TSTP Solution File: SEU200+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU200+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n013.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 15:23:46 EDT 2024
% Result : Theorem 0.15s 0.35s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 89
% Syntax : Number of formulae : 253 ( 64 unt; 0 def)
% Number of atoms : 609 ( 26 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 637 ( 281 ~; 239 |; 38 &)
% ( 53 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 59 ( 57 usr; 53 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 237 ( 218 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f405,plain,
$false,
inference(avatar_sat_refutation,[],[f120,f125,f130,f135,f140,f145,f150,f155,f160,f165,f169,f173,f177,f181,f185,f193,f197,f201,f205,f210,f214,f218,f222,f226,f241,f245,f249,f253,f257,f261,f266,f270,f274,f278,f282,f294,f307,f317,f327,f337,f341,f346,f356,f362,f370,f372,f376,f382,f386,f393,f403,f404]) ).
fof(f404,plain,
( ~ spl9_1
| ~ spl9_32
| spl9_44 ),
inference(avatar_split_clause,[],[f358,f353,f268,f117]) ).
fof(f117,plain,
( spl9_1
<=> relation(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).
fof(f268,plain,
( spl9_32
<=> ! [X0,X1] :
( subset(relation_rng_restriction(X0,X1),X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_32])]) ).
fof(f353,plain,
( spl9_44
<=> subset(relation_rng_restriction(sK0,sK1),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_44])]) ).
fof(f358,plain,
( ~ relation(sK1)
| ~ spl9_32
| spl9_44 ),
inference(resolution,[],[f355,f269]) ).
fof(f269,plain,
( ! [X0,X1] :
( subset(relation_rng_restriction(X0,X1),X1)
| ~ relation(X1) )
| ~ spl9_32 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f355,plain,
( ~ subset(relation_rng_restriction(sK0,sK1),sK1)
| spl9_44 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f403,plain,
( spl9_52
| ~ spl9_6
| ~ spl9_17
| ~ spl9_18 ),
inference(avatar_split_clause,[],[f234,f199,f195,f142,f401]) ).
fof(f401,plain,
( spl9_52
<=> ! [X0] :
( relation_dom(X0) = sK6
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_52])]) ).
fof(f142,plain,
( spl9_6
<=> empty(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_6])]) ).
fof(f195,plain,
( spl9_17
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_17])]) ).
fof(f199,plain,
( spl9_18
<=> ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_18])]) ).
fof(f234,plain,
( ! [X0] :
( relation_dom(X0) = sK6
| ~ empty(X0) )
| ~ spl9_6
| ~ spl9_17
| ~ spl9_18 ),
inference(forward_demodulation,[],[f232,f229]) ).
fof(f229,plain,
( empty_set = sK6
| ~ spl9_6
| ~ spl9_17 ),
inference(resolution,[],[f196,f144]) ).
fof(f144,plain,
( empty(sK6)
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f196,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl9_17 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f232,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = relation_dom(X0) )
| ~ spl9_17
| ~ spl9_18 ),
inference(resolution,[],[f200,f196]) ).
fof(f200,plain,
( ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) )
| ~ spl9_18 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f393,plain,
( spl9_50
| spl9_51
| ~ spl9_12
| ~ spl9_17
| ~ spl9_23
| ~ spl9_36
| ~ spl9_38 ),
inference(avatar_split_clause,[],[f323,f315,f291,f220,f195,f171,f391,f388]) ).
fof(f388,plain,
( spl9_50
<=> ! [X0] : ~ empty(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_50])]) ).
fof(f391,plain,
( spl9_51
<=> ! [X1] : ~ in(X1,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_51])]) ).
fof(f171,plain,
( spl9_12
<=> ! [X0] : empty(sK4(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_12])]) ).
fof(f220,plain,
( spl9_23
<=> ! [X0] : element(sK4(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_23])]) ).
fof(f291,plain,
( spl9_36
<=> empty_set = sK6 ),
introduced(avatar_definition,[new_symbols(naming,[spl9_36])]) ).
fof(f315,plain,
( spl9_38
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_38])]) ).
fof(f323,plain,
( ! [X0,X1] :
( ~ in(X1,sK6)
| ~ empty(X0) )
| ~ spl9_12
| ~ spl9_17
| ~ spl9_23
| ~ spl9_36
| ~ spl9_38 ),
inference(forward_demodulation,[],[f322,f293]) ).
fof(f293,plain,
( empty_set = sK6
| ~ spl9_36 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f322,plain,
( ! [X0,X1] :
( ~ in(X1,empty_set)
| ~ empty(X0) )
| ~ spl9_12
| ~ spl9_17
| ~ spl9_23
| ~ spl9_38 ),
inference(forward_demodulation,[],[f321,f228]) ).
fof(f228,plain,
( ! [X0] : empty_set = sK4(X0)
| ~ spl9_12
| ~ spl9_17 ),
inference(resolution,[],[f196,f172]) ).
fof(f172,plain,
( ! [X0] : empty(sK4(X0))
| ~ spl9_12 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f321,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK4(X0)) )
| ~ spl9_23
| ~ spl9_38 ),
inference(resolution,[],[f316,f221]) ).
fof(f221,plain,
( ! [X0] : element(sK4(X0),powerset(X0))
| ~ spl9_23 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f316,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl9_38 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f386,plain,
( spl9_49
| ~ spl9_6
| ~ spl9_35 ),
inference(avatar_split_clause,[],[f300,f280,f142,f384]) ).
fof(f384,plain,
( spl9_49
<=> ! [X0] :
( sK6 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_49])]) ).
fof(f280,plain,
( spl9_35
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_35])]) ).
fof(f300,plain,
( ! [X0] :
( sK6 = X0
| ~ empty(X0) )
| ~ spl9_6
| ~ spl9_35 ),
inference(resolution,[],[f281,f144]) ).
fof(f281,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl9_35 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f382,plain,
( spl9_48
| ~ spl9_15
| ~ spl9_33 ),
inference(avatar_split_clause,[],[f285,f272,f183,f380]) ).
fof(f380,plain,
( spl9_48
<=> ! [X0] : subset(sK3(powerset(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_48])]) ).
fof(f183,plain,
( spl9_15
<=> ! [X0] : element(sK3(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_15])]) ).
fof(f272,plain,
( spl9_33
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_33])]) ).
fof(f285,plain,
( ! [X0] : subset(sK3(powerset(X0)),X0)
| ~ spl9_15
| ~ spl9_33 ),
inference(resolution,[],[f273,f184]) ).
fof(f184,plain,
( ! [X0] : element(sK3(X0),X0)
| ~ spl9_15 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f273,plain,
( ! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) )
| ~ spl9_33 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f376,plain,
( spl9_47
| ~ spl9_36
| ~ spl9_46 ),
inference(avatar_split_clause,[],[f371,f368,f291,f374]) ).
fof(f374,plain,
( spl9_47
<=> ! [X0] : sK4(X0) = sK6 ),
introduced(avatar_definition,[new_symbols(naming,[spl9_47])]) ).
fof(f368,plain,
( spl9_46
<=> ! [X0] : empty_set = sK4(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_46])]) ).
fof(f371,plain,
( ! [X0] : sK4(X0) = sK6
| ~ spl9_36
| ~ spl9_46 ),
inference(forward_demodulation,[],[f369,f293]) ).
fof(f369,plain,
( ! [X0] : empty_set = sK4(X0)
| ~ spl9_46 ),
inference(avatar_component_clause,[],[f368]) ).
fof(f372,plain,
( ~ spl9_1
| ~ spl9_25
| spl9_43 ),
inference(avatar_split_clause,[],[f357,f349,f239,f117]) ).
fof(f239,plain,
( spl9_25
<=> ! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_25])]) ).
fof(f349,plain,
( spl9_43
<=> relation(relation_rng_restriction(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_43])]) ).
fof(f357,plain,
( ~ relation(sK1)
| ~ spl9_25
| spl9_43 ),
inference(resolution,[],[f351,f240]) ).
fof(f240,plain,
( ! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) )
| ~ spl9_25 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f351,plain,
( ~ relation(relation_rng_restriction(sK0,sK1))
| spl9_43 ),
inference(avatar_component_clause,[],[f349]) ).
fof(f370,plain,
( spl9_46
| ~ spl9_12
| ~ spl9_17 ),
inference(avatar_split_clause,[],[f228,f195,f171,f368]) ).
fof(f362,plain,
( spl9_45
| ~ spl9_6
| ~ spl9_12
| ~ spl9_17
| ~ spl9_23
| ~ spl9_33 ),
inference(avatar_split_clause,[],[f289,f272,f220,f195,f171,f142,f360]) ).
fof(f360,plain,
( spl9_45
<=> ! [X0] : subset(sK6,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_45])]) ).
fof(f289,plain,
( ! [X0] : subset(sK6,X0)
| ~ spl9_6
| ~ spl9_12
| ~ spl9_17
| ~ spl9_23
| ~ spl9_33 ),
inference(forward_demodulation,[],[f288,f229]) ).
fof(f288,plain,
( ! [X0] : subset(empty_set,X0)
| ~ spl9_12
| ~ spl9_17
| ~ spl9_23
| ~ spl9_33 ),
inference(forward_demodulation,[],[f286,f228]) ).
fof(f286,plain,
( ! [X0] : subset(sK4(X0),X0)
| ~ spl9_23
| ~ spl9_33 ),
inference(resolution,[],[f273,f221]) ).
fof(f356,plain,
( ~ spl9_43
| ~ spl9_1
| ~ spl9_44
| spl9_2
| ~ spl9_41 ),
inference(avatar_split_clause,[],[f347,f339,f122,f353,f117,f349]) ).
fof(f122,plain,
( spl9_2
<=> subset(relation_rng(relation_rng_restriction(sK0,sK1)),relation_rng(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).
fof(f339,plain,
( spl9_41
<=> ! [X0,X1] :
( subset(relation_rng(X0),relation_rng(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_41])]) ).
fof(f347,plain,
( ~ subset(relation_rng_restriction(sK0,sK1),sK1)
| ~ relation(sK1)
| ~ relation(relation_rng_restriction(sK0,sK1))
| spl9_2
| ~ spl9_41 ),
inference(resolution,[],[f340,f124]) ).
fof(f124,plain,
( ~ subset(relation_rng(relation_rng_restriction(sK0,sK1)),relation_rng(sK1))
| spl9_2 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f340,plain,
( ! [X0,X1] :
( subset(relation_rng(X0),relation_rng(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl9_41 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f346,plain,
( spl9_42
| ~ spl9_6
| ~ spl9_9
| ~ spl9_17 ),
inference(avatar_split_clause,[],[f231,f195,f157,f142,f343]) ).
fof(f343,plain,
( spl9_42
<=> sK6 = sK8 ),
introduced(avatar_definition,[new_symbols(naming,[spl9_42])]) ).
fof(f157,plain,
( spl9_9
<=> empty(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_9])]) ).
fof(f231,plain,
( sK6 = sK8
| ~ spl9_6
| ~ spl9_9
| ~ spl9_17 ),
inference(forward_demodulation,[],[f230,f229]) ).
fof(f230,plain,
( empty_set = sK8
| ~ spl9_9
| ~ spl9_17 ),
inference(resolution,[],[f196,f159]) ).
fof(f159,plain,
( empty(sK8)
| ~ spl9_9 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f341,plain,
spl9_41,
inference(avatar_split_clause,[],[f86,f339]) ).
fof(f86,plain,
! [X0,X1] :
( subset(relation_rng(X0),relation_rng(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( ( subset(relation_rng(X0),relation_rng(X1))
& subset(relation_dom(X0),relation_dom(X1)) )
| ~ subset(X0,X1)
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f39]) ).
fof(f39,plain,
! [X0] :
( ! [X1] :
( ( subset(relation_rng(X0),relation_rng(X1))
& subset(relation_dom(X0),relation_dom(X1)) )
| ~ subset(X0,X1)
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(X0,X1)
=> ( subset(relation_rng(X0),relation_rng(X1))
& subset(relation_dom(X0),relation_dom(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relat_1) ).
fof(f337,plain,
spl9_40,
inference(avatar_split_clause,[],[f85,f335]) ).
fof(f335,plain,
( spl9_40
<=> ! [X0,X1] :
( subset(relation_dom(X0),relation_dom(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_40])]) ).
fof(f85,plain,
! [X0,X1] :
( subset(relation_dom(X0),relation_dom(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f327,plain,
spl9_39,
inference(avatar_split_clause,[],[f108,f325]) ).
fof(f325,plain,
( spl9_39
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_39])]) ).
fof(f108,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f57]) ).
fof(f57,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f317,plain,
spl9_38,
inference(avatar_split_clause,[],[f109,f315]) ).
fof(f109,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f307,plain,
spl9_37,
inference(avatar_split_clause,[],[f103,f305]) ).
fof(f305,plain,
( spl9_37
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_37])]) ).
fof(f103,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f294,plain,
( spl9_36
| ~ spl9_6
| ~ spl9_17 ),
inference(avatar_split_clause,[],[f229,f195,f142,f291]) ).
fof(f282,plain,
spl9_35,
inference(avatar_split_clause,[],[f106,f280]) ).
fof(f106,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f278,plain,
spl9_34,
inference(avatar_split_clause,[],[f105,f276]) ).
fof(f276,plain,
( spl9_34
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_34])]) ).
fof(f105,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f274,plain,
spl9_33,
inference(avatar_split_clause,[],[f104,f272]) ).
fof(f104,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f68]) ).
fof(f270,plain,
spl9_32,
inference(avatar_split_clause,[],[f100,f268]) ).
fof(f100,plain,
! [X0,X1] :
( subset(relation_rng_restriction(X0,X1),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1] :
( subset(relation_rng_restriction(X0,X1),X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng_restriction(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_relat_1) ).
fof(f266,plain,
spl9_31,
inference(avatar_split_clause,[],[f94,f264]) ).
fof(f264,plain,
( spl9_31
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_31])]) ).
fof(f94,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f47]) ).
fof(f47,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f261,plain,
( spl9_30
| ~ spl9_12
| ~ spl9_14 ),
inference(avatar_split_clause,[],[f187,f179,f171,f259]) ).
fof(f259,plain,
( spl9_30
<=> ! [X0] : relation(sK4(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_30])]) ).
fof(f179,plain,
( spl9_14
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_14])]) ).
fof(f187,plain,
( ! [X0] : relation(sK4(X0))
| ~ spl9_12
| ~ spl9_14 ),
inference(resolution,[],[f180,f172]) ).
fof(f180,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl9_14 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f257,plain,
spl9_29,
inference(avatar_split_clause,[],[f93,f255]) ).
fof(f255,plain,
( spl9_29
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_29])]) ).
fof(f93,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f45]) ).
fof(f45,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f253,plain,
spl9_28,
inference(avatar_split_clause,[],[f83,f251]) ).
fof(f251,plain,
( spl9_28
<=> ! [X0] :
( element(sK2(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_28])]) ).
fof(f83,plain,
! [X0] :
( element(sK2(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0] :
( ( ~ empty(sK2(X0))
& element(sK2(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f38,f62]) ).
fof(f62,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK2(X0))
& element(sK2(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f38,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f249,plain,
spl9_27,
inference(avatar_split_clause,[],[f102,f247]) ).
fof(f247,plain,
( spl9_27
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_27])]) ).
fof(f102,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f245,plain,
spl9_26,
inference(avatar_split_clause,[],[f101,f243]) ).
fof(f243,plain,
( spl9_26
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_26])]) ).
fof(f101,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f241,plain,
spl9_25,
inference(avatar_split_clause,[],[f99,f239]) ).
fof(f99,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f226,plain,
spl9_24,
inference(avatar_split_clause,[],[f107,f224]) ).
fof(f224,plain,
( spl9_24
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_24])]) ).
fof(f107,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f222,plain,
spl9_23,
inference(avatar_split_clause,[],[f96,f220]) ).
fof(f96,plain,
! [X0] : element(sK4(X0),powerset(X0)),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0] :
( empty(sK4(X0))
& element(sK4(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f21,f66]) ).
fof(f66,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK4(X0))
& element(sK4(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f21,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f218,plain,
spl9_22,
inference(avatar_split_clause,[],[f92,f216]) ).
fof(f216,plain,
( spl9_22
<=> ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_22])]) ).
fof(f92,plain,
! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( ( relation(relation_rng(X0))
& empty(relation_rng(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f214,plain,
spl9_21,
inference(avatar_split_clause,[],[f91,f212]) ).
fof(f212,plain,
( spl9_21
<=> ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_21])]) ).
fof(f91,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f210,plain,
( spl9_20
| ~ spl9_6
| ~ spl9_14 ),
inference(avatar_split_clause,[],[f188,f179,f142,f207]) ).
fof(f207,plain,
( spl9_20
<=> relation(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_20])]) ).
fof(f188,plain,
( relation(sK6)
| ~ spl9_6
| ~ spl9_14 ),
inference(resolution,[],[f180,f144]) ).
fof(f205,plain,
spl9_19,
inference(avatar_split_clause,[],[f90,f203]) ).
fof(f203,plain,
( spl9_19
<=> ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_19])]) ).
fof(f90,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0] :
( ( relation(relation_dom(X0))
& empty(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f201,plain,
spl9_18,
inference(avatar_split_clause,[],[f89,f199]) ).
fof(f89,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f197,plain,
spl9_17,
inference(avatar_split_clause,[],[f88,f195]) ).
fof(f88,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f193,plain,
spl9_16,
inference(avatar_split_clause,[],[f84,f191]) ).
fof(f191,plain,
( spl9_16
<=> ! [X0] :
( ~ empty(sK2(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_16])]) ).
fof(f84,plain,
! [X0] :
( ~ empty(sK2(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f185,plain,
spl9_15,
inference(avatar_split_clause,[],[f95,f183]) ).
fof(f95,plain,
! [X0] : element(sK3(X0),X0),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] : element(sK3(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f9,f64]) ).
fof(f64,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK3(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f9,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f181,plain,
spl9_14,
inference(avatar_split_clause,[],[f87,f179]) ).
fof(f87,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f177,plain,
spl9_13,
inference(avatar_split_clause,[],[f98,f175]) ).
fof(f175,plain,
( spl9_13
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_13])]) ).
fof(f98,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f23]) ).
fof(f23,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f173,plain,
spl9_12,
inference(avatar_split_clause,[],[f97,f171]) ).
fof(f97,plain,
! [X0] : empty(sK4(X0)),
inference(cnf_transformation,[],[f67]) ).
fof(f169,plain,
spl9_11,
inference(avatar_split_clause,[],[f82,f167]) ).
fof(f167,plain,
( spl9_11
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_11])]) ).
fof(f82,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f165,plain,
spl9_10,
inference(avatar_split_clause,[],[f115,f162]) ).
fof(f162,plain,
( spl9_10
<=> relation(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_10])]) ).
fof(f115,plain,
relation(sK8),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
( relation(sK8)
& empty(sK8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f17,f75]) ).
fof(f75,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK8)
& empty(sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f17,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f160,plain,
spl9_9,
inference(avatar_split_clause,[],[f114,f157]) ).
fof(f114,plain,
empty(sK8),
inference(cnf_transformation,[],[f76]) ).
fof(f155,plain,
spl9_8,
inference(avatar_split_clause,[],[f113,f152]) ).
fof(f152,plain,
( spl9_8
<=> relation(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_8])]) ).
fof(f113,plain,
relation(sK7),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
( relation(sK7)
& ~ empty(sK7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f20,f73]) ).
fof(f73,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK7)
& ~ empty(sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f20,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f150,plain,
~ spl9_7,
inference(avatar_split_clause,[],[f112,f147]) ).
fof(f147,plain,
( spl9_7
<=> empty(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_7])]) ).
fof(f112,plain,
~ empty(sK7),
inference(cnf_transformation,[],[f74]) ).
fof(f145,plain,
spl9_6,
inference(avatar_split_clause,[],[f111,f142]) ).
fof(f111,plain,
empty(sK6),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
empty(sK6),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f19,f71]) ).
fof(f71,plain,
( ? [X0] : empty(X0)
=> empty(sK6) ),
introduced(choice_axiom,[]) ).
fof(f19,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f140,plain,
~ spl9_5,
inference(avatar_split_clause,[],[f110,f137]) ).
fof(f137,plain,
( spl9_5
<=> empty(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_5])]) ).
fof(f110,plain,
~ empty(sK5),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
~ empty(sK5),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f22,f69]) ).
fof(f69,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK5) ),
introduced(choice_axiom,[]) ).
fof(f22,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f135,plain,
spl9_4,
inference(avatar_split_clause,[],[f81,f132]) ).
fof(f132,plain,
( spl9_4
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_4])]) ).
fof(f81,plain,
relation(empty_set),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f130,plain,
spl9_3,
inference(avatar_split_clause,[],[f79,f127]) ).
fof(f127,plain,
( spl9_3
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_3])]) ).
fof(f79,plain,
empty(empty_set),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f125,plain,
~ spl9_2,
inference(avatar_split_clause,[],[f78,f122]) ).
fof(f78,plain,
~ subset(relation_rng(relation_rng_restriction(sK0,sK1)),relation_rng(sK1)),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
( ~ subset(relation_rng(relation_rng_restriction(sK0,sK1)),relation_rng(sK1))
& relation(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f37,f60]) ).
fof(f60,plain,
( ? [X0,X1] :
( ~ subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1))
& relation(X1) )
=> ( ~ subset(relation_rng(relation_rng_restriction(sK0,sK1)),relation_rng(sK1))
& relation(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
? [X0,X1] :
( ~ subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1))
& relation(X1) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1)) ),
inference(negated_conjecture,[],[f25]) ).
fof(f25,conjecture,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_relat_1) ).
fof(f120,plain,
spl9_1,
inference(avatar_split_clause,[],[f77,f117]) ).
fof(f77,plain,
relation(sK1),
inference(cnf_transformation,[],[f61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU200+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.33 % Computer : n013.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon Apr 29 21:00:04 EDT 2024
% 0.15/0.33 % CPUTime :
% 0.15/0.33 % (13726)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.34 % (13731)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)
% 0.15/0.35 % (13731)First to succeed.
% 0.15/0.35 % (13729)WARNING: value z3 for option sas not known
% 0.15/0.35 % (13731)Refutation found. Thanks to Tanya!
% 0.15/0.35 % SZS status Theorem for theBenchmark
% 0.15/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.35 % (13731)------------------------------
% 0.15/0.35 % (13731)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.35 % (13731)Termination reason: Refutation
% 0.15/0.35
% 0.15/0.35 % (13731)Memory used [KB]: 965
% 0.15/0.35 % (13731)Time elapsed: 0.006 s
% 0.15/0.35 % (13731)Instructions burned: 12 (million)
% 0.15/0.35 % (13731)------------------------------
% 0.15/0.35 % (13731)------------------------------
% 0.15/0.35 % (13726)Success in time 0.016 s
%------------------------------------------------------------------------------