( ( ( ( l_some @ nat @ ( diffprop @ X386 @ X387 ) )
=> ~ $true )
=> ( X387 = X386 ) )
=> ( ( l_some @ nat @ ( diffprop @ X384 @ X385 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ X386 @ X384 ) @ ( n_pl @ X387 @ X385 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_32]),c_0_29]),c_0_30]),c_0_33]) ).
thf(c_0_36,plain,
! [X704: $i,X705: $i,X706: $i,X707: $i] :
( ( ~ ( l_some @ nat @ ( diffprop @ X706 @ X707 ) )
| ~ $true
| ( l_some @ nat @ ( diffprop @ ( n_pl @ X704 @ X706 ) @ ( n_pl @ X705 @ X707 ) ) )
| ~ ( l_some @ nat @ ( diffprop @ X704 @ X705 ) )
| ~ ( in @ X707 @ nat )
| ~ ( in @ X706 @ nat )
| ~ ( in @ X705 @ nat )
| ~ ( in @ X704 @ nat ) )
& ( ( X706 != X707 )
| ( l_some @ nat @ ( diffprop @ ( n_pl @ X704 @ X706 ) @ ( n_pl @ X705 @ X707 ) ) )
| ~ ( l_some @ nat @ ( diffprop @ X704 @ X705 ) )
| ~ ( in @ X707 @ nat )
| ~ ( in @ X706 @ nat )
| ~ ( in @ X705 @ nat )
| ~ ( in @ X704 @ nat ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])])])]) ).
thf(c_0_37,negated_conjecture,
( ( in @ esk1_0 @ nat )
& ( in @ esk2_0 @ nat )
& ( in @ esk3_0 @ nat )
& ( in @ esk4_0 @ nat )
& ( ( l_some @ nat @ ( diffprop @ esk2_0 @ esk1_0 ) )
| ( esk1_0 = esk2_0 ) )
& ( $true
| ( esk1_0 = esk2_0 ) )
& ( l_some @ nat @ ( diffprop @ esk4_0 @ esk3_0 ) )
& ~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk2_0 @ esk4_0 ) @ ( n_pl @ esk1_0 @ esk3_0 ) ) ) ),
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_35])])])])]) ).
thf(c_0_38,plain,
! [X1: $i,X4: $i,X6: $i,X5: $i] :
( ( l_some @ nat @ ( diffprop @ ( n_pl @ X5 @ X1 ) @ ( n_pl @ X6 @ X4 ) ) )
| ~ ( l_some @ nat @ ( diffprop @ X1 @ X4 ) )
| ~ $true
| ~ ( l_some @ nat @ ( diffprop @ X5 @ X6 ) )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X6 @ nat )
| ~ ( in @ X5 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_39,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk2_0 @ esk4_0 ) @ ( n_pl @ esk1_0 @ esk3_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_40,plain,
! [X1: $i,X6: $i,X5: $i,X4: $i] :
( ( l_some @ nat @ ( diffprop @ ( n_pl @ X5 @ X1 ) @ ( n_pl @ X6 @ X4 ) ) )
| ~ ( in @ X6 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ X5 @ X6 ) )
| ~ ( l_some @ nat @ ( diffprop @ X1 @ X4 ) ) ),
inference(cn,[status(thm)],[c_0_38]) ).
thf(c_0_41,negated_conjecture,
l_some @ nat @ ( diffprop @ esk4_0 @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_42,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_43,negated_conjecture,
in @ esk2_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_44,negated_conjecture,
in @ esk3_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_45,negated_conjecture,
in @ esk4_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_46,negated_conjecture,
( ( l_some @ nat @ ( diffprop @ esk2_0 @ esk1_0 ) )
| ( esk1_0 = esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_47,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ esk2_0 @ esk1_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_42]),c_0_43]),c_0_44]),c_0_45])]) ).
thf(c_0_48,plain,
! [X436: $i] :
( ( in @ X436 @ nat )
=> ! [X435: $i] :
( ( in @ X435 @ nat )
=> ! [X434: $i] :
( ( in @ X434 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X435 @ X436 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ X434 @ X435 ) @ ( n_pl @ X434 @ X436 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz19f]),c_0_29]),c_0_30]) ).
thf(c_0_49,negated_conjecture,
esk2_0 = esk1_0,
inference(sr,[status(thm)],[c_0_46,c_0_47]) ).
thf(c_0_50,plain,
! [X625: $i,X626: $i,X627: $i] :
( ~ ( in @ X625 @ nat )
| ~ ( in @ X626 @ nat )
| ~ ( in @ X627 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ X626 @ X625 ) )
| ( l_some @ nat @ ( diffprop @ ( n_pl @ X627 @ X626 ) @ ( n_pl @ X627 @ X625 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])])]) ).
thf(c_0_51,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk1_0 @ esk4_0 ) @ ( n_pl @ esk1_0 @ esk3_0 ) ) ),
inference(spm,[status(thm)],[c_0_39,c_0_49]) ).
thf(c_0_52,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( l_some @ nat @ ( diffprop @ ( n_pl @ X5 @ X4 ) @ ( n_pl @ X5 @ X1 ) ) )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ X4 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
thf(c_0_53,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_41]),c_0_42]),c_0_45]),c_0_44])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM689^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n005.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 12:39:16 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.21/0.26 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.rpT9bcJgDp/E---3.1_1602490.p
% 0.65/0.47 % Version: 3.5.1-ho
% 0.65/0.47 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.65/0.47 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.65/0.47 % Starting lpo1_fix with 900s (3) cores
% 0.65/0.47 % Starting full_lambda_9 with 300s (1) cores
% 0.65/0.47 % Starting almost_fo_4 with 300s (1) cores
% 0.65/0.47 % Starting new_ho_9 with 300s (1) cores
% 0.65/0.47 % Starting pre_casc_4 with 300s (1) cores
% 0.65/0.47 % Starting ho_unfolding_6 with 300s (1) cores
% 0.65/0.47 % full_lambda_9 with pid 1602504 completed with status 0
% 0.65/0.47 % Result found by full_lambda_9
% 0.65/0.47 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.65/0.47 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.65/0.47 % Starting lpo1_fix with 900s (3) cores
% 0.65/0.47 % Starting full_lambda_9 with 300s (1) cores
% 0.65/0.47 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 0.65/0.47 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.65/0.47 % Search class: HGHSM-FSLM32-DHSMMSBN
% 0.65/0.47 % partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.65/0.47 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.65/0.47 % Starting SubtermCWHack with 28s (1) cores
% 0.65/0.47 % SubtermCWHack with pid 1602509 completed with status 0
% 0.65/0.47 % Result found by SubtermCWHack
% 0.65/0.47 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.65/0.47 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.65/0.47 % Starting lpo1_fix with 900s (3) cores
% 0.65/0.47 % Starting full_lambda_9 with 300s (1) cores
% 0.65/0.47 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 0.65/0.47 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.65/0.47 % Search class: HGHSM-FSLM32-DHSMMSBN
% 0.65/0.47 % partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.65/0.47 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.65/0.47 % Starting SubtermCWHack with 28s (1) cores
% 0.65/0.47 % Preprocessing time : 0.006 s
% 0.65/0.47
% 0.65/0.47 % Proof found!
% 0.65/0.47 % SZS status Theorem
% 0.65/0.47 % SZS output start CNFRefutation
% See solution above
% 0.65/0.47 % Parsed axioms : 393
% 0.65/0.47 % Removed by relevancy pruning/SinE : 263
% 0.65/0.47 % Initial clauses : 344
% 0.65/0.47 % Removed in clause preprocessing : 175
% 0.65/0.47 % Initial clauses in saturation : 169
% 0.65/0.47 % Processed clauses : 1115
% 0.65/0.47 % ...of these trivial : 8
% 0.65/0.47 % ...subsumed : 484
% 0.65/0.47 % ...remaining for further processing : 623
% 0.65/0.47 % Other redundant clauses eliminated : 30
% 0.65/0.47 % Clauses deleted for lack of memory : 0
% 0.65/0.47 % Backward-subsumed : 1
% 0.65/0.47 % Backward-rewritten : 2
% 0.65/0.47 % Generated clauses : 3231
% 0.65/0.47 % ...of the previous two non-redundant : 3029
% 0.65/0.47 % ...aggressively subsumed : 0
% 0.65/0.47 % Contextual simplify-reflections : 0
% 0.65/0.47 % Paramodulations : 3190
% 0.65/0.47 % Factorizations : 2
% 0.65/0.47 % NegExts : 0
% 0.65/0.47 % Equation resolutions : 35
% 0.65/0.47 % Disequality decompositions : 0
% 0.65/0.47 % Total rewrite steps : 1092
% 0.65/0.47 % ...of those cached : 1056
% 0.65/0.47 % Propositional unsat checks : 0
% 0.65/0.47 % Propositional check models : 0
% 0.65/0.47 % Propositional check unsatisfiable : 0
% 0.65/0.47 % Propositional clauses : 0
% 0.65/0.47 % Propositional clauses after purity: 0
% 1.43/0.47 % Propositional unsat core size : 0
% 1.43/0.47 % Propositional preprocessing time : 0.000
% 1.43/0.47 % Propositional encoding time : 0.000
% 1.43/0.47 % Propositional solver time : 0.000
% 1.43/0.47 % Success case prop preproc time : 0.000
% 1.43/0.47 % Success case prop encoding time : 0.000
% 1.43/0.47 % Success case prop solver time : 0.000
% 1.43/0.47 % Current number of processed clauses : 606
% 1.43/0.47 % Positive orientable unit clauses : 30
% 1.43/0.47 % Positive unorientable unit clauses: 0
% 1.43/0.47 % Negative unit clauses : 388
% 1.43/0.47 % Non-unit-clauses : 188
% 1.43/0.47 % Current number of unprocessed clauses: 2083
% 1.43/0.47 % ...number of literals in the above : 5234
% 1.43/0.47 % Current number of archived formulas : 0
% 1.43/0.47 % Current number of archived clauses : 4
% 1.43/0.47 % Clause-clause subsumption calls (NU) : 8970
% 1.43/0.47 % Rec. Clause-clause subsumption calls : 5201
% 1.43/0.47 % Non-unit clause-clause subsumptions : 339
% 1.43/0.47 % Unit Clause-clause subsumption calls : 41164
% 1.43/0.47 % Rewrite failures with RHS unbound : 0
% 1.43/0.47 % BW rewrite match attempts : 8
% 1.43/0.47 % BW rewrite match successes : 1
% 1.43/0.47 % Condensation attempts : 0
% 1.43/0.47 % Condensation successes : 0
% 1.43/0.47 % Termbank termtop insertions : 96051
% 1.43/0.47 % Search garbage collected termcells : 17083
% 1.43/0.47
% 1.43/0.47 % -------------------------------------------------
% 1.43/0.47 % User time : 0.144 s
% 1.43/0.47 % System time : 0.013 s
% 1.43/0.47 % Total time : 0.157 s
% 1.43/0.47 % Maximum resident set size: 6540 pages
% 1.43/0.47
% 1.43/0.47 % -------------------------------------------------
% 1.43/0.47 % User time : 0.155 s
% 1.43/0.47 % System time : 0.020 s
% 1.43/0.47 % Total time : 0.175 s
% 1.43/0.47 % Maximum resident set size: 5376 pages
% 1.43/0.47 % E exiting
%------------------------------------------------------------------------------