%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM945_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 : Tue Sep 29 12:26:16 PM UTC 2026
% Result : Theorem 0.18s 0.52s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 68 ( 30 unt; 0 typ; 3 def)
% Number of atoms : 107 ( 17 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 86 ( 47 ~; 32 |; 0 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 5 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 52 ( 0 sgn 49 !; 3 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(type_def_8,type,
real: $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,
min: int ).
tff(func_def_6,type,
pls: int ).
tff(func_def_7,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_8,type,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).
tff(func_def_9,type,
legendre: ( int * int ) > int ).
tff(func_def_10,type,
fFalse: bool ).
tff(func_def_11,type,
fTrue: bool ).
tff(func_def_12,type,
m: int ).
tff(func_def_13,type,
sK0: ( int * int ) > int ).
tff(func_def_14,type,
sK1: ( int * int * int ) > int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
semiring:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
semiring_1:
!>[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,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
zcong: ( int * int * int ) > $o ).
tff(pred_def_10,type,
zprime: int > $o ).
tff(pred_def_11,type,
quadRes: ( int * int ) > $o ).
tff(pred_def_12,type,
pp: bool > $o ).
tff(f1,axiom,
quadRes(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),number_number_of(int,min)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096) ).
tff(f44,axiom,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_nat__1__add__1) ).
tff(f51,axiom,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_number__of__is__id) ).
tff(f55,axiom,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_add__Pls__right) ).
tff(f57,axiom,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Bit0__def) ).
tff(f66,axiom,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_Bit1__def) ).
tff(f86,axiom,
! [X0: int,X1: int] :
( quadRes(X1,X0)
<=> ? [X2: int] : zcong(power_power(int,X2,number_number_of(nat,bit0(bit1(pls)))),X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_QuadRes__def) ).
tff(f94,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0] : ( times_times(X0,X2,X1) = times_times(X0,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
tff(f98,axiom,
comm_semiring_1(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
tff(f122,axiom,
! [X0: int] :
( zcong(power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
=> thesis ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f123,conjecture,
thesis,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(f124,negated_conjecture,
~ thesis,
inference(negated_conjecture,[status(cth)],[f123]) ).
tff(f125,plain,
~ thesis,
inference(flattening,[],[f124]) ).
tff(f126,plain,
! [X0: int,X1: int] :
( quadRes(X1,X0)
=> ? [X2: int] : zcong(power_power(int,X2,number_number_of(nat,bit0(bit1(pls)))),X0,X1) ),
inference(unused_predicate_definition_removal,[],[f86]) ).
tff(f169,plain,
! [X0: int,X1: int] :
( ? [X2: int] : zcong(power_power(int,X2,number_number_of(nat,bit0(bit1(pls)))),X0,X1)
| ~ quadRes(X1,X0) ),
inference(ennf_transformation,[],[f126]) ).
tff(f174,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( times_times(X0,X2,X1) = times_times(X0,X1,X2) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f94]) ).
tff(f178,plain,
! [X0: int] :
( thesis
| ~ zcong(power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ),
inference(ennf_transformation,[],[f122]) ).
tff(f189,plain,
! [X0: int,X1: int] :
( zcong(power_power(int,sK0(X0,X1),number_number_of(nat,bit0(bit1(pls)))),X0,X1)
| ~ quadRes(X1,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f169]) ).
tff(f193,plain,
quadRes(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),number_number_of(int,min)),
inference(cnf_transformation,[],[f1]) ).
tff(f243,plain,
number_number_of(nat,bit0(bit1(pls))) = plus_plus(nat,one_one(nat),one_one(nat)),
inference(cnf_transformation,[],[f44]) ).
tff(f251,plain,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
inference(cnf_transformation,[],[f51]) ).
tff(f255,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(cnf_transformation,[],[f55]) ).
tff(f257,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(cnf_transformation,[],[f57]) ).
tff(f266,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(cnf_transformation,[],[f66]) ).
tff(f291,plain,
! [X0: int,X1: int] :
( zcong(power_power(int,sK0(X0,X1),number_number_of(nat,bit0(bit1(pls)))),X0,X1)
| ~ quadRes(X1,X0) ),
inference(cnf_transformation,[],[f189]) ).
tff(f300,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ~ comm_semiring_1(X0)
| ( times_times(X0,X2,X1) = times_times(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f174]) ).
tff(f304,plain,
comm_semiring_1(int),
inference(cnf_transformation,[],[f98]) ).
tff(f328,plain,
! [X0: int] :
( thesis
| ~ zcong(power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ),
inference(cnf_transformation,[],[f178]) ).
tff(f329,plain,
~ thesis,
inference(cnf_transformation,[],[f125]) ).
tff(f330,plain,
quadRes(plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),m),one_one(int)),number_number_of(int,min)),
inference(definition_unfolding,[],[f193,f257,f257,f266]) ).
tff(f369,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))),
inference(definition_unfolding,[],[f243,f257,f266]) ).
tff(f393,plain,
! [X0: int,X1: int] :
( zcong(power_power(int,sK0(X0,X1),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),X0,X1)
| ~ quadRes(X1,X0) ),
inference(definition_unfolding,[],[f291,f257,f266]) ).
tff(f397,plain,
! [X0: int] :
( thesis
| ~ zcong(power_power(int,X0,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),m),one_one(int))) ),
inference(definition_unfolding,[],[f328,f257,f266,f257,f257,f266]) ).
tff(f413,definition,
( spl2_1
<=> ! [X0: int] : ~ zcong(power_power(int,X0,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),m),one_one(int))) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
tff(f414,plain,
( ! [X0: int] : ~ zcong(power_power(int,X0,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),m),one_one(int)))
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f413]) ).
tff(f416,definition,
( spl2_2
<=> thesis ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f419,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f397,f416,f413]) ).
tff(f421,definition,
( spl2_3
<=> quadRes(plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),m),one_one(int)),number_number_of(int,min)) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
tff(f423,plain,
( quadRes(plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),m),one_one(int)),number_number_of(int,min))
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f421]) ).
tff(f430,plain,
spl2_3,
inference(avatar_split_clause,[],[f330,f421]) ).
tff(f431,plain,
~ spl2_2,
inference(avatar_split_clause,[],[f329,f416]) ).
tff(f454,plain,
! [X0: int,X1: int] : ( times_times(int,X1,X0) = times_times(int,X0,X1) ),
inference(resolution,[],[f300,f304]) ).
tff(f989,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls))),
inference(forward_demodulation,[],[f369,f255]) ).
tff(f990,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,plus_plus(int,one_one(int),one_one(int))),
inference(forward_demodulation,[],[f989,f255]) ).
tff(f1382,plain,
! [X0: int,X1: int] :
( zcong(power_power(int,sK0(X0,X1),number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))),X0,X1)
| ~ quadRes(X1,X0) ),
inference(forward_demodulation,[],[f393,f255]) ).
tff(f1383,plain,
! [X0: int,X1: int] :
( zcong(power_power(int,sK0(X0,X1),number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),X0,X1)
| ~ quadRes(X1,X0) ),
inference(forward_demodulation,[],[f1382,f255]) ).
tff(f1384,plain,
! [X0: int,X1: int] :
( zcong(power_power(int,sK0(X0,X1),plus_plus(nat,one_one(nat),one_one(nat))),X0,X1)
| ~ quadRes(X1,X0) ),
inference(forward_demodulation,[],[f1383,f990]) ).
tff(f1556,plain,
( quadRes(plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),m),one_one(int)),min)
| ~ spl2_3 ),
inference(forward_demodulation,[],[f423,f251]) ).
tff(f1557,plain,
( quadRes(plus_plus(int,times_times(int,m,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))),one_one(int)),min)
| ~ spl2_3 ),
inference(forward_demodulation,[],[f1556,f454]) ).
tff(f1558,plain,
( quadRes(plus_plus(int,times_times(int,m,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),one_one(int)),min)
| ~ spl2_3 ),
inference(forward_demodulation,[],[f1557,f251]) ).
tff(f1559,plain,
( quadRes(plus_plus(int,times_times(int,m,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)),plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))),one_one(int)),min)
| ~ spl2_3 ),
inference(forward_demodulation,[],[f1558,f255]) ).
tff(f1560,plain,
( quadRes(plus_plus(int,times_times(int,m,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int)))),one_one(int)),min)
| ~ spl2_3 ),
inference(forward_demodulation,[],[f1559,f255]) ).
tff(f1793,plain,
( ! [X0: int] : ~ zcong(power_power(int,X0,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),number_number_of(int,min),plus_plus(int,times_times(int,m,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))),one_one(int)))
| ~ spl2_1 ),
inference(forward_demodulation,[],[f414,f454]) ).
tff(f1794,plain,
( ! [X0: int] : ~ zcong(power_power(int,X0,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),number_number_of(int,min),plus_plus(int,times_times(int,m,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),one_one(int)))
| ~ spl2_1 ),
inference(forward_demodulation,[],[f1793,f251]) ).
tff(f1795,plain,
( ! [X0: int] : ~ zcong(power_power(int,X0,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))),number_number_of(int,min),plus_plus(int,times_times(int,m,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)),plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))),one_one(int)))
| ~ spl2_1 ),
inference(forward_demodulation,[],[f1794,f255]) ).
tff(f1796,plain,
( ! [X0: int] : ~ zcong(power_power(int,X0,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),number_number_of(int,min),plus_plus(int,times_times(int,m,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int)))),one_one(int)))
| ~ spl2_1 ),
inference(forward_demodulation,[],[f1795,f255]) ).
tff(f1797,plain,
( ! [X0: int] : ~ zcong(power_power(int,X0,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),min,plus_plus(int,times_times(int,m,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int)))),one_one(int)))
| ~ spl2_1 ),
inference(forward_demodulation,[],[f1796,f251]) ).
tff(f1798,plain,
( ! [X0: int] : ~ zcong(power_power(int,X0,plus_plus(nat,one_one(nat),one_one(nat))),min,plus_plus(int,times_times(int,m,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int)))),one_one(int)))
| ~ spl2_1 ),
inference(forward_demodulation,[],[f1797,f990]) ).
tff(f1799,plain,
( ~ quadRes(plus_plus(int,times_times(int,m,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int)))),one_one(int)),min)
| ~ spl2_1 ),
inference(resolution,[],[f1798,f1384]) ).
tff(f1813,plain,
( $false
| ~ spl2_1
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f1799,f1560]) ).
tff(f1814,plain,
( ~ spl2_1
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f1813]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f419]) ).
cnf(s4,plain,
spl2_3,
inference(sat_conversion,[],[f430]) ).
cnf(s5,plain,
~ spl2_2,
inference(sat_conversion,[],[f431]) ).
cnf(s14,plain,
( ~ spl2_1
| ~ spl2_3 ),
inference(sat_conversion,[],[f1814]) ).
cnf(s15,plain,
~ spl2_1,
inference(rat,[],[s14,s4]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s1,s5,s15]) ).
tff(f1815,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM945_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.39 % Computer : n020.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sun Sep 27 21:48:19 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.43 Running first-order model finding
% 0.14/0.43 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.52 % (3788090)Will run a generic schedule for satisfiability detection.
% 0.18/0.52 % (3788100)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2086875011:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.52 % (3788096)% WARNING: option uhcvi not known.
% 0.18/0.52 % (3788096)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2665116291:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.52 % (3788095)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1055686088_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.52 % (3788097)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1605567082:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.52 % (3788098)dis+10_1_sil=32000:sp=arity:random_seed=1146011786:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.52 % (3788099)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3896788347:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.52 % (3788101)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=453015102:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.52 % Exception at run slice level
% 0.18/0.52 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.52 % (3788109)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4123222053:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.18/0.52 % Exception at run slice level
% 0.18/0.52 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.52 % (3788100)Instruction limit reached!
% 0.18/0.52 % (3788100)------------------------------
% 0.18/0.52 % (3788100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.52 % (3788100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.52 % (3788100)CaDiCaL version: 2.1.3
% 0.18/0.52 % (3788100)Termination reason: Instruction limit
% 0.18/0.52 % (3788100)Termination phase: Saturation
% 0.18/0.52 % (3788100)Time elapsed: 0.038 s
% 0.18/0.52 % (3788100)Peak memory usage: 13 MB
% 0.18/0.52 % (3788100)Instructions burned: 133 (million)
% 0.18/0.52 % (3788112)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1555895821:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.18/0.52 % (3788098) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3788090-3788098"...
% 0.18/0.52 % (3788111)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1635026907:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.52 % (3788098)...printing done.
% 0.18/0.52 % (3788098)Refutation found. Thanks to Tanya!
% 0.18/0.52 % SZS status Theorem for theBenchmark
% 0.18/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.53 % (3788098)------------------------------
% 0.18/0.53 % (3788098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.53 % (3788098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.53 % (3788098)CaDiCaL version: 2.1.3
% 0.18/0.53 % (3788098)Termination reason: Refutation
% 0.18/0.53 % (3788098)Time elapsed: 0.045 s
% 0.18/0.53 % (3788098)Peak memory usage: 13 MB
% 0.18/0.53 % (3788098)Instructions burned: 77 (million)
% 0.18/0.53 % (3788090)Success in time 0.084 s
% 0.18/0.53 % Vampire exiting
%------------------------------------------------------------------------------