TSTP Solution File: SWW485_5 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SWW485_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n032.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 : Mon Jun 24 18:33:14 EDT 2024
% Result : Theorem 0.16s 0.38s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 62 ( 24 ~; 17 |; 10 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 19 ( 18 usr; 5 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 5 con; 0-4 aty)
% Number of variables : 26 ( 20 !; 6 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
complex: $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(type_def_8,type,
poly1: $tType > $tType ).
tff(type_def_9,type,
real: $tType ).
tff(type_def_10,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_1,type,
order1:
!>[X0: $tType] : ( ( X0 * poly1(X0) ) > nat ) ).
tff(func_def_2,type,
poly:
!>[X0: $tType] : ( poly1(X0) > fun(X0,X0) ) ).
tff(func_def_3,type,
norm_norm:
!>[X0: $tType] : ( X0 > real ) ).
tff(func_def_4,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_5,type,
fFalse: bool ).
tff(func_def_6,type,
fTrue: bool ).
tff(func_def_7,type,
cs: poly1(complex) ).
tff(func_def_8,type,
r: real ).
tff(func_def_9,type,
sK0: real > complex ).
tff(func_def_10,type,
sK1:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_11,type,
sK2:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_12,type,
sK3:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_13,type,
sK4:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_14,type,
sK5:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_15,type,
sK6:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_16,type,
sK7:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_17,type,
sK8:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(func_def_18,type,
sK9:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(func_def_19,type,
sK10:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(func_def_20,type,
sK11:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(func_def_21,type,
sK12: real ).
tff(func_def_22,type,
sK13: ( real * real ) > real ).
tff(pred_def_1,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
idom:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
ord:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
order:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
preorder:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
comm_semiring_0:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
dense_linorder:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
real_normed_vector:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_13,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_14,type,
pp: bool > $o ).
tff(f394,plain,
$false,
inference(avatar_sat_refutation,[],[f335,f339,f340,f393]) ).
tff(f393,plain,
( ~ spl14_1
| ~ spl14_3 ),
inference(avatar_contradiction_clause,[],[f392]) ).
tff(f392,plain,
( $false
| ~ spl14_1
| ~ spl14_3 ),
inference(resolution,[],[f373,f338]) ).
tff(f338,plain,
( ! [X0: real] : ord_less_eq(real,norm_norm(complex,sK0(X0)),r)
| ~ spl14_3 ),
inference(avatar_component_clause,[],[f337]) ).
tff(f337,plain,
( spl14_3
<=> ! [X0: real] : ord_less_eq(real,norm_norm(complex,sK0(X0)),r) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_3])]) ).
tff(f373,plain,
( ~ ord_less_eq(real,norm_norm(complex,sK0(sK12)),r)
| ~ spl14_1 ),
inference(resolution,[],[f274,f330]) ).
tff(f330,plain,
( ! [X0: real] : ~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),sK0(X0))),X0)
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f329]) ).
tff(f329,plain,
( spl14_1
<=> ! [X0: real] : ~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),sK0(X0))),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_1])]) ).
tff(f274,plain,
! [X1: complex] :
( ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),sK12)
| ~ ord_less_eq(real,norm_norm(complex,X1),r) ),
inference(cnf_transformation,[],[f235]) ).
tff(f235,plain,
( ! [X1: complex] :
( ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),sK12)
| ~ ord_less_eq(real,norm_norm(complex,X1),r) )
& ord_less(real,zero_zero(real),sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f197,f234]) ).
tff(f234,plain,
( ? [X0: real] :
( ! [X1: complex] :
( ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),X0)
| ~ ord_less_eq(real,norm_norm(complex,X1),r) )
& ord_less(real,zero_zero(real),X0) )
=> ( ! [X1: complex] :
( ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),sK12)
| ~ ord_less_eq(real,norm_norm(complex,X1),r) )
& ord_less(real,zero_zero(real),sK12) ) ),
introduced(choice_axiom,[]) ).
tff(f197,plain,
? [X0: real] :
( ! [X1: complex] :
( ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),X0)
| ~ ord_less_eq(real,norm_norm(complex,X1),r) )
& ord_less(real,zero_zero(real),X0) ),
inference(ennf_transformation,[],[f156]) ).
tff(f156,plain,
? [X0: real] :
( ! [X1: complex] :
( ord_less_eq(real,norm_norm(complex,X1),r)
=> ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),X0) )
& ord_less(real,zero_zero(real),X0) ),
inference(rectify,[],[f1]) ).
tff(f1,axiom,
? [X2: real] :
( ! [X3: complex] :
( ord_less_eq(real,norm_norm(complex,X3),r)
=> ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X3)),X2) )
& ord_less(real,zero_zero(real),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f340,plain,
~ spl14_2,
inference(avatar_split_clause,[],[f249,f332]) ).
tff(f332,plain,
( spl14_2
<=> thesis ),
introduced(avatar_definition,[new_symbols(naming,[spl14_2])]) ).
tff(f249,plain,
~ thesis,
inference(cnf_transformation,[],[f143]) ).
tff(f143,plain,
~ thesis,
inference(flattening,[],[f142]) ).
tff(f142,negated_conjecture,
~ thesis,
inference(negated_conjecture,[],[f141]) ).
tff(f141,conjecture,
thesis,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f339,plain,
( spl14_3
| spl14_2 ),
inference(avatar_split_clause,[],[f250,f332,f337]) ).
tff(f250,plain,
! [X0: real] :
( thesis
| ord_less_eq(real,norm_norm(complex,sK0(X0)),r) ),
inference(cnf_transformation,[],[f218]) ).
tff(f218,plain,
! [X0: real] :
( thesis
| ( ~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),sK0(X0))),X0)
& ord_less_eq(real,norm_norm(complex,sK0(X0)),r) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f179,f217]) ).
tff(f217,plain,
! [X0: real] :
( ? [X1: complex] :
( ~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),X0)
& ord_less_eq(real,norm_norm(complex,X1),r) )
=> ( ~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),sK0(X0))),X0)
& ord_less_eq(real,norm_norm(complex,sK0(X0)),r) ) ),
introduced(choice_axiom,[]) ).
tff(f179,plain,
! [X0: real] :
( thesis
| ? [X1: complex] :
( ~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),X0)
& ord_less_eq(real,norm_norm(complex,X1),r) ) ),
inference(ennf_transformation,[],[f144]) ).
tff(f144,plain,
! [X0: real] :
( ! [X1: complex] :
( ord_less_eq(real,norm_norm(complex,X1),r)
=> ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),X0) )
=> thesis ),
inference(rectify,[],[f140]) ).
tff(f140,axiom,
! [X40: real] :
( ! [X41: complex] :
( ord_less_eq(real,norm_norm(complex,X41),r)
=> ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X41)),X40) )
=> thesis ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f335,plain,
( spl14_1
| spl14_2 ),
inference(avatar_split_clause,[],[f251,f332,f329]) ).
tff(f251,plain,
! [X0: real] :
( thesis
| ~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),sK0(X0))),X0) ),
inference(cnf_transformation,[],[f218]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SWW485_5 : TPTP v8.2.0. Released v6.0.0.
% 0.00/0.09 % Command : run_vampire %s %d THM
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Wed Jun 19 06:36:54 EDT 2024
% 0.09/0.29 % CPUTime :
% 0.09/0.31 This is a TF1_THM_EQU_NAR problem
% 0.09/0.31 Running first-order theorem proving
% 0.09/0.31 Running /export/starexec/sandbox2/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.37 % (6770)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.37 % (6774)lrs+1010_2201:262144_anc=all:drc=encompass:sil=256000:sims=off:sp=frequency:spb=goal_then_units:rp=on:lwlo=on:st=3.0:i=179501:bs=unit_only:nm=6:ins=2:fsd=on:ss=axioms:sgt=16:afr=on:tgt=ground:awrs=decay:awrsf=200:acc=on:ccuc=first_0 on theBenchmark for (2999ds/179501Mi)
% 0.16/0.37 % (6770)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.37 % (6776)dis+1011_3:1_sil=256000:tgt=ground:sac=on:i=109:sd=1:ss=included_0 on theBenchmark for (2999ds/109Mi)
% 0.16/0.37 % (6770)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.37 % (6777)dis+1010_1:1_sil=2000:nwc=3.0:s2a=on:i=132:ins=5:fsr=off:ss=axioms:sd=2:fd=off_0 on theBenchmark for (2999ds/132Mi)
% 0.16/0.37 % (6770)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.37 % (6778)dis+1010_159245:1048576_to=lpo:sil=2000:etr=on:sp=unary_frequency:spb=goal:rnwc=on:nwc=10.9066:st=2:i=124:sd=1:nm=3:av=off:ss=axioms:rawr=on:drc=encompass:foolp=on:sgt=5:cond=fast:er=filter:erape=on:erml=2:s2a=on_0 on theBenchmark for (2999ds/124Mi)
% 0.16/0.37 % (6770)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.37 % (6773)dis+11_1:1_nwc=5.0:s2a=on:i=66616:s2at=3.0:sil=128000:bd=off_0 on theBenchmark for (2999ds/66616Mi)
% 0.16/0.37 % (6770)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.37 % (6775)lrs+10_1:3_drc=off:sil=256000:sp=unary_first:lwlo=on:i=216875:kws=precedence:ins=3:rawr=on:nwc=10.0_0 on theBenchmark for (2999ds/216875Mi)
% 0.16/0.37 % (6770)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.37 % (6771)lrs+1011_1:12_anc=none:drc=off:sil=64000:sims=off:sp=unary_first:spb=goal_then_units:lsd=20:rnwc=on:nwc=2.0:i=53554:add=off:awrs=converge:bd=off:uhcvi=on:tgt=ground:afp=300:afq=1.63_0 on theBenchmark for (2999ds/53554Mi)
% 0.16/0.37 % (6777)First to succeed.
% 0.16/0.38 % (6777)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-6770"
% 0.16/0.38 % (6770)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.38 % (6777)Refutation found. Thanks to Tanya!
% 0.16/0.38 % SZS status Theorem for theBenchmark
% 0.16/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.38 % (6777)------------------------------
% 0.16/0.38 % (6777)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.16/0.38 % (6777)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.16/0.38 % (6777)Termination reason: Refutation
% 0.16/0.38
% 0.16/0.38 % (6777)Memory used [KB]: 1287
% 0.16/0.38 % (6777)Time elapsed: 0.007 s
% 0.16/0.38 % (6777)Instructions burned: 8 (million)
% 0.16/0.38 % (6777)------------------------------
% 0.16/0.38 % (6777)------------------------------
% 0.16/0.38 % (6770)Success in time 0.062 s
%------------------------------------------------------------------------------