TSTP Solution File: NUM933_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM933_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 14:39:14 EDT 2024
% Result : Theorem 1.96s 0.76s
% Output : Refutation 1.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 60
% Syntax : Number of formulae : 171 ( 64 unt; 32 typ; 0 def)
% Number of atoms : 268 ( 64 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 218 ( 89 ~; 94 |; 3 &)
% ( 10 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 12 ( 9 >; 3 *; 0 +; 0 <<)
% Number of predicates : 25 ( 23 usr; 5 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 177 ( 157 !; 0 ?; 177 :)
% ( 20 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(func_def_0,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_1,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_2,type,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_3,type,
bit0: int > int ).
tff(func_def_4,type,
bit1: int > int ).
tff(func_def_5,type,
pls: int ).
tff(func_def_6,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_7,type,
fFalse: bool ).
tff(func_def_8,type,
fTrue: bool ).
tff(func_def_9,type,
m: int ).
tff(pred_def_1,type,
one:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
semiring:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
comm_monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
ab_semigroup_mult:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
ordere779506340up_add:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
ordere236663937imp_le:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
zprime: int > $o ).
tff(pred_def_17,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_18,type,
twoSqu1567020053sum2sq: int > $o ).
tff(pred_def_19,type,
pp: bool > $o ).
tff(f3960,plain,
$false,
inference(avatar_sat_refutation,[],[f3666,f3685,f3841,f3909,f3957]) ).
tff(f3957,plain,
( ~ spl0_28
| ~ spl0_33 ),
inference(avatar_contradiction_clause,[],[f3956]) ).
tff(f3956,plain,
( $false
| ~ spl0_28
| ~ spl0_33 ),
inference(subsumption_resolution,[],[f3955,f3745]) ).
tff(f3745,plain,
( ord_less_eq(int,pls,bit0(m))
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f3744]) ).
tff(f3744,plain,
( spl0_33
<=> ord_less_eq(int,pls,bit0(m)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
tff(f3955,plain,
( ~ ord_less_eq(int,pls,bit0(m))
| ~ spl0_28 ),
inference(forward_demodulation,[],[f3951,f333]) ).
tff(f333,plain,
pls = bit0(pls),
inference(cnf_transformation,[],[f25]) ).
tff(f25,axiom,
pls = bit0(pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_Bit0__Pls) ).
tff(f3951,plain,
( ~ ord_less_eq(int,bit0(pls),bit0(m))
| ~ spl0_28 ),
inference(resolution,[],[f3913,f437]) ).
tff(f437,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,bit0(X1),bit0(X0)) ),
inference(cnf_transformation,[],[f295]) ).
tff(f295,plain,
! [X0: int,X1: int] :
( ( ord_less_eq(int,bit0(X1),bit0(X0))
| ~ ord_less_eq(int,X1,X0) )
& ( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,bit0(X1),bit0(X0)) ) ),
inference(nnf_transformation,[],[f204]) ).
tff(f204,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,bit0(X1),bit0(X0))
<=> ord_less_eq(int,X1,X0) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X17: int,X18: int] :
( ord_less_eq(int,bit0(X18),bit0(X17))
<=> ord_less_eq(int,X18,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_less__eq__int__code_I13_J) ).
tff(f3913,plain,
( ~ ord_less_eq(int,pls,m)
| ~ spl0_28 ),
inference(subsumption_resolution,[],[f3864,f3678]) ).
tff(f3678,plain,
( ! [X0: int] : ord_less_eq(int,bit1(X0),bit0(X0))
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f3677]) ).
tff(f3677,plain,
( spl0_28
<=> ! [X0: int] : ord_less_eq(int,bit1(X0),bit0(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
tff(f3864,plain,
! [X0: int] :
( ~ ord_less_eq(int,bit1(X0),bit0(X0))
| ~ ord_less_eq(int,pls,m) ),
inference(resolution,[],[f2122,f2010]) ).
tff(f2010,plain,
! [X0: int] : ~ ord_less_eq(int,bit1(X0),plus_plus(int,m,bit0(X0))),
inference(superposition,[],[f1045,f632]) ).
tff(f632,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,one_one(int),bit0(X0)) ),
inference(forward_demodulation,[],[f629,f347]) ).
tff(f347,plain,
! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
inference(cnf_transformation,[],[f135]) ).
tff(f135,plain,
! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X8: int] : ( plus_plus(int,pls,X8) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_add__Pls) ).
tff(f629,plain,
! [X0: int] : ( bit1(plus_plus(int,pls,X0)) = plus_plus(int,one_one(int),bit0(X0)) ),
inference(superposition,[],[f426,f482]) ).
tff(f482,plain,
one_one(int) = bit1(pls),
inference(superposition,[],[f338,f344]) ).
tff(f344,plain,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
inference(cnf_transformation,[],[f132]) ).
tff(f132,plain,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X8: int] : ( number_number_of(int,X8) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_number__of__is__id) ).
tff(f338,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(cnf_transformation,[],[f63]) ).
tff(f63,axiom,
one_one(int) = number_number_of(int,bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_one__is__num__one) ).
tff(f426,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit1(X1),bit0(X0)) ),
inference(cnf_transformation,[],[f195]) ).
tff(f195,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit1(X1),bit0(X0)) ),
inference(rectify,[],[f13]) ).
tff(f13,axiom,
! [X7: int,X8: int] : ( bit1(plus_plus(int,X8,X7)) = plus_plus(int,bit1(X8),bit0(X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_add__Bit1__Bit0) ).
tff(f1045,plain,
! [X0: int] : ~ ord_less_eq(int,plus_plus(int,one_one(int),X0),plus_plus(int,m,X0)),
inference(subsumption_resolution,[],[f1012,f329]) ).
tff(f329,plain,
ordere236663937imp_le(int),
inference(cnf_transformation,[],[f98]) ).
tff(f98,axiom,
ordere236663937imp_le(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) ).
tff(f1012,plain,
! [X0: int] :
( ~ ord_less_eq(int,plus_plus(int,one_one(int),X0),plus_plus(int,m,X0))
| ~ ordere236663937imp_le(int) ),
inference(resolution,[],[f387,f335]) ).
tff(f335,plain,
~ ord_less_eq(int,one_one(int),m),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
~ ord_less_eq(int,one_one(int),m),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096_126_A1_A_060_061_Am_096) ).
tff(f387,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ord_less_eq(X0,X3,X1)
| ~ ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
| ~ ordere236663937imp_le(X0) ),
inference(cnf_transformation,[],[f249]) ).
tff(f249,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ord_less_eq(X0,X3,X1)
| ~ ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2)) )
| ~ ordere236663937imp_le(X0) ),
inference(ennf_transformation,[],[f171]) ).
tff(f171,plain,
! [X0: $tType] :
( ordere236663937imp_le(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
=> ord_less_eq(X0,X3,X1) ) ),
inference(rectify,[],[f92]) ).
tff(f92,axiom,
! [X0: $tType] :
( ordere236663937imp_le(X0)
=> ! [X12: X0,X14: X0,X13: X0] :
( ord_less_eq(X0,plus_plus(X0,X13,X14),plus_plus(X0,X12,X14))
=> ord_less_eq(X0,X13,X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_add__le__imp__le__right) ).
tff(f2122,plain,
! [X2: int,X0: int,X1: int] :
( ord_less_eq(int,X0,plus_plus(int,X1,X2))
| ~ ord_less_eq(int,X0,X2)
| ~ ord_less_eq(int,pls,X1) ),
inference(subsumption_resolution,[],[f2082,f326]) ).
tff(f326,plain,
ordere779506340up_add(int),
inference(cnf_transformation,[],[f99]) ).
tff(f99,axiom,
ordere779506340up_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__semigroup__add) ).
tff(f2082,plain,
! [X2: int,X0: int,X1: int] :
( ord_less_eq(int,X0,plus_plus(int,X1,X2))
| ~ ord_less_eq(int,X0,X2)
| ~ ord_less_eq(int,pls,X1)
| ~ ordere779506340up_add(int) ),
inference(superposition,[],[f384,f347]) ).
tff(f384,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0] :
( ord_less_eq(X0,plus_plus(X0,X4,X2),plus_plus(X0,X3,X1))
| ~ ord_less_eq(X0,X2,X1)
| ~ ord_less_eq(X0,X4,X3)
| ~ ordere779506340up_add(X0) ),
inference(cnf_transformation,[],[f246]) ).
tff(f246,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( ord_less_eq(X0,plus_plus(X0,X4,X2),plus_plus(X0,X3,X1))
| ~ ord_less_eq(X0,X2,X1)
| ~ ord_less_eq(X0,X4,X3) )
| ~ ordere779506340up_add(X0) ),
inference(flattening,[],[f245]) ).
tff(f245,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( ord_less_eq(X0,plus_plus(X0,X4,X2),plus_plus(X0,X3,X1))
| ~ ord_less_eq(X0,X2,X1)
| ~ ord_less_eq(X0,X4,X3) )
| ~ ordere779506340up_add(X0) ),
inference(ennf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: $tType] :
( ordere779506340up_add(X0)
=> ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( ord_less_eq(X0,X4,X3)
=> ( ord_less_eq(X0,X2,X1)
=> ord_less_eq(X0,plus_plus(X0,X4,X2),plus_plus(X0,X3,X1)) ) ) ),
inference(rectify,[],[f91]) ).
tff(f91,axiom,
! [X0: $tType] :
( ordere779506340up_add(X0)
=> ! [X28: X0,X14: X0,X12: X0,X13: X0] :
( ord_less_eq(X0,X13,X12)
=> ( ord_less_eq(X0,X14,X28)
=> ord_less_eq(X0,plus_plus(X0,X13,X14),plus_plus(X0,X12,X28)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_add__mono) ).
tff(f3909,plain,
spl0_34,
inference(avatar_contradiction_clause,[],[f3908]) ).
tff(f3908,plain,
( $false
| spl0_34 ),
inference(subsumption_resolution,[],[f3899,f536]) ).
tff(f536,plain,
ord_less_eq(int,pls,one_one(int)),
inference(subsumption_resolution,[],[f535,f334]) ).
tff(f334,plain,
ord_less_eq(int,pls,pls),
inference(cnf_transformation,[],[f27]) ).
tff(f27,axiom,
ord_less_eq(int,pls,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_rel__simps_I19_J) ).
tff(f535,plain,
( ord_less_eq(int,pls,one_one(int))
| ~ ord_less_eq(int,pls,pls) ),
inference(superposition,[],[f420,f482]) ).
tff(f420,plain,
! [X0: int] :
( ord_less_eq(int,pls,bit1(X0))
| ~ ord_less_eq(int,pls,X0) ),
inference(cnf_transformation,[],[f291]) ).
tff(f291,plain,
! [X0: int] :
( ( ord_less_eq(int,pls,bit1(X0))
| ~ ord_less_eq(int,pls,X0) )
& ( ord_less_eq(int,pls,X0)
| ~ ord_less_eq(int,pls,bit1(X0)) ) ),
inference(nnf_transformation,[],[f190]) ).
tff(f190,plain,
! [X0: int] :
( ord_less_eq(int,pls,bit1(X0))
<=> ord_less_eq(int,pls,X0) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X9: int] :
( ord_less_eq(int,pls,bit1(X9))
<=> ord_less_eq(int,pls,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_rel__simps_I22_J) ).
tff(f3899,plain,
( ~ ord_less_eq(int,pls,one_one(int))
| spl0_34 ),
inference(resolution,[],[f3749,f420]) ).
tff(f3749,plain,
( ~ ord_less_eq(int,pls,bit1(one_one(int)))
| spl0_34 ),
inference(avatar_component_clause,[],[f3748]) ).
tff(f3748,plain,
( spl0_34
<=> ord_less_eq(int,pls,bit1(one_one(int))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
tff(f3841,plain,
( ~ spl0_34
| spl0_33 ),
inference(avatar_split_clause,[],[f3840,f3744,f3748]) ).
tff(f3840,plain,
( ~ ord_less_eq(int,pls,bit1(one_one(int)))
| spl0_33 ),
inference(forward_demodulation,[],[f3833,f3662]) ).
tff(f3662,plain,
bit1(one_one(int)) = bit1(bit0(m)),
inference(subsumption_resolution,[],[f3650,f680]) ).
tff(f680,plain,
zprime(bit1(bit0(m))),
inference(backward_demodulation,[],[f607,f678]) ).
tff(f678,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,bit0(X0),one_one(int)) ),
inference(forward_demodulation,[],[f676,f346]) ).
tff(f346,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(cnf_transformation,[],[f134]) ).
tff(f134,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(rectify,[],[f45]) ).
tff(f45,axiom,
! [X8: int] : ( plus_plus(int,X8,pls) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_add__Pls__right) ).
tff(f676,plain,
! [X0: int] : ( bit1(plus_plus(int,X0,pls)) = plus_plus(int,bit0(X0),one_one(int)) ),
inference(superposition,[],[f428,f482]) ).
tff(f428,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit0(X1),bit1(X0)) ),
inference(cnf_transformation,[],[f197]) ).
tff(f197,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit0(X1),bit1(X0)) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X7: int,X8: int] : ( plus_plus(int,bit0(X8),bit1(X7)) = bit1(plus_plus(int,X8,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_add__Bit0__Bit1) ).
tff(f607,plain,
zprime(plus_plus(int,bit0(bit0(m)),one_one(int))),
inference(backward_demodulation,[],[f507,f605]) ).
tff(f605,plain,
! [X0: int] : ( bit0(bit0(X0)) = times_times(int,bit0(bit0(one_one(int))),X0) ),
inference(superposition,[],[f425,f579]) ).
tff(f579,plain,
! [X0: int] : ( bit0(X0) = times_times(int,bit0(one_one(int)),X0) ),
inference(superposition,[],[f425,f531]) ).
tff(f531,plain,
! [X0: int] : ( times_times(int,one_one(int),X0) = X0 ),
inference(resolution,[],[f378,f320]) ).
tff(f320,plain,
monoid_mult(int),
inference(cnf_transformation,[],[f107]) ).
tff(f107,axiom,
monoid_mult(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
tff(f378,plain,
! [X0: $tType,X1: X0] :
( ~ monoid_mult(X0)
| ( times_times(X0,one_one(X0),X1) = X1 ) ),
inference(cnf_transformation,[],[f240]) ).
tff(f240,plain,
! [X0: $tType] :
( ! [X1: X0] : ( times_times(X0,one_one(X0),X1) = X1 )
| ~ monoid_mult(X0) ),
inference(ennf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X1: X0] : ( times_times(X0,one_one(X0),X1) = X1 ) ),
inference(rectify,[],[f94]) ).
tff(f94,axiom,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X13: X0] : ( times_times(X0,one_one(X0),X13) = X13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_mult__1__left) ).
tff(f425,plain,
! [X0: int,X1: int] : ( bit0(times_times(int,X1,X0)) = times_times(int,bit0(X1),X0) ),
inference(cnf_transformation,[],[f194]) ).
tff(f194,plain,
! [X0: int,X1: int] : ( bit0(times_times(int,X1,X0)) = times_times(int,bit0(X1),X0) ),
inference(rectify,[],[f30]) ).
tff(f30,axiom,
! [X7: int,X8: int] : ( bit0(times_times(int,X8,X7)) = times_times(int,bit0(X8),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_mult__Bit0) ).
tff(f507,plain,
zprime(plus_plus(int,times_times(int,bit0(bit0(one_one(int))),m),one_one(int))),
inference(backward_demodulation,[],[f469,f482]) ).
tff(f469,plain,
zprime(plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int))),
inference(backward_demodulation,[],[f340,f344]) ).
tff(f340,plain,
zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_p) ).
tff(f3650,plain,
( ~ zprime(bit1(bit0(m)))
| ( bit1(one_one(int)) = bit1(bit0(m)) ) ),
inference(resolution,[],[f2050,f548]) ).
tff(f548,plain,
~ ord_less_eq(int,bit0(one_one(int)),bit0(m)),
inference(resolution,[],[f437,f335]) ).
tff(f2050,plain,
! [X0: int] :
( ord_less_eq(int,bit0(one_one(int)),X0)
| ~ zprime(bit1(X0))
| ( bit1(X0) = bit1(one_one(int)) ) ),
inference(subsumption_resolution,[],[f2028,f423]) ).
tff(f423,plain,
! [X0: int,X1: int] : ( bit1(X0) != bit0(X1) ),
inference(cnf_transformation,[],[f192]) ).
tff(f192,plain,
! [X0: int,X1: int] : ( bit1(X0) != bit0(X1) ),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X7: int,X8: int] : ( bit0(X8) != bit1(X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_rel__simps_I49_J) ).
tff(f2028,plain,
! [X0: int] :
( ( bit1(X0) = bit0(one_one(int)) )
| ( bit1(X0) = bit1(one_one(int)) )
| ~ zprime(bit1(X0))
| ord_less_eq(int,bit0(one_one(int)),X0) ),
inference(resolution,[],[f510,f445]) ).
tff(f445,plain,
! [X0: int,X1: int] :
( ~ ord_less_eq(int,bit1(X1),bit1(X0))
| ord_less_eq(int,X1,X0) ),
inference(cnf_transformation,[],[f299]) ).
tff(f299,plain,
! [X0: int,X1: int] :
( ( ord_less_eq(int,bit1(X1),bit1(X0))
| ~ ord_less_eq(int,X1,X0) )
& ( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,bit1(X1),bit1(X0)) ) ),
inference(nnf_transformation,[],[f208]) ).
tff(f208,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,bit1(X1),bit1(X0))
<=> ord_less_eq(int,X1,X0) ),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X10: int,X9: int] :
( ord_less_eq(int,bit1(X9),bit1(X10))
<=> ord_less_eq(int,X9,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_rel__simps_I34_J) ).
tff(f510,plain,
! [X0: int] :
( ord_less_eq(int,bit1(bit0(one_one(int))),X0)
| ( bit0(one_one(int)) = X0 )
| ( bit1(one_one(int)) = X0 )
| ~ zprime(X0) ),
inference(forward_demodulation,[],[f509,f482]) ).
tff(f509,plain,
! [X0: int] :
( ( bit0(one_one(int)) = X0 )
| ord_less_eq(int,bit1(bit0(one_one(int))),X0)
| ( bit1(bit1(pls)) = X0 )
| ~ zprime(X0) ),
inference(forward_demodulation,[],[f508,f482]) ).
tff(f508,plain,
! [X0: int] :
( ord_less_eq(int,bit1(bit0(one_one(int))),X0)
| ( bit0(bit1(pls)) = X0 )
| ( bit1(bit1(pls)) = X0 )
| ~ zprime(X0) ),
inference(backward_demodulation,[],[f472,f482]) ).
tff(f472,plain,
! [X0: int] :
( ( bit0(bit1(pls)) = X0 )
| ( bit1(bit1(pls)) = X0 )
| ord_less_eq(int,bit1(bit0(bit1(pls))),X0)
| ~ zprime(X0) ),
inference(forward_demodulation,[],[f471,f344]) ).
tff(f471,plain,
! [X0: int] :
( ( bit1(bit1(pls)) = X0 )
| ord_less_eq(int,bit1(bit0(bit1(pls))),X0)
| ( number_number_of(int,bit0(bit1(pls))) = X0 )
| ~ zprime(X0) ),
inference(forward_demodulation,[],[f470,f344]) ).
tff(f470,plain,
! [X0: int] :
( ord_less_eq(int,bit1(bit0(bit1(pls))),X0)
| ( number_number_of(int,bit1(bit1(pls))) = X0 )
| ( number_number_of(int,bit0(bit1(pls))) = X0 )
| ~ zprime(X0) ),
inference(forward_demodulation,[],[f370,f344]) ).
tff(f370,plain,
! [X0: int] :
( ord_less_eq(int,number_number_of(int,bit1(bit0(bit1(pls)))),X0)
| ( number_number_of(int,bit1(bit1(pls))) = X0 )
| ( number_number_of(int,bit0(bit1(pls))) = X0 )
| ~ zprime(X0) ),
inference(cnf_transformation,[],[f233]) ).
tff(f233,plain,
! [X0: int] :
( ord_less_eq(int,number_number_of(int,bit1(bit0(bit1(pls)))),X0)
| ( number_number_of(int,bit1(bit1(pls))) = X0 )
| ( number_number_of(int,bit0(bit1(pls))) = X0 )
| ~ zprime(X0) ),
inference(flattening,[],[f232]) ).
tff(f232,plain,
! [X0: int] :
( ord_less_eq(int,number_number_of(int,bit1(bit0(bit1(pls)))),X0)
| ( number_number_of(int,bit1(bit1(pls))) = X0 )
| ( number_number_of(int,bit0(bit1(pls))) = X0 )
| ~ zprime(X0) ),
inference(ennf_transformation,[],[f156]) ).
tff(f156,plain,
! [X0: int] :
( zprime(X0)
=> ( ( number_number_of(int,bit0(bit1(pls))) != X0 )
=> ( ( number_number_of(int,bit1(bit1(pls))) != X0 )
=> ord_less_eq(int,number_number_of(int,bit1(bit0(bit1(pls)))),X0) ) ) ),
inference(rectify,[],[f71]) ).
tff(f71,axiom,
! [X21: int] :
( zprime(X21)
=> ( ( number_number_of(int,bit0(bit1(pls))) != X21 )
=> ( ( number_number_of(int,bit1(bit1(pls))) != X21 )
=> ord_less_eq(int,number_number_of(int,bit1(bit0(bit1(pls)))),X21) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_prime__g__5) ).
tff(f3833,plain,
( ~ ord_less_eq(int,pls,bit1(bit0(m)))
| spl0_33 ),
inference(resolution,[],[f3746,f419]) ).
tff(f419,plain,
! [X0: int] :
( ord_less_eq(int,pls,X0)
| ~ ord_less_eq(int,pls,bit1(X0)) ),
inference(cnf_transformation,[],[f291]) ).
tff(f3746,plain,
( ~ ord_less_eq(int,pls,bit0(m))
| spl0_33 ),
inference(avatar_component_clause,[],[f3744]) ).
tff(f3685,plain,
( ~ spl0_5
| spl0_28 ),
inference(avatar_split_clause,[],[f1410,f3677,f689]) ).
tff(f689,plain,
( spl0_5
<=> ord_less_eq(int,one_one(int),pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
tff(f1410,plain,
! [X0: int] :
( ord_less_eq(int,bit1(X0),bit0(X0))
| ~ ord_less_eq(int,one_one(int),pls) ),
inference(superposition,[],[f908,f678]) ).
tff(f908,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,plus_plus(int,X0,X1),X0)
| ~ ord_less_eq(int,X1,pls) ),
inference(subsumption_resolution,[],[f877,f326]) ).
tff(f877,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,plus_plus(int,X0,X1),X0)
| ~ ord_less_eq(int,X1,pls)
| ~ ordere779506340up_add(int) ),
inference(superposition,[],[f382,f346]) ).
tff(f382,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ord_less_eq(X0,plus_plus(X0,X1,X3),plus_plus(X0,X1,X2))
| ~ ord_less_eq(X0,X3,X2)
| ~ ordere779506340up_add(X0) ),
inference(cnf_transformation,[],[f243]) ).
tff(f243,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ord_less_eq(X0,plus_plus(X0,X1,X3),plus_plus(X0,X1,X2))
| ~ ord_less_eq(X0,X3,X2) )
| ~ ordere779506340up_add(X0) ),
inference(ennf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: $tType] :
( ordere779506340up_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ord_less_eq(X0,X3,X2)
=> ord_less_eq(X0,plus_plus(X0,X1,X3),plus_plus(X0,X1,X2)) ) ),
inference(rectify,[],[f90]) ).
tff(f90,axiom,
! [X0: $tType] :
( ordere779506340up_add(X0)
=> ! [X14: X0,X12: X0,X13: X0] :
( ord_less_eq(X0,X13,X12)
=> ord_less_eq(X0,plus_plus(X0,X14,X13),plus_plus(X0,X14,X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_add__left__mono) ).
tff(f3666,plain,
spl0_5,
inference(avatar_contradiction_clause,[],[f3665]) ).
tff(f3665,plain,
( $false
| spl0_5 ),
inference(subsumption_resolution,[],[f3664,f696]) ).
tff(f696,plain,
( ~ ord_less_eq(int,bit1(one_one(int)),one_one(int))
| spl0_5 ),
inference(resolution,[],[f691,f563]) ).
tff(f563,plain,
! [X0: int] :
( ord_less_eq(int,X0,pls)
| ~ ord_less_eq(int,bit1(X0),one_one(int)) ),
inference(superposition,[],[f445,f482]) ).
tff(f691,plain,
( ~ ord_less_eq(int,one_one(int),pls)
| spl0_5 ),
inference(avatar_component_clause,[],[f689]) ).
tff(f3664,plain,
ord_less_eq(int,bit1(one_one(int)),one_one(int)),
inference(backward_demodulation,[],[f679,f3662]) ).
tff(f679,plain,
ord_less_eq(int,bit1(bit0(m)),one_one(int)),
inference(backward_demodulation,[],[f608,f678]) ).
tff(f608,plain,
ord_less_eq(int,plus_plus(int,bit0(bit0(m)),one_one(int)),one_one(int)),
inference(backward_demodulation,[],[f506,f605]) ).
tff(f506,plain,
ord_less_eq(int,plus_plus(int,times_times(int,bit0(bit0(one_one(int))),m),one_one(int)),one_one(int)),
inference(backward_demodulation,[],[f468,f482]) ).
tff(f468,plain,
ord_less_eq(int,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int)),one_one(int)),
inference(backward_demodulation,[],[f341,f344]) ).
tff(f341,plain,
ord_less_eq(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int)),
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
ord_less_eq(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__0964_A_K_Am_A_L_A1_A_060_061_A1_096) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : NUM933_5 : TPTP v8.1.2. Released v6.0.0.
% 0.10/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.33 % Computer : n022.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Apr 29 23:32:28 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % (24711)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.35 % (24714)WARNING: value z3 for option sas not known
% 0.11/0.35 % (24716)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.11/0.35 % (24718)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.11/0.35 % (24714)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.11/0.35 % (24717)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.11/0.36 % (24718)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.11/0.36 % (24713)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.37 % (24715)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.37 % Exception at run slice level
% 0.11/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.37 % (24712)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.38 % Exception at run slice level
% 0.11/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.38 % Exception at run slice level
% 0.11/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.41 % (24719)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.17/0.41 % (24719)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/0.41 % Exception at run slice level
% 0.17/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.42 % (24720)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.17/0.42 % (24720)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/0.43 % (24721)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.17/0.46 % (24722)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 1.96/0.75 % (24721)First to succeed.
% 1.96/0.76 % (24721)Refutation found. Thanks to Tanya!
% 1.96/0.76 % SZS status Theorem for theBenchmark
% 1.96/0.76 % SZS output start Proof for theBenchmark
% See solution above
% 1.96/0.76 % (24721)------------------------------
% 1.96/0.76 % (24721)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.96/0.76 % (24721)Termination reason: Refutation
% 1.96/0.76
% 1.96/0.76 % (24721)Memory used [KB]: 2243
% 1.96/0.76 % (24721)Time elapsed: 0.353 s
% 1.96/0.76 % (24721)Instructions burned: 203 (million)
% 1.96/0.76 % (24721)------------------------------
% 1.96/0.76 % (24721)------------------------------
% 1.96/0.76 % (24711)Success in time 0.421 s
%------------------------------------------------------------------------------