TSTP Solution File: NUM945_5 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : NUM945_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n005.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 : Sun May 5 08:16:53 EDT 2024
% Result : Theorem 0.57s 0.75s
% Output : Refutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 42
% Syntax : Number of formulae : 70 ( 16 unt; 32 typ; 0 def)
% Number of atoms : 61 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 20 ~; 14 |; 0 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 25 ( 14 >; 11 *; 0 +; 0 <<)
% Number of predicates : 19 ( 17 usr; 5 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 48 ( 29 !; 5 ?; 48 :)
% ( 14 !>; 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(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 ) > int ).
tff(func_def_14,type,
sK1: ( 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(pred_def_14,type,
sQ2_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f564,plain,
$false,
inference(avatar_sat_refutation,[],[f484,f485,f496,f563]) ).
tff(f563,plain,
( ~ spl3_1
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f562]) ).
tff(f562,plain,
( $false
| ~ spl3_1
| ~ spl3_3 ),
inference(subsumption_resolution,[],[f559,f479]) ).
tff(f479,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)))
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f478]) ).
tff(f478,plain,
( spl3_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(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
tff(f559,plain,
( zcong(power_power(int,sK1(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))),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)))
| ~ spl3_3 ),
inference(resolution,[],[f489,f380]) ).
tff(f380,plain,
! [X0: int,X1: int] :
( ~ quadRes(X1,X0)
| zcong(power_power(int,sK1(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) ),
inference(definition_unfolding,[],[f327,f274,f257]) ).
tff(f257,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(cnf_transformation,[],[f132]) ).
tff(f132,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(rectify,[],[f66]) ).
tff(f66,axiom,
! [X5: int] : ( bit1(X5) = plus_plus(int,plus_plus(int,one_one(int),X5),X5) ),
file('/export/starexec/sandbox/tmp/tmp.RlUrg03JyU/Vampire---4.8_25712',fact_65_Bit1__def) ).
tff(f274,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(cnf_transformation,[],[f144]) ).
tff(f144,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X5: int] : ( bit0(X5) = plus_plus(int,X5,X5) ),
file('/export/starexec/sandbox/tmp/tmp.RlUrg03JyU/Vampire---4.8_25712',fact_56_Bit0__def) ).
tff(f327,plain,
! [X0: int,X1: int] :
( zcong(power_power(int,sK1(X0,X1),number_number_of(nat,bit0(bit1(pls)))),X0,X1)
| ~ quadRes(X1,X0) ),
inference(cnf_transformation,[],[f242]) ).
tff(f242,plain,
! [X0: int,X1: int] :
( zcong(power_power(int,sK1(X0,X1),number_number_of(nat,bit0(bit1(pls)))),X0,X1)
| ~ quadRes(X1,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f227,f241]) ).
tff(f241,plain,
! [X0: int,X1: int] :
( ? [X2: int] : zcong(power_power(int,X2,number_number_of(nat,bit0(bit1(pls)))),X0,X1)
=> zcong(power_power(int,sK1(X0,X1),number_number_of(nat,bit0(bit1(pls)))),X0,X1) ),
introduced(choice_axiom,[]) ).
tff(f227,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,[],[f193]) ).
tff(f193,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,[],[f192]) ).
tff(f192,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(rectify,[],[f86]) ).
tff(f86,axiom,
! [X11: int,X22: int] :
( quadRes(X22,X11)
<=> ? [X23: int] : zcong(power_power(int,X23,number_number_of(nat,bit0(bit1(pls)))),X11,X22) ),
file('/export/starexec/sandbox/tmp/tmp.RlUrg03JyU/Vampire---4.8_25712',fact_85_QuadRes__def) ).
tff(f489,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))
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f487]) ).
tff(f487,plain,
( spl3_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(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
tff(f496,plain,
spl3_3,
inference(avatar_split_clause,[],[f383,f487]) ).
tff(f383,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,[],[f330,f274,f274,f257]) ).
tff(f330,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(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/tmp/tmp.RlUrg03JyU/Vampire---4.8_25712',fact_0__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096) ).
tff(f485,plain,
~ spl3_2,
inference(avatar_split_clause,[],[f244,f481]) ).
tff(f481,plain,
( spl3_2
<=> thesis ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
tff(f244,plain,
~ thesis,
inference(cnf_transformation,[],[f126]) ).
tff(f126,plain,
~ thesis,
inference(flattening,[],[f124]) ).
tff(f124,negated_conjecture,
~ thesis,
inference(negated_conjecture,[],[f123]) ).
tff(f123,conjecture,
thesis,
file('/export/starexec/sandbox/tmp/tmp.RlUrg03JyU/Vampire---4.8_25712',conj_1) ).
tff(f484,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f331,f481,f478]) ).
tff(f331,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,[],[f243,f274,f257,f274,f274,f257]) ).
tff(f243,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,[],[f203]) ).
tff(f203,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,[],[f125]) ).
tff(f125,plain,
! [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 ),
inference(rectify,[],[f122]) ).
tff(f122,axiom,
! [X32: int] :
( zcong(power_power(int,X32,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/tmp/tmp.RlUrg03JyU/Vampire---4.8_25712',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM945_5 : TPTP v8.1.2. Released v6.0.0.
% 0.13/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 14:41:22 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TF1_THM_EQU_NAR problem
% 0.21/0.35 Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.RlUrg03JyU/Vampire---4.8_25712
% 0.57/0.73 % (25827)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.57/0.73 % (25820)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.57/0.73 % (25823)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.57/0.73 % (25821)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.57/0.73 % (25824)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.57/0.73 % (25827)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
% 0.57/0.73 % (25825)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.57/0.73 % (25826)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.57/0.73 % (25827)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.57/0.73 % (25825)Refutation not found, incomplete strategy% (25825)------------------------------
% 0.57/0.73 % (25825)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.73 % (25825)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.73
% 0.57/0.73 % (25825)Memory used [KB]: 1241
% 0.57/0.73 % (25825)Time elapsed: 0.007 s
% 0.57/0.73 % (25825)Instructions burned: 11 (million)
% 0.57/0.73 % (25828)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.57/0.73 % (25825)------------------------------
% 0.57/0.73 % (25825)------------------------------
% 0.57/0.74 % (25820)First to succeed.
% 0.57/0.74 % (25820)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-25819"
% 0.57/0.74 % (25828)Refutation not found, incomplete strategy% (25828)------------------------------
% 0.57/0.74 % (25828)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.74 % (25828)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.74
% 0.57/0.74 % (25828)Memory used [KB]: 1112
% 0.57/0.74 % (25828)Time elapsed: 0.006 s
% 0.57/0.74 % (25828)Instructions burned: 10 (million)
% 0.57/0.74 % (25828)------------------------------
% 0.57/0.74 % (25828)------------------------------
% 0.57/0.75 % (25820)Refutation found. Thanks to Tanya!
% 0.57/0.75 % SZS status Theorem for Vampire---4
% 0.57/0.75 % SZS output start Proof for Vampire---4
% See solution above
% 0.57/0.75 % (25820)------------------------------
% 0.57/0.75 % (25820)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.75 % (25820)Termination reason: Refutation
% 0.57/0.75
% 0.57/0.75 % (25820)Memory used [KB]: 1218
% 0.57/0.75 % (25820)Time elapsed: 0.011 s
% 0.57/0.75 % (25820)Instructions burned: 18 (million)
% 0.57/0.75 % (25819)Success in time 0.376 s
% 0.57/0.75 % Vampire---4.8 exiting
%------------------------------------------------------------------------------