%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP262_1 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 : Thu Sep 24 12:55:04 PM UTC 2026
% Result : Theorem 174.06s 28.10s
% Output : CNFRefutation 174.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 49 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 84 ( 36 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 65 ( 30 ~; 24 |; 5 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 13 ( 12 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 31 ( 31 usr; 19 con; 0-3 aty)
% Number of variables : 42 ( 0 sgn 39 !; 3 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
vEBT_VEBT: $tType ).
tff(decl_sort2,type,
fun_nat_fun_nat_bool: $tType ).
tff(decl_sort3,type,
fun_nat_bool: $tType ).
tff(decl_sort4,type,
fun_nat_fun_nat_nat: $tType ).
tff(decl_sort5,type,
fun_nat_nat: $tType ).
tff(decl_sort6,type,
nat: $tType ).
tff(decl_sort7,type,
num: $tType ).
tff(decl_sort8,type,
fun_VE3763956218935105199t_bool: $tType ).
tff(decl_sort9,type,
bool: $tType ).
tff(decl_sort10,type,
list_VEBT_VEBT: $tType ).
tff(decl_sort11,type,
fun_num_nat: $tType ).
tff(decl_sort12,type,
fun_num_num: $tType ).
tff(decl_672,type,
one_one_nat: nat ).
tff(decl_710,type,
zero_zero_nat: nat ).
tff(decl_804,type,
list_u1324408373059187874T_VEBT: ( vEBT_VEBT * ( nat * list_VEBT_VEBT ) ) > list_VEBT_VEBT ).
tff(decl_821,type,
nth_VEBT_VEBT: ( nat * list_VEBT_VEBT ) > vEBT_VEBT ).
tff(decl_844,type,
suc: fun_nat_nat ).
tff(decl_908,type,
bit0: fun_num_num ).
tff(decl_910,type,
one: num ).
tff(decl_918,type,
numeral_numeral_nat: fun_num_nat ).
tff(decl_955,type,
ord_less_nat: fun_nat_fun_nat_bool ).
tff(decl_1015,type,
power_power_nat: fun_nat_fun_nat_nat ).
tff(decl_1119,type,
zero_n2687167440665602831ol_nat: bool > nat ).
tff(decl_1230,type,
vEBT_V8194947554948674370ptions: fun_VE3763956218935105199t_bool ).
tff(decl_1231,type,
vEBT_VEBT_high: fun_nat_fun_nat_nat ).
tff(decl_1233,type,
vEBT_VEBT_low: fun_nat_fun_nat_nat ).
tff(decl_1244,type,
vEBT_vebt_delete: ( nat * vEBT_VEBT ) > vEBT_VEBT ).
tff(decl_1349,type,
aa_nat_bool: ( nat * fun_nat_bool ) > bool ).
tff(decl_1351,type,
aa_nat_nat: ( nat * fun_nat_nat ) > nat ).
tff(decl_1370,type,
aa_nat_fun_nat_bool: ( nat * fun_nat_fun_nat_bool ) > fun_nat_bool ).
tff(decl_1372,type,
aa_nat_fun_nat_nat: ( nat * fun_nat_fun_nat_nat ) > fun_nat_nat ).
tff(decl_1393,type,
aa_num_nat: ( num * fun_num_nat ) > nat ).
tff(decl_1394,type,
aa_num_num: ( num * fun_num_num ) > num ).
tff(decl_1484,type,
aa_VEB4832260192069861672t_bool: ( vEBT_VEBT * fun_VE3763956218935105199t_bool ) > fun_nat_bool ).
tff(decl_1586,type,
fFalse: bool ).
tff(decl_1588,type,
fTrue: bool ).
tff(decl_1614,type,
pp: bool > $o ).
tff(decl_1616,type,
m: nat ).
tff(decl_1618,type,
maxs: nat ).
tff(decl_1620,type,
na: nat ).
tff(decl_1621,type,
summary: vEBT_VEBT ).
tff(decl_1622,type,
treeList: list_VEBT_VEBT ).
tff(decl_1623,type,
xa: nat ).
tff(decl_1908,type,
esk278_1: nat > nat ).
tff(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
! [X18557: bool] :
( ( X18557 = fFalse )
| ( X18557 = fTrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T) ).
tff(help_fFalse_1_1_U,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
tff(fact_6243_of__bool__eq_I1_J,axiom,
zero_n2687167440665602831ol_nat(fFalse) = zero_zero_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6243_of__bool__eq_I1_J) ).
tff(fact_6293_of__bool__less__one__iff,axiom,
! [X11149: bool] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_n2687167440665602831ol_nat(X11149)),one_one_nat))
<=> ~ pp(X11149) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6293_of__bool__less__one__iff) ).
tff(conj_0,conjecture,
? [X25: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),maxs)),X25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(fact_22_nth__list__update__neq,axiom,
! [X6: nat,X15: nat,X18: list_VEBT_VEBT,X19: vEBT_VEBT] :
( ( X6 != X15 )
=> ( nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(X18,X6,X19),X15) = nth_VEBT_VEBT(X18,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_nth__list__update__neq) ).
tff(fact_10_bb,axiom,
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,maxs),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),m)))
& ( maxs != aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_bb) ).
tff(help_fTrue_1_1_U,axiom,
pp(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
tff(fact_13__C4_C,axiom,
! [X7: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X7),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),m)))
=> ( ? [X8: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(treeList,X7)),X8))
<=> pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,summary),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13__C4_C) ).
tff(fact_1997_less__numeral__extra_I1_J,axiom,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),one_one_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1997_less__numeral__extra_I1_J) ).
tff(fact_2830_Suc__1,axiom,
aa_nat_nat(suc,one_one_nat) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2830_Suc__1) ).
tff(fact_2__C8_C,axiom,
na = m,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__C8_C) ).
tff(fact_1__092_060open_062both__member__options_Asummary_Amaxs_092_060close_062,axiom,
pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,summary),maxs)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062both__member__options_Asummary_Amaxs_092_060close_062) ).
tff(c_0_13,plain,
! [X21032: bool] :
( ( X21032 = fFalse )
| ( X21032 = fTrue ) ),
inference(variable_rename,[status(thm)],[help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T]) ).
tff(c_0_14,plain,
~ pp(fFalse),
inference(fof_simplification,[status(thm)],[help_fFalse_1_1_U]) ).
tcf(c_0_15,plain,
! [X88: bool] :
( ( X88 = fFalse )
| ( X88 = fTrue ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
tff(c_0_16,plain,
~ pp(fFalse),
inference(fof_nnf,[status(thm)],[c_0_14]) ).
tcf(c_0_17,plain,
zero_n2687167440665602831ol_nat(fFalse) = zero_zero_nat,
inference(split_conjunct,[status(thm)],[fact_6243_of__bool__eq_I1_J]) ).
tcf(c_0_18,plain,
! [X119: bool,X88: bool] :
( ( X119 = X88 )
| ( X119 = fFalse )
| ( X88 = fFalse ) ),
inference(spm,[status(thm)],[c_0_15,c_0_15]) ).
tff(c_0_19,plain,
! [X11149: bool] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_n2687167440665602831ol_nat(X11149)),one_one_nat))
<=> ~ pp(X11149) ),
inference(fof_simplification,[status(thm)],[fact_6293_of__bool__less__one__iff]) ).
tcf(c_0_20,plain,
~ pp(fFalse),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
tcf(c_0_21,plain,
! [X88: bool,X119: bool] :
( ( X88 = X119 )
| ( X119 = fFalse )
| ( zero_n2687167440665602831ol_nat(X88) = zero_zero_nat ) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
tff(c_0_22,negated_conjecture,
~ ? [X25: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),maxs)),X25)),
inference(assume_negation,[status(cth)],[conj_0]) ).
tff(c_0_23,plain,
! [X6: nat,X15: nat,X18: list_VEBT_VEBT,X19: vEBT_VEBT] :
( ( X6 != X15 )
=> ( nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(X18,X6,X19),X15) = nth_VEBT_VEBT(X18,X15) ) ),
inference(fof_simplification,[status(thm)],[fact_22_nth__list__update__neq]) ).
tff(c_0_24,plain,
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,maxs),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),m)))
& ( maxs != aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na) ) ),
inference(fof_simplification,[status(thm)],[fact_10_bb]) ).
tff(c_0_25,plain,
! [X24740: bool] :
( ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_n2687167440665602831ol_nat(X24740)),one_one_nat))
| pp(X24740) )
& ( ~ pp(X24740)
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_n2687167440665602831ol_nat(X24740)),one_one_nat)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
tcf(c_0_26,plain,
! [X88: bool,X119: bool] :
( ~ pp(X119)
| ( X88 = X119 )
| ( zero_n2687167440665602831ol_nat(X88) = zero_zero_nat ) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
tcf(c_0_27,plain,
pp(fTrue),
inference(split_conjunct,[status(thm)],[help_fTrue_1_1_U]) ).
tff(c_0_28,negated_conjecture,
! [X18571: nat] : ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),maxs)),X18571)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])]) ).
tff(c_0_29,plain,
! [X18695: nat,X18696: nat,X18697: list_VEBT_VEBT,X18698: vEBT_VEBT] :
( ( nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(X18697,X18695,X18698),X18696) = nth_VEBT_VEBT(X18697,X18696) )
| ( X18695 = X18696 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])]) ).
tff(c_0_30,plain,
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,maxs),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),m)))
& ( maxs != aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na) ) ),
inference(fof_nnf,[status(thm)],[c_0_24]) ).
tff(c_0_31,plain,
! [X20835: nat,X20836: nat] :
( ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X20835),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),m)))
| pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(treeList,X20835)),esk278_1(X20835)))
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,summary),X20835)) )
& ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X20835),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),m)))
| pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,summary),X20835))
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(treeList,X20835)),X20836)) ) ),
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)],[fact_13__C4_C])])])])])]) ).
tcf(c_0_32,plain,
! [X88: bool] :
( ~ pp(X88)
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_n2687167440665602831ol_nat(X88)),one_one_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
tcf(c_0_33,plain,
! [X88: bool] :
( ( X88 = fTrue )
| ( zero_n2687167440665602831ol_nat(X88) = zero_zero_nat ) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
tcf(c_0_34,plain,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),one_one_nat)),
inference(split_conjunct,[status(thm)],[fact_1997_less__numeral__extra_I1_J]) ).
tcf(c_0_35,negated_conjecture,
! [X1: nat] : ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),maxs)),X1)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
tcf(c_0_36,plain,
! [X1: nat,X9: list_VEBT_VEBT,X3: vEBT_VEBT,X2: nat] :
( ( nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(X9,X1,X3),X2) = nth_VEBT_VEBT(X9,X2) )
| ( X1 = X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
tcf(c_0_37,plain,
maxs != aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
tcf(c_0_38,plain,
! [X1: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X1),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),m)))
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,summary),X1))
| pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(treeList,X1)),esk278_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
tcf(c_0_39,plain,
aa_nat_nat(suc,one_one_nat) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)),
inference(split_conjunct,[status(thm)],[fact_2830_Suc__1]) ).
tcf(c_0_40,plain,
na = m,
inference(split_conjunct,[status(thm)],[fact_2__C8_C]) ).
tcf(c_0_41,plain,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,maxs),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),m))),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
tcf(c_0_42,plain,
! [X88: bool] :
( ~ pp(X88)
| ( X88 = fTrue ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
tcf(c_0_43,plain,
pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,summary),maxs)),
inference(split_conjunct,[status(thm)],[fact_1__092_060open_062both__member__options_Asummary_Amaxs_092_060close_062]) ).
tcf(c_0_44,negated_conjecture,
! [X1: nat] : ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(treeList,maxs)),X1)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
tcf(c_0_45,plain,
! [X1: nat] :
( ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,summary),X1))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X1),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))
| pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(treeList,X1)),esk278_1(X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
tcf(c_0_46,plain,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,maxs),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_39]),c_0_40]) ).
tcf(c_0_47,plain,
aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,summary),maxs) = fTrue,
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_47]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP262_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.45 % Computer : n020.cluster.edu
% 0.09/0.45 % Model : x86_64 x86_64
% 0.09/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.45 % Memory : 8046.5625MB
% 0.09/0.45 % OS : Linux 6.8.0-71-generic
% 0.09/0.45 % CPULimit : 300
% 0.09/0.45 % WCLimit : 300
% 0.09/0.45 % DateTime : Sun Sep 20 22:23:32 UTC 2026
% 0.09/0.45 % CPUTime :
% 0.09/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.51 Running first-order theorem proving
% 0.13/0.51 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 174.06/28.10 % Version: 3.5.1
% 174.06/28.10 % Preprocessing class: FMLLSMLLSSSNFFN.
% 174.06/28.10 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 174.06/28.10 % Starting new_bool_3 with 897s (3) cores
% 174.06/28.10 % Starting new_bool_1 with 897s (3) cores
% 174.06/28.10 % Starting sh5l with 299s (1) cores
% 174.06/28.10 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 299s (1) cores
% 174.06/28.10 % new_bool_1 with pid 1346905 completed with status 0
% 174.06/28.10 % Result found by new_bool_1
% 174.06/28.10 % Preprocessing class: FMLLSMLLSSSNFFN.
% 174.06/28.10 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 174.06/28.10 % Starting new_bool_3 with 897s (3) cores
% 174.06/28.10 % Starting new_bool_1 with 897s (3) cores
% 174.06/28.10 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 174.06/28.10 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 174.06/28.10 % Search class: FGHSM-SMLM32-DFFFFFNN
% 174.06/28.10 % Scheduled 13 strats onto 3 cores with 896 seconds (896 total)
% 174.06/28.10 % Starting SubtermCWHack with 81s (1) cores
% 174.06/28.10 % Starting new_bool_1 with 90s (1) cores
% 174.06/28.10 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 68s (1) cores
% 174.06/28.10 % SubtermCWHack with pid 1346911 completed with status 0
% 174.06/28.10 % Result found by SubtermCWHack
% 174.06/28.10 % Preprocessing class: FMLLSMLLSSSNFFN.
% 174.06/28.10 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 174.06/28.10 % Starting new_bool_3 with 897s (3) cores
% 174.06/28.10 % Starting new_bool_1 with 897s (3) cores
% 174.06/28.10 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 174.06/28.10 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 174.06/28.10 % Search class: FGHSM-SMLM32-DFFFFFNN
% 174.06/28.10 % Scheduled 13 strats onto 3 cores with 896 seconds (896 total)
% 174.06/28.10 % Starting SubtermCWHack with 81s (1) cores
% 174.06/28.10 % Preprocessing time : 0.170 s
% 174.06/28.10
% 174.06/28.10 % Proof found!
% 174.06/28.10 % SZS status Theorem
% 174.06/28.10 % SZS output start CNFRefutation
% See solution above
% 174.06/28.10 % Parsed axioms : 12739
% 174.06/28.10 % Removed by relevancy pruning/SinE : 9336
% 174.06/28.10 % Initial clauses : 9080
% 174.06/28.10 % Removed in clause preprocessing : 1951
% 174.06/28.10 % Initial clauses in saturation : 7129
% 174.06/28.10 % Processed clauses : 59948
% 174.06/28.10 % ...of these trivial : 2177
% 174.06/28.10 % ...subsumed : 43369
% 174.06/28.10 % ...remaining for further processing : 14402
% 174.06/28.10 % Other redundant clauses eliminated : 3246
% 174.06/28.10 % Clauses deleted for lack of memory : 0
% 174.06/28.10 % Backward-subsumed : 561
% 174.06/28.10 % Backward-rewritten : 1961
% 174.06/28.10 % Generated clauses : 629851
% 174.06/28.10 % ...of the previous two non-redundant : 535911
% 174.06/28.10 % ...aggressively subsumed : 0
% 174.06/28.10 % Contextual simplify-reflections : 50
% 174.06/28.10 % Paramodulations : 626457
% 174.06/28.10 % Factorizations : 106
% 174.06/28.10 % NegExts : 0
% 174.06/28.10 % Equation resolutions : 3335
% 174.06/28.10 % Disequality decompositions : 0
% 174.06/28.10 % Total rewrite steps : 301284
% 174.06/28.10 % ...of those cached : 276099
% 174.06/28.10 % Propositional unsat checks : 0
% 174.06/28.10 % Propositional check models : 0
% 174.06/28.10 % Propositional check unsatisfiable : 0
% 174.06/28.10 % Propositional clauses : 0
% 174.06/28.10 % Propositional clauses after purity: 0
% 174.06/28.10 % Propositional unsat core size : 0
% 174.06/28.10 % Propositional preprocessing time : 0.000
% 174.06/28.10 % Propositional encoding time : 0.000
% 174.06/28.10 % Propositional solver time : 0.000
% 174.06/28.10 % Success case prop preproc time : 0.000
% 174.06/28.10 % Success case prop encoding time : 0.000
% 174.06/28.10 % Success case prop solver time : 0.000
% 174.06/28.10 % Current number of processed clauses : 11206
% 174.06/28.10 % Positive orientable unit clauses : 3271
% 174.06/28.10 % Positive unorientable unit clauses: 45
% 174.06/28.10 % Negative unit clauses : 2920
% 174.06/28.10 % Non-unit-clauses : 4970
% 174.06/28.10 % Current number of unprocessed clauses: 478636
% 174.06/28.10 % ...number of literals in the above : 1809526
% 174.06/28.10 % Current number of archived formulas : 0
% 174.06/28.10 % Current number of archived clauses : 2526
% 174.06/28.10 % Clause-clause subsumption calls (NU) : 6752430
% 174.06/28.10 % Rec. Clause-clause subsumption calls : 2868142
% 174.06/28.10 % Non-unit clause-clause subsumptions : 10109
% 174.06/28.10 % Unit Clause-clause subsumption calls : 3000461
% 174.06/28.10 % Rewrite failures with RHS unbound : 0
% 174.06/28.10 % BW rewrite match attempts : 48314
% 174.06/28.10 % BW rewrite match successes : 2062
% 174.06/28.10 % Condensation attempts : 0
% 174.06/28.10 % Condensation successes : 0
% 174.06/28.10 % Termbank termtop insertions : 14267050
% 174.06/28.10 % Search garbage collected termcells : 191488
% 174.06/28.10
% 174.06/28.10 % -------------------------------------------------
% 174.06/28.10 % User time : 24.314 s
% 174.06/28.10 % System time : 0.515 s
% 174.06/28.10 % Total time : 24.829 s
% 174.06/28.10 % Maximum resident set size: 52104 pages
% 174.06/28.10
% 174.06/28.10 % -------------------------------------------------
% 174.06/28.10 % User time : 73.763 s
% 174.06/28.10 % System time : 0.988 s
% 174.06/28.10 % Total time : 74.751 s
% 174.06/28.10 % Maximum resident set size: 31744 pages
% 174.06/28.10 % E exiting
%------------------------------------------------------------------------------