TSTP Solution File: SWV376+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV376+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 : n019.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 16:46:37 EDT 2024
% Result : Theorem 0.20s 0.38s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 115
% Syntax : Number of formulae : 339 ( 93 unt; 0 def)
% Number of atoms : 837 ( 176 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 817 ( 319 ~; 331 |; 52 &)
% ( 76 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 79 ( 77 usr; 69 prp; 0-3 aty)
% Number of functors : 31 ( 31 usr; 15 con; 0-3 aty)
% Number of variables : 803 ( 761 !; 42 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f540,plain,
$false,
inference(avatar_sat_refutation,[],[f166,f171,f176,f181,f185,f189,f193,f197,f201,f205,f209,f213,f217,f221,f226,f230,f234,f238,f242,f246,f250,f256,f260,f264,f269,f273,f277,f281,f296,f302,f307,f311,f319,f323,f330,f334,f338,f342,f348,f353,f359,f364,f372,f376,f380,f384,f403,f411,f415,f423,f428,f435,f445,f450,f456,f468,f475,f481,f485,f494,f499,f504,f511,f512,f519,f525,f531,f537,f539]) ).
fof(f539,plain,
( ~ spl12_35
| ~ spl12_68 ),
inference(avatar_contradiction_clause,[],[f538]) ).
fof(f538,plain,
( $false
| ~ spl12_35
| ~ spl12_68 ),
inference(resolution,[],[f536,f329]) ).
fof(f329,plain,
( ! [X0,X1] : ~ ok(triple(X0,X1,sK2))
| ~ spl12_35 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f328,plain,
( spl12_35
<=> ! [X0,X1] : ~ ok(triple(X0,X1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_35])]) ).
fof(f536,plain,
( ok(triple(sK9,sK10,sK2))
| ~ spl12_68 ),
inference(avatar_component_clause,[],[f534]) ).
fof(f534,plain,
( spl12_68
<=> ok(triple(sK9,sK10,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_68])]) ).
fof(f537,plain,
( spl12_68
| ~ spl12_33
| ~ spl12_59 ),
inference(avatar_split_clause,[],[f520,f478,f317,f534]) ).
fof(f317,plain,
( spl12_33
<=> ! [X2,X0,X1] :
( ~ ok(im_succ_cpq(triple(X0,X1,X2)))
| ok(triple(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_33])]) ).
fof(f478,plain,
( spl12_59
<=> ok(im_succ_cpq(triple(sK9,sK10,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_59])]) ).
fof(f520,plain,
( ok(triple(sK9,sK10,sK2))
| ~ spl12_33
| ~ spl12_59 ),
inference(resolution,[],[f480,f318]) ).
fof(f318,plain,
( ! [X2,X0,X1] :
( ~ ok(im_succ_cpq(triple(X0,X1,X2)))
| ok(triple(X0,X1,X2)) )
| ~ spl12_33 ),
inference(avatar_component_clause,[],[f317]) ).
fof(f480,plain,
( ok(im_succ_cpq(triple(sK9,sK10,sK2)))
| ~ spl12_59 ),
inference(avatar_component_clause,[],[f478]) ).
fof(f531,plain,
( spl12_67
| ~ spl12_65
| ~ spl12_66 ),
inference(avatar_split_clause,[],[f526,f522,f516,f528]) ).
fof(f528,plain,
( spl12_67
<=> succ_cpq(triple(sK6,sK7,sK8),triple(sK9,sK10,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_67])]) ).
fof(f516,plain,
( spl12_65
<=> sK2 = sK11 ),
introduced(avatar_definition,[new_symbols(naming,[spl12_65])]) ).
fof(f522,plain,
( spl12_66
<=> succ_cpq(triple(sK6,sK7,sK8),triple(sK9,sK10,sK11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_66])]) ).
fof(f526,plain,
( succ_cpq(triple(sK6,sK7,sK8),triple(sK9,sK10,sK2))
| ~ spl12_65
| ~ spl12_66 ),
inference(forward_demodulation,[],[f524,f518]) ).
fof(f518,plain,
( sK2 = sK11
| ~ spl12_65 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f524,plain,
( succ_cpq(triple(sK6,sK7,sK8),triple(sK9,sK10,sK11))
| ~ spl12_66 ),
inference(avatar_component_clause,[],[f522]) ).
fof(f525,plain,
( spl12_66
| spl12_57 ),
inference(avatar_split_clause,[],[f105,f466,f522]) ).
fof(f466,plain,
( spl12_57
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ ok(triple(X3,X4,X5))
| ok(triple(X0,X1,X2))
| ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_57])]) ).
fof(f105,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ ok(triple(X3,X4,X5))
| ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
| ok(triple(X0,X1,X2))
| succ_cpq(triple(sK6,sK7,sK8),triple(sK9,sK10,sK11)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
( ! [X0,X1,X2] :
( ! [X3,X4,X5] :
( ~ ok(triple(X3,X4,X5))
| ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) )
| ok(triple(X0,X1,X2)) )
| ( ok(im_succ_cpq(triple(sK9,sK10,sK11)))
& ~ ok(triple(sK9,sK10,sK11))
& succ_cpq(triple(sK6,sK7,sK8),triple(sK9,sK10,sK11)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10,sK11])],[f91,f92]) ).
fof(f92,plain,
( ? [X6,X7,X8,X9,X10,X11] :
( ok(im_succ_cpq(triple(X9,X10,X11)))
& ~ ok(triple(X9,X10,X11))
& succ_cpq(triple(X6,X7,X8),triple(X9,X10,X11)) )
=> ( ok(im_succ_cpq(triple(sK9,sK10,sK11)))
& ~ ok(triple(sK9,sK10,sK11))
& succ_cpq(triple(sK6,sK7,sK8),triple(sK9,sK10,sK11)) ) ),
introduced(choice_axiom,[]) ).
fof(f91,plain,
( ! [X0,X1,X2] :
( ! [X3,X4,X5] :
( ~ ok(triple(X3,X4,X5))
| ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) )
| ok(triple(X0,X1,X2)) )
| ? [X6,X7,X8,X9,X10,X11] :
( ok(im_succ_cpq(triple(X9,X10,X11)))
& ~ ok(triple(X9,X10,X11))
& succ_cpq(triple(X6,X7,X8),triple(X9,X10,X11)) ) ),
inference(rectify,[],[f58]) ).
fof(f58,plain,
( ! [X6,X7,X8] :
( ! [X9,X10,X11] :
( ~ ok(triple(X9,X10,X11))
| ~ succ_cpq(triple(X6,X7,X8),triple(X9,X10,X11)) )
| ok(triple(X6,X7,X8)) )
| ? [X0,X1,X2,X3,X4,X5] :
( ok(im_succ_cpq(triple(X3,X4,X5)))
& ~ ok(triple(X3,X4,X5))
& succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) ) ),
inference(flattening,[],[f57]) ).
fof(f57,plain,
( ! [X6,X7,X8] :
( ! [X9,X10,X11] :
( ~ ok(triple(X9,X10,X11))
| ~ succ_cpq(triple(X6,X7,X8),triple(X9,X10,X11)) )
| ok(triple(X6,X7,X8)) )
| ? [X0,X1,X2,X3,X4,X5] :
( ok(im_succ_cpq(triple(X3,X4,X5)))
& ~ ok(triple(X3,X4,X5))
& succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
( ! [X0,X1,X2,X3,X4,X5] :
( succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
=> ( ~ ok(triple(X3,X4,X5))
=> ~ ok(im_succ_cpq(triple(X3,X4,X5))) ) )
=> ! [X6,X7,X8] :
( ~ ok(triple(X6,X7,X8))
=> ! [X9,X10,X11] :
( succ_cpq(triple(X6,X7,X8),triple(X9,X10,X11))
=> ~ ok(triple(X9,X10,X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l12_induction) ).
fof(f519,plain,
( spl12_65
| ~ spl12_20
| ~ spl12_25
| spl12_56 ),
inference(avatar_split_clause,[],[f470,f462,f266,f244,f516]) ).
fof(f244,plain,
( spl12_20
<=> ! [X2,X0,X1] :
( bad = X2
| ok(triple(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_20])]) ).
fof(f266,plain,
( spl12_25
<=> bad = sK2 ),
introduced(avatar_definition,[new_symbols(naming,[spl12_25])]) ).
fof(f462,plain,
( spl12_56
<=> ok(triple(sK9,sK10,sK11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_56])]) ).
fof(f470,plain,
( sK2 = sK11
| ~ spl12_20
| ~ spl12_25
| spl12_56 ),
inference(forward_demodulation,[],[f469,f268]) ).
fof(f268,plain,
( bad = sK2
| ~ spl12_25 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f469,plain,
( bad = sK11
| ~ spl12_20
| spl12_56 ),
inference(resolution,[],[f464,f245]) ).
fof(f245,plain,
( ! [X2,X0,X1] :
( ok(triple(X0,X1,X2))
| bad = X2 )
| ~ spl12_20 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f464,plain,
( ~ ok(triple(sK9,sK10,sK11))
| spl12_56 ),
inference(avatar_component_clause,[],[f462]) ).
fof(f512,plain,
( ~ spl12_2
| spl12_1
| ~ spl12_4
| ~ spl12_57 ),
inference(avatar_split_clause,[],[f487,f466,f178,f163,f168]) ).
fof(f168,plain,
( spl12_2
<=> ok(triple(sK3,sK4,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_2])]) ).
fof(f163,plain,
( spl12_1
<=> ok(triple(sK0,sK1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_1])]) ).
fof(f178,plain,
( spl12_4
<=> succ_cpq(triple(sK0,sK1,sK2),triple(sK3,sK4,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_4])]) ).
fof(f487,plain,
( ok(triple(sK0,sK1,sK2))
| ~ ok(triple(sK3,sK4,sK5))
| ~ spl12_4
| ~ spl12_57 ),
inference(resolution,[],[f467,f180]) ).
fof(f180,plain,
( succ_cpq(triple(sK0,sK1,sK2),triple(sK3,sK4,sK5))
| ~ spl12_4 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f467,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
| ok(triple(X0,X1,X2))
| ~ ok(triple(X3,X4,X5)) )
| ~ spl12_57 ),
inference(avatar_component_clause,[],[f466]) ).
fof(f511,plain,
( spl12_64
| ~ spl12_20
| ~ spl12_25
| ~ spl12_43 ),
inference(avatar_split_clause,[],[f394,f370,f266,f244,f509]) ).
fof(f509,plain,
( spl12_64
<=> ! [X2,X0,X1,X3] :
( sK2 = X3
| ok(insert_cpq(triple(X0,X2,X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_64])]) ).
fof(f370,plain,
( spl12_43
<=> ! [X0,X3,X2,X1] : insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_43])]) ).
fof(f394,plain,
( ! [X2,X3,X0,X1] :
( sK2 = X3
| ok(insert_cpq(triple(X0,X2,X3),X1)) )
| ~ spl12_20
| ~ spl12_25
| ~ spl12_43 ),
inference(forward_demodulation,[],[f391,f268]) ).
fof(f391,plain,
( ! [X2,X3,X0,X1] :
( ok(insert_cpq(triple(X0,X2,X3),X1))
| bad = X3 )
| ~ spl12_20
| ~ spl12_43 ),
inference(superposition,[],[f245,f371]) ).
fof(f371,plain,
( ! [X2,X3,X0,X1] : insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2)
| ~ spl12_43 ),
inference(avatar_component_clause,[],[f370]) ).
fof(f504,plain,
spl12_63,
inference(avatar_split_clause,[],[f140,f502]) ).
fof(f502,plain,
( spl12_63
<=> ! [X2,X0,X1] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
| ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_63])]) ).
fof(f140,plain,
! [X2,X0,X1] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
| ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1,X2] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
| ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ),
inference(flattening,[],[f80]) ).
fof(f80,plain,
! [X0,X1,X2] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
| ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
& contains_slb(X1,findmin_pqp_res(X0))
& create_slb != X1 )
=> findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2) ),
inference(rectify,[],[f37]) ).
fof(f37,axiom,
! [X0,X1,X2,X3] :
( ( less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
& contains_slb(X1,findmin_pqp_res(X0))
& create_slb != X1 )
=> findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax49) ).
fof(f499,plain,
( spl12_62
| ~ spl12_25
| ~ spl12_61 ),
inference(avatar_split_clause,[],[f495,f492,f266,f497]) ).
fof(f497,plain,
( spl12_62
<=> ! [X2,X0,X1] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),sK2)
| ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_62])]) ).
fof(f492,plain,
( spl12_61
<=> ! [X2,X0,X1] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
| ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_61])]) ).
fof(f495,plain,
( ! [X2,X0,X1] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),sK2)
| ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 )
| ~ spl12_25
| ~ spl12_61 ),
inference(forward_demodulation,[],[f493,f268]) ).
fof(f493,plain,
( ! [X2,X0,X1] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
| ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 )
| ~ spl12_61 ),
inference(avatar_component_clause,[],[f492]) ).
fof(f494,plain,
spl12_61,
inference(avatar_split_clause,[],[f139,f492]) ).
fof(f139,plain,
! [X2,X0,X1] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
| ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1,X2] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
| ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ),
inference(flattening,[],[f78]) ).
fof(f78,plain,
! [X0,X1,X2] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
| ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ( strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
& contains_slb(X1,findmin_pqp_res(X0))
& create_slb != X1 )
=> findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
inference(rectify,[],[f36]) ).
fof(f36,axiom,
! [X0,X1,X2,X3] :
( ( strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
& contains_slb(X1,findmin_pqp_res(X0))
& create_slb != X1 )
=> findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax48) ).
fof(f485,plain,
( spl12_60
| ~ spl12_43
| ~ spl12_47 ),
inference(avatar_split_clause,[],[f441,f401,f370,f483]) ).
fof(f483,plain,
( spl12_60
<=> ! [X2,X0,X1,X3] : ~ ok(insert_cpq(insert_cpq(triple(X0,X2,sK2),X1),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_60])]) ).
fof(f401,plain,
( spl12_47
<=> ! [X2,X0,X1] : ~ ok(insert_cpq(triple(X0,X2,sK2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_47])]) ).
fof(f441,plain,
( ! [X2,X3,X0,X1] : ~ ok(insert_cpq(insert_cpq(triple(X0,X2,sK2),X1),X3))
| ~ spl12_43
| ~ spl12_47 ),
inference(superposition,[],[f402,f371]) ).
fof(f402,plain,
( ! [X2,X0,X1] : ~ ok(insert_cpq(triple(X0,X2,sK2),X1))
| ~ spl12_47 ),
inference(avatar_component_clause,[],[f401]) ).
fof(f481,plain,
( spl12_59
| ~ spl12_20
| ~ spl12_25
| spl12_56
| ~ spl12_58 ),
inference(avatar_split_clause,[],[f476,f472,f462,f266,f244,f478]) ).
fof(f472,plain,
( spl12_58
<=> ok(im_succ_cpq(triple(sK9,sK10,sK11))) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_58])]) ).
fof(f476,plain,
( ok(im_succ_cpq(triple(sK9,sK10,sK2)))
| ~ spl12_20
| ~ spl12_25
| spl12_56
| ~ spl12_58 ),
inference(forward_demodulation,[],[f474,f470]) ).
fof(f474,plain,
( ok(im_succ_cpq(triple(sK9,sK10,sK11)))
| ~ spl12_58 ),
inference(avatar_component_clause,[],[f472]) ).
fof(f475,plain,
( spl12_58
| spl12_57 ),
inference(avatar_split_clause,[],[f107,f466,f472]) ).
fof(f107,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ ok(triple(X3,X4,X5))
| ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
| ok(triple(X0,X1,X2))
| ok(im_succ_cpq(triple(sK9,sK10,sK11))) ),
inference(cnf_transformation,[],[f93]) ).
fof(f468,plain,
( ~ spl12_56
| spl12_57 ),
inference(avatar_split_clause,[],[f106,f466,f462]) ).
fof(f106,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ ok(triple(X3,X4,X5))
| ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
| ok(triple(X0,X1,X2))
| ~ ok(triple(sK9,sK10,sK11)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f456,plain,
spl12_55,
inference(avatar_split_clause,[],[f142,f454]) ).
fof(f454,plain,
( spl12_55
<=> ! [X0,X3,X2,X1] :
( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2)
| ~ less_than(lookup_slb(X1,X3),X3)
| ~ contains_slb(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_55])]) ).
fof(f142,plain,
! [X2,X3,X0,X1] :
( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2)
| ~ less_than(lookup_slb(X1,X3),X3)
| ~ contains_slb(X1,X3) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1,X2,X3] :
( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2)
| ~ less_than(lookup_slb(X1,X3),X3)
| ~ contains_slb(X1,X3) ),
inference(flattening,[],[f84]) ).
fof(f84,plain,
! [X0,X1,X2,X3] :
( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2)
| ~ less_than(lookup_slb(X1,X3),X3)
| ~ contains_slb(X1,X3) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1,X2,X3] :
( ( less_than(lookup_slb(X1,X3),X3)
& contains_slb(X1,X3) )
=> remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax44) ).
fof(f450,plain,
( spl12_54
| ~ spl12_25
| ~ spl12_53 ),
inference(avatar_split_clause,[],[f446,f443,f266,f448]) ).
fof(f448,plain,
( spl12_54
<=> ! [X0,X3,X2,X1] :
( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),sK2)
| ~ strictly_less_than(X3,lookup_slb(X1,X3))
| ~ contains_slb(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_54])]) ).
fof(f443,plain,
( spl12_53
<=> ! [X0,X3,X2,X1] :
( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad)
| ~ strictly_less_than(X3,lookup_slb(X1,X3))
| ~ contains_slb(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_53])]) ).
fof(f446,plain,
( ! [X2,X3,X0,X1] :
( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),sK2)
| ~ strictly_less_than(X3,lookup_slb(X1,X3))
| ~ contains_slb(X1,X3) )
| ~ spl12_25
| ~ spl12_53 ),
inference(forward_demodulation,[],[f444,f268]) ).
fof(f444,plain,
( ! [X2,X3,X0,X1] :
( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad)
| ~ strictly_less_than(X3,lookup_slb(X1,X3))
| ~ contains_slb(X1,X3) )
| ~ spl12_53 ),
inference(avatar_component_clause,[],[f443]) ).
fof(f445,plain,
spl12_53,
inference(avatar_split_clause,[],[f141,f443]) ).
fof(f141,plain,
! [X2,X3,X0,X1] :
( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad)
| ~ strictly_less_than(X3,lookup_slb(X1,X3))
| ~ contains_slb(X1,X3) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1,X2,X3] :
( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad)
| ~ strictly_less_than(X3,lookup_slb(X1,X3))
| ~ contains_slb(X1,X3) ),
inference(flattening,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2,X3] :
( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad)
| ~ strictly_less_than(X3,lookup_slb(X1,X3))
| ~ contains_slb(X1,X3) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0,X1,X2,X3] :
( ( strictly_less_than(X3,lookup_slb(X1,X3))
& contains_slb(X1,X3) )
=> remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45) ).
fof(f435,plain,
spl12_52,
inference(avatar_split_clause,[],[f137,f433]) ).
fof(f433,plain,
( spl12_52
<=> ! [X0,X3,X2,X1] :
( remove_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(remove_slb(X0,X2),pair(X1,X3))
| ~ contains_slb(X0,X2)
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_52])]) ).
fof(f137,plain,
! [X2,X3,X0,X1] :
( remove_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(remove_slb(X0,X2),pair(X1,X3))
| ~ contains_slb(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1,X2,X3] :
( remove_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(remove_slb(X0,X2),pair(X1,X3))
| ~ contains_slb(X0,X2)
| X1 = X2 ),
inference(flattening,[],[f74]) ).
fof(f74,plain,
! [X0,X1,X2,X3] :
( remove_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(remove_slb(X0,X2),pair(X1,X3))
| ~ contains_slb(X0,X2)
| X1 = X2 ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1,X2,X3] :
( ( contains_slb(X0,X2)
& X1 != X2 )
=> remove_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(remove_slb(X0,X2),pair(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax25) ).
fof(f428,plain,
( spl12_51
| ~ spl12_25
| ~ spl12_50 ),
inference(avatar_split_clause,[],[f424,f421,f266,f426]) ).
fof(f426,plain,
( spl12_51
<=> ! [X2,X0,X1] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),sK2)
| contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_51])]) ).
fof(f421,plain,
( spl12_50
<=> ! [X2,X0,X1] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
| contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_50])]) ).
fof(f424,plain,
( ! [X2,X0,X1] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),sK2)
| contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 )
| ~ spl12_25
| ~ spl12_50 ),
inference(forward_demodulation,[],[f422,f268]) ).
fof(f422,plain,
( ! [X2,X0,X1] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
| contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 )
| ~ spl12_50 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f423,plain,
spl12_50,
inference(avatar_split_clause,[],[f138,f421]) ).
fof(f138,plain,
! [X2,X0,X1] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
| contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1,X2] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
| contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ),
inference(flattening,[],[f76]) ).
fof(f76,plain,
! [X0,X1,X2] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
| contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( ~ contains_slb(X1,findmin_pqp_res(X0))
& create_slb != X1 )
=> findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
inference(rectify,[],[f35]) ).
fof(f35,axiom,
! [X0,X1,X2,X3] :
( ( ~ contains_slb(X1,findmin_pqp_res(X0))
& create_slb != X1 )
=> findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax47) ).
fof(f415,plain,
spl12_49,
inference(avatar_split_clause,[],[f135,f413]) ).
fof(f413,plain,
( spl12_49
<=> ! [X0,X3,X2,X1] :
( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X3))
| ~ less_than(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_49])]) ).
fof(f135,plain,
! [X2,X3,X0,X1] :
( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X3))
| ~ less_than(X2,X3) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1,X2,X3] :
( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X3))
| ~ less_than(X2,X3) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1,X2,X3] :
( less_than(X2,X3)
=> update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax30) ).
fof(f411,plain,
spl12_48,
inference(avatar_split_clause,[],[f134,f409]) ).
fof(f409,plain,
( spl12_48
<=> ! [X0,X3,X2,X1] :
( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X2))
| ~ strictly_less_than(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_48])]) ).
fof(f134,plain,
! [X2,X3,X0,X1] :
( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X2))
| ~ strictly_less_than(X3,X2) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1,X2,X3] :
( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X2))
| ~ strictly_less_than(X3,X2) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0,X1,X2,X3] :
( strictly_less_than(X3,X2)
=> update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax29) ).
fof(f403,plain,
( spl12_47
| ~ spl12_12
| ~ spl12_25
| ~ spl12_43 ),
inference(avatar_split_clause,[],[f393,f370,f266,f211,f401]) ).
fof(f211,plain,
( spl12_12
<=> ! [X0,X1] : ~ ok(triple(X0,X1,bad)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_12])]) ).
fof(f393,plain,
( ! [X2,X0,X1] : ~ ok(insert_cpq(triple(X0,X2,sK2),X1))
| ~ spl12_12
| ~ spl12_25
| ~ spl12_43 ),
inference(forward_demodulation,[],[f386,f268]) ).
fof(f386,plain,
( ! [X2,X0,X1] : ~ ok(insert_cpq(triple(X0,X2,bad),X1))
| ~ spl12_12
| ~ spl12_43 ),
inference(superposition,[],[f212,f371]) ).
fof(f212,plain,
( ! [X0,X1] : ~ ok(triple(X0,X1,bad))
| ~ spl12_12 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f384,plain,
spl12_46,
inference(avatar_split_clause,[],[f150,f382]) ).
fof(f382,plain,
( spl12_46
<=> ! [X4,X0,X3,X2,X1] :
( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ check_cpq(triple(X0,X1,X2))
| ~ less_than(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_46])]) ).
fof(f150,plain,
! [X2,X3,X0,X1,X4] :
( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ check_cpq(triple(X0,X1,X2))
| ~ less_than(X4,X3) ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1,X2,X3,X4] :
( ( ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ check_cpq(triple(X0,X1,X2)) )
& ( check_cpq(triple(X0,X1,X2))
| ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) ) )
| ~ less_than(X4,X3) ),
inference(nnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1,X2,X3,X4] :
( ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
<=> check_cpq(triple(X0,X1,X2)) )
| ~ less_than(X4,X3) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0,X1,X2,X3,X4] :
( less_than(X4,X3)
=> ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
<=> check_cpq(triple(X0,X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).
fof(f380,plain,
spl12_45,
inference(avatar_split_clause,[],[f149,f378]) ).
fof(f378,plain,
( spl12_45
<=> ! [X4,X0,X3,X2,X1] :
( check_cpq(triple(X0,X1,X2))
| ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ less_than(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_45])]) ).
fof(f149,plain,
! [X2,X3,X0,X1,X4] :
( check_cpq(triple(X0,X1,X2))
| ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ less_than(X4,X3) ),
inference(cnf_transformation,[],[f97]) ).
fof(f376,plain,
spl12_44,
inference(avatar_split_clause,[],[f136,f374]) ).
fof(f374,plain,
( spl12_44
<=> ! [X0,X3,X2,X1] :
( lookup_slb(insert_slb(X0,pair(X1,X3)),X2) = lookup_slb(X0,X2)
| ~ contains_slb(X0,X2)
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_44])]) ).
fof(f136,plain,
! [X2,X3,X0,X1] :
( lookup_slb(insert_slb(X0,pair(X1,X3)),X2) = lookup_slb(X0,X2)
| ~ contains_slb(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1,X2,X3] :
( lookup_slb(insert_slb(X0,pair(X1,X3)),X2) = lookup_slb(X0,X2)
| ~ contains_slb(X0,X2)
| X1 = X2 ),
inference(flattening,[],[f72]) ).
fof(f72,plain,
! [X0,X1,X2,X3] :
( lookup_slb(insert_slb(X0,pair(X1,X3)),X2) = lookup_slb(X0,X2)
| ~ contains_slb(X0,X2)
| X1 = X2 ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1,X2,X3] :
( ( contains_slb(X0,X2)
& X1 != X2 )
=> lookup_slb(insert_slb(X0,pair(X1,X3)),X2) = lookup_slb(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax27) ).
fof(f372,plain,
spl12_43,
inference(avatar_split_clause,[],[f131,f370]) ).
fof(f131,plain,
! [X2,X3,X0,X1] : insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2),
inference(cnf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0,X1,X2,X3] : insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax42) ).
fof(f364,plain,
spl12_42,
inference(avatar_split_clause,[],[f152,f362]) ).
fof(f362,plain,
( spl12_42
<=> ! [X4,X0,X3,X2,X1] :
( X3 = X4
| pair_in_list(X0,X2,X4)
| ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_42])]) ).
fof(f152,plain,
! [X2,X3,X0,X1,X4] :
( X3 = X4
| pair_in_list(X0,X2,X4)
| ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0,X1,X2,X3,X4] :
( ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| ( ( X3 != X4
| X1 != X2 )
& ~ pair_in_list(X0,X2,X4) ) )
& ( ( X3 = X4
& X1 = X2 )
| pair_in_list(X0,X2,X4)
| ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
inference(flattening,[],[f98]) ).
fof(f98,plain,
! [X0,X1,X2,X3,X4] :
( ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| ( ( X3 != X4
| X1 != X2 )
& ~ pair_in_list(X0,X2,X4) ) )
& ( ( X3 = X4
& X1 = X2 )
| pair_in_list(X0,X2,X4)
| ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1,X2,X3,X4] :
( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
<=> ( ( X3 = X4
& X1 = X2 )
| pair_in_list(X0,X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23) ).
fof(f359,plain,
spl12_41,
inference(avatar_split_clause,[],[f151,f357]) ).
fof(f357,plain,
( spl12_41
<=> ! [X4,X0,X3,X2,X1] :
( X1 = X2
| pair_in_list(X0,X2,X4)
| ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_41])]) ).
fof(f151,plain,
! [X2,X3,X0,X1,X4] :
( X1 = X2
| pair_in_list(X0,X2,X4)
| ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ),
inference(cnf_transformation,[],[f99]) ).
fof(f353,plain,
( spl12_40
| ~ spl12_25
| ~ spl12_39 ),
inference(avatar_split_clause,[],[f349,f346,f266,f351]) ).
fof(f351,plain,
( spl12_40
<=> ! [X0,X3,X2,X1] :
( remove_cpq(triple(X0,X1,X2),X3) = triple(X0,X1,sK2)
| contains_slb(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_40])]) ).
fof(f346,plain,
( spl12_39
<=> ! [X0,X3,X2,X1] :
( triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3)
| contains_slb(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_39])]) ).
fof(f349,plain,
( ! [X2,X3,X0,X1] :
( remove_cpq(triple(X0,X1,X2),X3) = triple(X0,X1,sK2)
| contains_slb(X1,X3) )
| ~ spl12_25
| ~ spl12_39 ),
inference(forward_demodulation,[],[f347,f268]) ).
fof(f347,plain,
( ! [X2,X3,X0,X1] :
( triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3)
| contains_slb(X1,X3) )
| ~ spl12_39 ),
inference(avatar_component_clause,[],[f346]) ).
fof(f348,plain,
spl12_39,
inference(avatar_split_clause,[],[f133,f346]) ).
fof(f133,plain,
! [X2,X3,X0,X1] :
( triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3)
| contains_slb(X1,X3) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3)
| contains_slb(X1,X3) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1,X2,X3] :
( ~ contains_slb(X1,X3)
=> triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax43) ).
fof(f342,plain,
spl12_38,
inference(avatar_split_clause,[],[f145,f340]) ).
fof(f340,plain,
( spl12_38
<=> ! [X0,X3,X2,X1] :
( X1 = X2
| contains_slb(X0,X2)
| ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_38])]) ).
fof(f145,plain,
! [X2,X3,X0,X1] :
( X1 = X2
| contains_slb(X0,X2)
| ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0,X1,X2,X3] :
( ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| ( X1 != X2
& ~ contains_slb(X0,X2) ) )
& ( X1 = X2
| contains_slb(X0,X2)
| ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ) ),
inference(flattening,[],[f95]) ).
fof(f95,plain,
! [X0,X1,X2,X3] :
( ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| ( X1 != X2
& ~ contains_slb(X0,X2) ) )
& ( X1 = X2
| contains_slb(X0,X2)
| ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1,X2,X3] :
( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
<=> ( X1 = X2
| contains_slb(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).
fof(f338,plain,
spl12_37,
inference(avatar_split_clause,[],[f153,f336]) ).
fof(f336,plain,
( spl12_37
<=> ! [X4,X0,X3,X2,X1] :
( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| ~ pair_in_list(X0,X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_37])]) ).
fof(f153,plain,
! [X2,X3,X0,X1,X4] :
( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| ~ pair_in_list(X0,X2,X4) ),
inference(cnf_transformation,[],[f99]) ).
fof(f334,plain,
spl12_36,
inference(avatar_split_clause,[],[f148,f332]) ).
fof(f332,plain,
( spl12_36
<=> ! [X4,X0,X3,X2,X1] :
( ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ strictly_less_than(X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_36])]) ).
fof(f148,plain,
! [X2,X3,X0,X1,X4] :
( ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ strictly_less_than(X3,X4) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1,X2,X3,X4] :
( ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ strictly_less_than(X3,X4) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0,X1,X2,X3,X4] :
( strictly_less_than(X3,X4)
=> ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) ),
inference(flattening,[],[f52]) ).
fof(f52,plain,
! [X0,X1,X2,X3,X4] :
( strictly_less_than(X3,X4)
=> ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) ),
inference(true_and_false_elimination,[],[f26]) ).
fof(f26,axiom,
! [X0,X1,X2,X3,X4] :
( strictly_less_than(X3,X4)
=> ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
<=> $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
fof(f330,plain,
( spl12_35
| ~ spl12_12
| ~ spl12_25 ),
inference(avatar_split_clause,[],[f298,f266,f211,f328]) ).
fof(f298,plain,
( ! [X0,X1] : ~ ok(triple(X0,X1,sK2))
| ~ spl12_12
| ~ spl12_25 ),
inference(superposition,[],[f212,f268]) ).
fof(f323,plain,
spl12_34,
inference(avatar_split_clause,[],[f158,f321]) ).
fof(f321,plain,
( spl12_34
<=> ! [X2,X0,X1] :
( findmin_pqp_res(X0) = removemin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_34])]) ).
fof(f158,plain,
! [X2,X0,X1] :
( findmin_pqp_res(X0) = removemin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 ),
inference(definition_unfolding,[],[f132,f113]) ).
fof(f113,plain,
! [X0] : findmin_cpq_res(X0) = removemin_cpq_res(X0),
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0] : findmin_cpq_res(X0) = removemin_cpq_res(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax53) ).
fof(f132,plain,
! [X2,X0,X1] :
( findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1,X2] :
( findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0,X1,X2] :
( create_slb != X1
=> findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2)) ),
inference(rectify,[],[f39]) ).
fof(f39,axiom,
! [X0,X1,X2,X3] :
( create_slb != X1
=> findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51) ).
fof(f319,plain,
spl12_33,
inference(avatar_split_clause,[],[f103,f317]) ).
fof(f103,plain,
! [X2,X0,X1] :
( ~ ok(im_succ_cpq(triple(X0,X1,X2)))
| ok(triple(X0,X1,X2)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ~ ok(im_succ_cpq(triple(X0,X1,X2)))
| ok(triple(X0,X1,X2)) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0,X1,X2] :
( ~ ok(triple(X0,X1,X2))
=> ~ ok(im_succ_cpq(triple(X0,X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l12_l13) ).
fof(f311,plain,
spl12_32,
inference(avatar_split_clause,[],[f157,f309]) ).
fof(f309,plain,
( spl12_32
<=> ! [X0,X1] :
( succ_cpq(X0,remove_cpq(findmin_cpq_eff(X1),removemin_cpq_res(X1)))
| ~ succ_cpq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_32])]) ).
fof(f157,plain,
! [X0,X1] :
( succ_cpq(X0,remove_cpq(findmin_cpq_eff(X1),removemin_cpq_res(X1)))
| ~ succ_cpq(X0,X1) ),
inference(definition_unfolding,[],[f120,f155]) ).
fof(f155,plain,
! [X0] : removemin_cpq_eff(X0) = remove_cpq(findmin_cpq_eff(X0),removemin_cpq_res(X0)),
inference(definition_unfolding,[],[f114,f113]) ).
fof(f114,plain,
! [X0] : removemin_cpq_eff(X0) = remove_cpq(findmin_cpq_eff(X0),findmin_cpq_res(X0)),
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] : removemin_cpq_eff(X0) = remove_cpq(findmin_cpq_eff(X0),findmin_cpq_res(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).
fof(f120,plain,
! [X0,X1] :
( succ_cpq(X0,removemin_cpq_eff(X1))
| ~ succ_cpq(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( succ_cpq(X0,removemin_cpq_eff(X1))
| ~ succ_cpq(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0,X1] :
( succ_cpq(X0,X1)
=> succ_cpq(X0,removemin_cpq_eff(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax35) ).
fof(f307,plain,
spl12_31,
inference(avatar_split_clause,[],[f146,f305]) ).
fof(f305,plain,
( spl12_31
<=> ! [X0,X3,X2,X1] :
( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| ~ contains_slb(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_31])]) ).
fof(f146,plain,
! [X2,X3,X0,X1] :
( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| ~ contains_slb(X0,X2) ),
inference(cnf_transformation,[],[f96]) ).
fof(f302,plain,
( spl12_30
| ~ spl12_25
| ~ spl12_29 ),
inference(avatar_split_clause,[],[f297,f294,f266,f300]) ).
fof(f300,plain,
( spl12_30
<=> ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_30])]) ).
fof(f294,plain,
( spl12_29
<=> ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_29])]) ).
fof(f297,plain,
( ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,sK2)
| ~ spl12_25
| ~ spl12_29 ),
inference(forward_demodulation,[],[f295,f268]) ).
fof(f295,plain,
( ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad)
| ~ spl12_29 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f296,plain,
spl12_29,
inference(avatar_split_clause,[],[f118,f294]) ).
fof(f118,plain,
! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad),
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46) ).
fof(f281,plain,
spl12_28,
inference(avatar_split_clause,[],[f144,f279]) ).
fof(f279,plain,
( spl12_28
<=> ! [X0,X3,X2,X1] :
( contains_cpq(triple(X0,X1,X2),X3)
| ~ contains_slb(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_28])]) ).
fof(f144,plain,
! [X2,X3,X0,X1] :
( contains_cpq(triple(X0,X1,X2),X3)
| ~ contains_slb(X1,X3) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1,X2,X3] :
( ( contains_cpq(triple(X0,X1,X2),X3)
| ~ contains_slb(X1,X3) )
& ( contains_slb(X1,X3)
| ~ contains_cpq(triple(X0,X1,X2),X3) ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0,X1,X2,X3] :
( contains_cpq(triple(X0,X1,X2),X3)
<=> contains_slb(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).
fof(f277,plain,
spl12_27,
inference(avatar_split_clause,[],[f143,f275]) ).
fof(f275,plain,
( spl12_27
<=> ! [X2,X0,X1,X3] :
( contains_slb(X1,X3)
| ~ contains_cpq(triple(X0,X1,X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_27])]) ).
fof(f143,plain,
! [X2,X3,X0,X1] :
( contains_slb(X1,X3)
| ~ contains_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[],[f94]) ).
fof(f273,plain,
spl12_26,
inference(avatar_split_clause,[],[f130,f271]) ).
fof(f271,plain,
( spl12_26
<=> ! [X2,X0,X1] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_26])]) ).
fof(f130,plain,
! [X2,X0,X1] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1,X2] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ),
inference(flattening,[],[f66]) ).
fof(f66,plain,
! [X0,X1,X2] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1,X2] :
( ( less_than(X1,X2)
& less_than(X0,X1) )
=> less_than(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
fof(f269,plain,
( spl12_25
| spl12_1
| ~ spl12_20 ),
inference(avatar_split_clause,[],[f251,f244,f163,f266]) ).
fof(f251,plain,
( bad = sK2
| spl12_1
| ~ spl12_20 ),
inference(resolution,[],[f245,f165]) ).
fof(f165,plain,
( ~ ok(triple(sK0,sK1,sK2))
| spl12_1 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f264,plain,
spl12_24,
inference(avatar_split_clause,[],[f126,f262]) ).
fof(f262,plain,
( spl12_24
<=> ! [X2,X0,X1] : lookup_slb(insert_slb(X0,pair(X1,X2)),X1) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl12_24])]) ).
fof(f126,plain,
! [X2,X0,X1] : lookup_slb(insert_slb(X0,pair(X1,X2)),X1) = X2,
inference(cnf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2] : lookup_slb(insert_slb(X0,pair(X1,X2)),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f260,plain,
spl12_23,
inference(avatar_split_clause,[],[f125,f258]) ).
fof(f258,plain,
( spl12_23
<=> ! [X2,X0,X1] : remove_slb(insert_slb(X0,pair(X1,X2)),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl12_23])]) ).
fof(f125,plain,
! [X2,X0,X1] : remove_slb(insert_slb(X0,pair(X1,X2)),X1) = X0,
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1,X2] : remove_slb(insert_slb(X0,pair(X1,X2)),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
fof(f256,plain,
spl12_22,
inference(avatar_split_clause,[],[f122,f254]) ).
fof(f254,plain,
( spl12_22
<=> ! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_22])]) ).
fof(f122,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(flattening,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1] :
( ( ~ less_than(X1,X0)
& less_than(X0,X1) )
=> strictly_less_than(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( strictly_less_than(X0,X1)
<=> ( ~ less_than(X1,X0)
& less_than(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stricly_smaller_definition) ).
fof(f250,plain,
spl12_21,
inference(avatar_split_clause,[],[f161,f248]) ).
fof(f248,plain,
( spl12_21
<=> ! [X4,X0,X2] : pair_in_list(insert_slb(X0,pair(X2,X4)),X2,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_21])]) ).
fof(f161,plain,
! [X2,X0,X4] : pair_in_list(insert_slb(X0,pair(X2,X4)),X2,X4),
inference(equality_resolution,[],[f160]) ).
fof(f160,plain,
! [X2,X0,X1,X4] :
( pair_in_list(insert_slb(X0,pair(X1,X4)),X2,X4)
| X1 != X2 ),
inference(equality_resolution,[],[f154]) ).
fof(f154,plain,
! [X2,X3,X0,X1,X4] :
( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| X3 != X4
| X1 != X2 ),
inference(cnf_transformation,[],[f99]) ).
fof(f246,plain,
spl12_20,
inference(avatar_split_clause,[],[f129,f244]) ).
fof(f129,plain,
! [X2,X0,X1] :
( bad = X2
| ok(triple(X0,X1,X2)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1,X2] :
( bad = X2
| ok(triple(X0,X1,X2)) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0,X1,X2] :
( ~ ok(triple(X0,X1,X2))
=> bad = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).
fof(f242,plain,
spl12_19,
inference(avatar_split_clause,[],[f128,f240]) ).
fof(f240,plain,
( spl12_19
<=> ! [X2,X0,X1] :
( succ_cpq(X0,remove_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_19])]) ).
fof(f128,plain,
! [X2,X0,X1] :
( succ_cpq(X0,remove_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1,X2] :
( succ_cpq(X0,remove_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0,X1,X2] :
( succ_cpq(X0,X1)
=> succ_cpq(X0,remove_cpq(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax33) ).
fof(f238,plain,
spl12_18,
inference(avatar_split_clause,[],[f127,f236]) ).
fof(f236,plain,
( spl12_18
<=> ! [X2,X0,X1] :
( succ_cpq(X0,insert_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_18])]) ).
fof(f127,plain,
! [X2,X0,X1] :
( succ_cpq(X0,insert_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1,X2] :
( succ_cpq(X0,insert_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0,X1,X2] :
( succ_cpq(X0,X1)
=> succ_cpq(X0,insert_cpq(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax32) ).
fof(f234,plain,
spl12_17,
inference(avatar_split_clause,[],[f159,f232]) ).
fof(f232,plain,
( spl12_17
<=> ! [X2,X0,X3] : contains_slb(insert_slb(X0,pair(X2,X3)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_17])]) ).
fof(f159,plain,
! [X2,X3,X0] : contains_slb(insert_slb(X0,pair(X2,X3)),X2),
inference(equality_resolution,[],[f147]) ).
fof(f147,plain,
! [X2,X3,X0,X1] :
( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| X1 != X2 ),
inference(cnf_transformation,[],[f96]) ).
fof(f230,plain,
spl12_16,
inference(avatar_split_clause,[],[f156,f228]) ).
fof(f228,plain,
( spl12_16
<=> ! [X0,X1] : bottom = removemin_cpq_res(triple(X0,create_slb,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_16])]) ).
fof(f156,plain,
! [X0,X1] : bottom = removemin_cpq_res(triple(X0,create_slb,X1)),
inference(definition_unfolding,[],[f117,f113]) ).
fof(f117,plain,
! [X0,X1] : bottom = findmin_cpq_res(triple(X0,create_slb,X1)),
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1] : bottom = findmin_cpq_res(triple(X0,create_slb,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax50) ).
fof(f226,plain,
spl12_15,
inference(avatar_split_clause,[],[f121,f224]) ).
fof(f224,plain,
( spl12_15
<=> ! [X0,X1] :
( succ_cpq(X0,findmin_cpq_eff(X1))
| ~ succ_cpq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_15])]) ).
fof(f121,plain,
! [X0,X1] :
( succ_cpq(X0,findmin_cpq_eff(X1))
| ~ succ_cpq(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1] :
( succ_cpq(X0,findmin_cpq_eff(X1))
| ~ succ_cpq(X0,X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0,X1] :
( succ_cpq(X0,X1)
=> succ_cpq(X0,findmin_cpq_eff(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax34) ).
fof(f221,plain,
spl12_14,
inference(avatar_split_clause,[],[f124,f219]) ).
fof(f219,plain,
( spl12_14
<=> ! [X2,X0,X1] : isnonempty_slb(insert_slb(X0,pair(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_14])]) ).
fof(f124,plain,
! [X2,X0,X1] : isnonempty_slb(insert_slb(X0,pair(X1,X2))),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2] : isnonempty_slb(insert_slb(X0,pair(X1,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax19) ).
fof(f217,plain,
spl12_13,
inference(avatar_split_clause,[],[f119,f215]) ).
fof(f215,plain,
( spl12_13
<=> ! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_13])]) ).
fof(f119,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality) ).
fof(f213,plain,
spl12_12,
inference(avatar_split_clause,[],[f123,f211]) ).
fof(f123,plain,
! [X0,X1] : ~ ok(triple(X0,X1,bad)),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X1] : ~ ok(triple(X0,X1,bad)),
inference(flattening,[],[f46]) ).
fof(f46,plain,
! [X0,X1] : ~ ok(triple(X0,X1,bad)),
inference(true_and_false_elimination,[],[f28]) ).
fof(f28,axiom,
! [X0,X1] :
( ok(triple(X0,X1,bad))
<=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax40) ).
fof(f209,plain,
spl12_11,
inference(avatar_split_clause,[],[f116,f207]) ).
fof(f207,plain,
( spl12_11
<=> ! [X0,X1] : check_cpq(triple(X0,create_slb,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_11])]) ).
fof(f116,plain,
! [X0,X1] : check_cpq(triple(X0,create_slb,X1)),
inference(cnf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0,X1] : check_cpq(triple(X0,create_slb,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax36) ).
fof(f205,plain,
spl12_10,
inference(avatar_split_clause,[],[f112,f203]) ).
fof(f203,plain,
( spl12_10
<=> ! [X0] : create_slb = update_slb(create_slb,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_10])]) ).
fof(f112,plain,
! [X0] : create_slb = update_slb(create_slb,X0),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] : create_slb = update_slb(create_slb,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
fof(f201,plain,
spl12_9,
inference(avatar_split_clause,[],[f115,f199]) ).
fof(f199,plain,
( spl12_9
<=> ! [X0,X1] : ~ pair_in_list(create_slb,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_9])]) ).
fof(f115,plain,
! [X0,X1] : ~ pair_in_list(create_slb,X0,X1),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] : ~ pair_in_list(create_slb,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
fof(f197,plain,
spl12_8,
inference(avatar_split_clause,[],[f111,f195]) ).
fof(f195,plain,
( spl12_8
<=> ! [X0] : succ_cpq(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_8])]) ).
fof(f111,plain,
! [X0] : succ_cpq(X0,X0),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] : succ_cpq(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax31) ).
fof(f193,plain,
spl12_7,
inference(avatar_split_clause,[],[f110,f191]) ).
fof(f191,plain,
( spl12_7
<=> ! [X0] : less_than(bottom,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_7])]) ).
fof(f110,plain,
! [X0] : less_than(bottom,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] : less_than(bottom,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bottom_smallest) ).
fof(f189,plain,
spl12_6,
inference(avatar_split_clause,[],[f109,f187]) ).
fof(f187,plain,
( spl12_6
<=> ! [X0] : less_than(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_6])]) ).
fof(f109,plain,
! [X0] : less_than(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : less_than(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
fof(f185,plain,
spl12_5,
inference(avatar_split_clause,[],[f108,f183]) ).
fof(f183,plain,
( spl12_5
<=> ! [X0] : ~ contains_slb(create_slb,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_5])]) ).
fof(f108,plain,
! [X0] : ~ contains_slb(create_slb,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] : ~ contains_slb(create_slb,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).
fof(f181,plain,
spl12_4,
inference(avatar_split_clause,[],[f101,f178]) ).
fof(f101,plain,
succ_cpq(triple(sK0,sK1,sK2),triple(sK3,sK4,sK5)),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
( ok(triple(sK3,sK4,sK5))
& succ_cpq(triple(sK0,sK1,sK2),triple(sK3,sK4,sK5))
& ~ ok(triple(sK0,sK1,sK2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f55,f89,f88]) ).
fof(f88,plain,
( ? [X0,X1,X2] :
( ? [X3,X4,X5] :
( ok(triple(X3,X4,X5))
& succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) )
& ~ ok(triple(X0,X1,X2)) )
=> ( ? [X5,X4,X3] :
( ok(triple(X3,X4,X5))
& succ_cpq(triple(sK0,sK1,sK2),triple(X3,X4,X5)) )
& ~ ok(triple(sK0,sK1,sK2)) ) ),
introduced(choice_axiom,[]) ).
fof(f89,plain,
( ? [X5,X4,X3] :
( ok(triple(X3,X4,X5))
& succ_cpq(triple(sK0,sK1,sK2),triple(X3,X4,X5)) )
=> ( ok(triple(sK3,sK4,sK5))
& succ_cpq(triple(sK0,sK1,sK2),triple(sK3,sK4,sK5)) ) ),
introduced(choice_axiom,[]) ).
fof(f55,plain,
? [X0,X1,X2] :
( ? [X3,X4,X5] :
( ok(triple(X3,X4,X5))
& succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) )
& ~ ok(triple(X0,X1,X2)) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,negated_conjecture,
~ ! [X0,X1,X2] :
( ~ ok(triple(X0,X1,X2))
=> ! [X3,X4,X5] :
( succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
=> ~ ok(triple(X3,X4,X5)) ) ),
inference(negated_conjecture,[],[f44]) ).
fof(f44,conjecture,
! [X0,X1,X2] :
( ~ ok(triple(X0,X1,X2))
=> ! [X3,X4,X5] :
( succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
=> ~ ok(triple(X3,X4,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l12_co) ).
fof(f176,plain,
~ spl12_3,
inference(avatar_split_clause,[],[f104,f173]) ).
fof(f173,plain,
( spl12_3
<=> isnonempty_slb(create_slb) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_3])]) ).
fof(f104,plain,
~ isnonempty_slb(create_slb),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
~ isnonempty_slb(create_slb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
fof(f171,plain,
spl12_2,
inference(avatar_split_clause,[],[f102,f168]) ).
fof(f102,plain,
ok(triple(sK3,sK4,sK5)),
inference(cnf_transformation,[],[f90]) ).
fof(f166,plain,
~ spl12_1,
inference(avatar_split_clause,[],[f100,f163]) ).
fof(f100,plain,
~ ok(triple(sK0,sK1,sK2)),
inference(cnf_transformation,[],[f90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV376+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
% 0.14/0.35 % Computer : n019.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 : Tue Apr 30 04:54:44 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (31108)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.37 % (31111)WARNING: value z3 for option sas not known
% 0.20/0.37 % (31112)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.37 % (31115)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)
% 0.20/0.37 % (31110)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.37 % (31113)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)
% 0.20/0.37 % (31114)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)
% 0.20/0.37 % (31111)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)
% 0.20/0.37 % (31109)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.37 TRYING [1]
% 0.20/0.38 TRYING [2]
% 0.20/0.38 % (31113)First to succeed.
% 0.20/0.38 TRYING [1]
% 0.20/0.38 % (31113)Refutation found. Thanks to Tanya!
% 0.20/0.38 % SZS status Theorem for theBenchmark
% 0.20/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.39 % (31113)------------------------------
% 0.20/0.39 % (31113)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.20/0.39 % (31113)Termination reason: Refutation
% 0.20/0.39
% 0.20/0.39 % (31113)Memory used [KB]: 1081
% 0.20/0.39 % (31113)Time elapsed: 0.016 s
% 0.20/0.39 % (31113)Instructions burned: 27 (million)
% 0.20/0.39 % (31113)------------------------------
% 0.20/0.39 % (31113)------------------------------
% 0.20/0.39 % (31108)Success in time 0.031 s
%------------------------------------------------------------------------------