TSTP Solution File: SWV383+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV383+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 : n003.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 16:46:38 EDT 2024
% Result : Theorem 0.14s 0.39s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 100
% Syntax : Number of formulae : 281 ( 96 unt; 0 def)
% Number of atoms : 668 ( 143 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 616 ( 229 ~; 239 |; 51 &)
% ( 63 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 66 ( 64 usr; 56 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 9 con; 0-3 aty)
% Number of variables : 683 ( 659 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f466,plain,
$false,
inference(avatar_sat_refutation,[],[f161,f166,f171,f176,f181,f185,f189,f193,f197,f201,f205,f209,f213,f217,f221,f226,f230,f234,f238,f242,f246,f250,f255,f259,f263,f267,f271,f275,f290,f294,f298,f302,f311,f318,f322,f326,f330,f336,f342,f346,f355,f359,f363,f367,f386,f390,f404,f411,f420,f424,f435,f439,f443,f455,f459,f465]) ).
fof(f465,plain,
( spl6_1
| ~ spl6_3
| ~ spl6_2
| ~ spl6_5
| ~ spl6_52 ),
inference(avatar_split_clause,[],[f444,f437,f178,f163,f168,f158]) ).
fof(f158,plain,
( spl6_1
<=> check_cpq(triple(sK0,sK1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).
fof(f168,plain,
( spl6_3
<=> check_cpq(triple(sK3,sK4,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_3])]) ).
fof(f163,plain,
( spl6_2
<=> ok(triple(sK3,sK4,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).
fof(f178,plain,
( spl6_5
<=> succ_cpq(triple(sK0,sK1,sK2),triple(sK3,sK4,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_5])]) ).
fof(f437,plain,
( spl6_52
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ check_cpq(triple(X3,X4,X5))
| ~ ok(triple(X3,X4,X5))
| ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
| check_cpq(triple(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_52])]) ).
fof(f444,plain,
( ~ ok(triple(sK3,sK4,sK5))
| ~ check_cpq(triple(sK3,sK4,sK5))
| check_cpq(triple(sK0,sK1,sK2))
| ~ spl6_5
| ~ spl6_52 ),
inference(resolution,[],[f438,f180]) ).
fof(f180,plain,
( succ_cpq(triple(sK0,sK1,sK2),triple(sK3,sK4,sK5))
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f438,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
| ~ ok(triple(X3,X4,X5))
| ~ check_cpq(triple(X3,X4,X5))
| check_cpq(triple(X0,X1,X2)) )
| ~ spl6_52 ),
inference(avatar_component_clause,[],[f437]) ).
fof(f459,plain,
spl6_55,
inference(avatar_split_clause,[],[f135,f457]) ).
fof(f457,plain,
( spl6_55
<=> ! [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,[spl6_55])]) ).
fof(f135,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,[],[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(flattening,[],[f79]) ).
fof(f79,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,[],[f50]) ).
fof(f50,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/sandbox/benchmark/theBenchmark.p',ax49) ).
fof(f455,plain,
spl6_54,
inference(avatar_split_clause,[],[f134,f453]) ).
fof(f453,plain,
( spl6_54
<=> ! [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,[spl6_54])]) ).
fof(f134,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,[],[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(flattening,[],[f77]) ).
fof(f77,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,[],[f49]) ).
fof(f49,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/sandbox/benchmark/theBenchmark.p',ax48) ).
fof(f443,plain,
spl6_53,
inference(avatar_split_clause,[],[f101,f441]) ).
fof(f441,plain,
( spl6_53
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ check_cpq(triple(X3,X4,X5))
| ~ ok(triple(X3,X4,X5))
| ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
| ok(triple(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_53])]) ).
fof(f101,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ check_cpq(triple(X3,X4,X5))
| ~ ok(triple(X3,X4,X5))
| ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
| ok(triple(X0,X1,X2)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ! [X3,X4,X5] :
( ~ check_cpq(triple(X3,X4,X5))
| ~ ok(triple(X3,X4,X5))
| ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) )
| ( ok(triple(X0,X1,X2))
& check_cpq(triple(X0,X1,X2)) ) ),
inference(flattening,[],[f56]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ! [X3,X4,X5] :
( ~ check_cpq(triple(X3,X4,X5))
| ~ ok(triple(X3,X4,X5))
| ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) )
| ( ok(triple(X0,X1,X2))
& check_cpq(triple(X0,X1,X2)) ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0,X1,X2] :
( ( ~ ok(triple(X0,X1,X2))
| ~ check_cpq(triple(X0,X1,X2)) )
=> ! [X3,X4,X5] :
( succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
=> ( ~ check_cpq(triple(X3,X4,X5))
| ~ ok(triple(X3,X4,X5)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l19_l20) ).
fof(f439,plain,
spl6_52,
inference(avatar_split_clause,[],[f100,f437]) ).
fof(f100,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ check_cpq(triple(X3,X4,X5))
| ~ ok(triple(X3,X4,X5))
| ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
| check_cpq(triple(X0,X1,X2)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f435,plain,
( spl6_51
| ~ spl6_29
| ~ spl6_36 ),
inference(avatar_split_clause,[],[f393,f324,f288,f433]) ).
fof(f433,plain,
( spl6_51
<=> ! [X0,X1] :
( less_than(X0,X1)
| strictly_less_than(bottom,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_51])]) ).
fof(f288,plain,
( spl6_29
<=> ! [X0,X1] :
( less_than(X0,X1)
| strictly_less_than(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_29])]) ).
fof(f324,plain,
( spl6_36
<=> ! [X0,X1] :
( less_than(X0,X1)
| ~ less_than(X0,bottom) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_36])]) ).
fof(f393,plain,
( ! [X0,X1] :
( less_than(X0,X1)
| strictly_less_than(bottom,X0) )
| ~ spl6_29
| ~ spl6_36 ),
inference(resolution,[],[f325,f289]) ).
fof(f289,plain,
( ! [X0,X1] :
( less_than(X0,X1)
| strictly_less_than(X1,X0) )
| ~ spl6_29 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f325,plain,
( ! [X0,X1] :
( ~ less_than(X0,bottom)
| less_than(X0,X1) )
| ~ spl6_36 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f424,plain,
spl6_50,
inference(avatar_split_clause,[],[f137,f422]) ).
fof(f422,plain,
( spl6_50
<=> ! [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,[spl6_50])]) ).
fof(f137,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,[],[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(flattening,[],[f83]) ).
fof(f83,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/sandbox/benchmark/theBenchmark.p',ax44) ).
fof(f420,plain,
spl6_49,
inference(avatar_split_clause,[],[f136,f418]) ).
fof(f418,plain,
( spl6_49
<=> ! [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,[spl6_49])]) ).
fof(f136,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,[],[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(flattening,[],[f81]) ).
fof(f81,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/sandbox/benchmark/theBenchmark.p',ax45) ).
fof(f411,plain,
spl6_48,
inference(avatar_split_clause,[],[f132,f409]) ).
fof(f409,plain,
( spl6_48
<=> ! [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,[spl6_48])]) ).
fof(f132,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,[],[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(flattening,[],[f73]) ).
fof(f73,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/sandbox/benchmark/theBenchmark.p',ax25) ).
fof(f404,plain,
spl6_47,
inference(avatar_split_clause,[],[f133,f402]) ).
fof(f402,plain,
( spl6_47
<=> ! [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,[spl6_47])]) ).
fof(f133,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,[],[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(flattening,[],[f75]) ).
fof(f75,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,[],[f48]) ).
fof(f48,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/sandbox/benchmark/theBenchmark.p',ax47) ).
fof(f390,plain,
spl6_46,
inference(avatar_split_clause,[],[f130,f388]) ).
fof(f388,plain,
( spl6_46
<=> ! [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,[spl6_46])]) ).
fof(f130,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,[],[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,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/sandbox/benchmark/theBenchmark.p',ax30) ).
fof(f386,plain,
spl6_45,
inference(avatar_split_clause,[],[f129,f384]) ).
fof(f384,plain,
( spl6_45
<=> ! [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,[spl6_45])]) ).
fof(f129,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,[],[f69]) ).
fof(f69,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/sandbox/benchmark/theBenchmark.p',ax29) ).
fof(f367,plain,
spl6_44,
inference(avatar_split_clause,[],[f145,f365]) ).
fof(f365,plain,
( spl6_44
<=> ! [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,[spl6_44])]) ).
fof(f145,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,[],[f93]) ).
fof(f93,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,[],[f86]) ).
fof(f86,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/sandbox/benchmark/theBenchmark.p',ax37) ).
fof(f363,plain,
spl6_43,
inference(avatar_split_clause,[],[f144,f361]) ).
fof(f361,plain,
( spl6_43
<=> ! [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,[spl6_43])]) ).
fof(f144,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,[],[f93]) ).
fof(f359,plain,
spl6_42,
inference(avatar_split_clause,[],[f131,f357]) ).
fof(f357,plain,
( spl6_42
<=> ! [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,[spl6_42])]) ).
fof(f131,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,[],[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(flattening,[],[f71]) ).
fof(f71,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/sandbox/benchmark/theBenchmark.p',ax27) ).
fof(f355,plain,
spl6_41,
inference(avatar_split_clause,[],[f126,f353]) ).
fof(f353,plain,
( spl6_41
<=> ! [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,[spl6_41])]) ).
fof(f126,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/sandbox/benchmark/theBenchmark.p',ax42) ).
fof(f346,plain,
spl6_40,
inference(avatar_split_clause,[],[f147,f344]) ).
fof(f344,plain,
( spl6_40
<=> ! [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,[spl6_40])]) ).
fof(f147,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,[],[f95]) ).
fof(f95,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,[],[f94]) ).
fof(f94,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/sandbox/benchmark/theBenchmark.p',ax23) ).
fof(f342,plain,
spl6_39,
inference(avatar_split_clause,[],[f146,f340]) ).
fof(f340,plain,
( spl6_39
<=> ! [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,[spl6_39])]) ).
fof(f146,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,[],[f95]) ).
fof(f336,plain,
spl6_38,
inference(avatar_split_clause,[],[f128,f334]) ).
fof(f334,plain,
( spl6_38
<=> ! [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,[spl6_38])]) ).
fof(f128,plain,
! [X2,X3,X0,X1] :
( triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3)
| contains_slb(X1,X3) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,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/sandbox/benchmark/theBenchmark.p',ax43) ).
fof(f330,plain,
spl6_37,
inference(avatar_split_clause,[],[f140,f328]) ).
fof(f328,plain,
( spl6_37
<=> ! [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,[spl6_37])]) ).
fof(f140,plain,
! [X2,X3,X0,X1] :
( X1 = X2
| contains_slb(X0,X2)
| ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,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,[],[f91]) ).
fof(f91,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/sandbox/benchmark/theBenchmark.p',ax21) ).
fof(f326,plain,
( spl6_36
| ~ spl6_8
| ~ spl6_26 ),
inference(avatar_split_clause,[],[f283,f265,f191,f324]) ).
fof(f191,plain,
( spl6_8
<=> ! [X0] : less_than(bottom,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_8])]) ).
fof(f265,plain,
( spl6_26
<=> ! [X2,X0,X1] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_26])]) ).
fof(f283,plain,
( ! [X0,X1] :
( less_than(X0,X1)
| ~ less_than(X0,bottom) )
| ~ spl6_8
| ~ spl6_26 ),
inference(resolution,[],[f266,f192]) ).
fof(f192,plain,
( ! [X0] : less_than(bottom,X0)
| ~ spl6_8 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f266,plain,
( ! [X2,X0,X1] :
( ~ less_than(X1,X2)
| less_than(X0,X2)
| ~ less_than(X0,X1) )
| ~ spl6_26 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f322,plain,
spl6_35,
inference(avatar_split_clause,[],[f148,f320]) ).
fof(f320,plain,
( spl6_35
<=> ! [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,[spl6_35])]) ).
fof(f148,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,[],[f95]) ).
fof(f318,plain,
spl6_34,
inference(avatar_split_clause,[],[f143,f316]) ).
fof(f316,plain,
( spl6_34
<=> ! [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,[spl6_34])]) ).
fof(f143,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,[],[f85]) ).
fof(f85,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,[],[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(flattening,[],[f51]) ).
fof(f51,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/sandbox/benchmark/theBenchmark.p',ax38) ).
fof(f311,plain,
spl6_33,
inference(avatar_split_clause,[],[f153,f309]) ).
fof(f309,plain,
( spl6_33
<=> ! [X2,X0,X1] :
( findmin_pqp_res(X0) = removemin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_33])]) ).
fof(f153,plain,
! [X2,X0,X1] :
( findmin_pqp_res(X0) = removemin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 ),
inference(definition_unfolding,[],[f127,f108]) ).
fof(f108,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/sandbox/benchmark/theBenchmark.p',ax53) ).
fof(f127,plain,
! [X2,X0,X1] :
( findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1,X2] :
( findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,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/sandbox/benchmark/theBenchmark.p',ax51) ).
fof(f302,plain,
spl6_32,
inference(avatar_split_clause,[],[f152,f300]) ).
fof(f300,plain,
( spl6_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,[spl6_32])]) ).
fof(f152,plain,
! [X0,X1] :
( succ_cpq(X0,remove_cpq(findmin_cpq_eff(X1),removemin_cpq_res(X1)))
| ~ succ_cpq(X0,X1) ),
inference(definition_unfolding,[],[f115,f150]) ).
fof(f150,plain,
! [X0] : removemin_cpq_eff(X0) = remove_cpq(findmin_cpq_eff(X0),removemin_cpq_res(X0)),
inference(definition_unfolding,[],[f109,f108]) ).
fof(f109,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/sandbox/benchmark/theBenchmark.p',ax52) ).
fof(f115,plain,
! [X0,X1] :
( succ_cpq(X0,removemin_cpq_eff(X1))
| ~ succ_cpq(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,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/sandbox/benchmark/theBenchmark.p',ax35) ).
fof(f298,plain,
spl6_31,
inference(avatar_split_clause,[],[f141,f296]) ).
fof(f296,plain,
( spl6_31
<=> ! [X0,X3,X2,X1] :
( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| ~ contains_slb(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_31])]) ).
fof(f141,plain,
! [X2,X3,X0,X1] :
( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| ~ contains_slb(X0,X2) ),
inference(cnf_transformation,[],[f92]) ).
fof(f294,plain,
spl6_30,
inference(avatar_split_clause,[],[f113,f292]) ).
fof(f292,plain,
( spl6_30
<=> ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_30])]) ).
fof(f113,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/sandbox/benchmark/theBenchmark.p',ax46) ).
fof(f290,plain,
( spl6_29
| ~ spl6_14
| ~ spl6_23 ),
inference(avatar_split_clause,[],[f281,f253,f215,f288]) ).
fof(f215,plain,
( spl6_14
<=> ! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_14])]) ).
fof(f253,plain,
( spl6_23
<=> ! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_23])]) ).
fof(f281,plain,
( ! [X0,X1] :
( less_than(X0,X1)
| strictly_less_than(X1,X0) )
| ~ spl6_14
| ~ spl6_23 ),
inference(duplicate_literal_removal,[],[f278]) ).
fof(f278,plain,
( ! [X0,X1] :
( less_than(X0,X1)
| strictly_less_than(X1,X0)
| less_than(X0,X1) )
| ~ spl6_14
| ~ spl6_23 ),
inference(resolution,[],[f254,f216]) ).
fof(f216,plain,
( ! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) )
| ~ spl6_14 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f254,plain,
( ! [X0,X1] :
( ~ less_than(X0,X1)
| less_than(X1,X0)
| strictly_less_than(X0,X1) )
| ~ spl6_23 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f275,plain,
spl6_28,
inference(avatar_split_clause,[],[f139,f273]) ).
fof(f273,plain,
( spl6_28
<=> ! [X0,X3,X2,X1] :
( contains_cpq(triple(X0,X1,X2),X3)
| ~ contains_slb(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_28])]) ).
fof(f139,plain,
! [X2,X3,X0,X1] :
( contains_cpq(triple(X0,X1,X2),X3)
| ~ contains_slb(X1,X3) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,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/sandbox/benchmark/theBenchmark.p',ax39) ).
fof(f271,plain,
spl6_27,
inference(avatar_split_clause,[],[f138,f269]) ).
fof(f269,plain,
( spl6_27
<=> ! [X2,X0,X1,X3] :
( contains_slb(X1,X3)
| ~ contains_cpq(triple(X0,X1,X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_27])]) ).
fof(f138,plain,
! [X2,X3,X0,X1] :
( contains_slb(X1,X3)
| ~ contains_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[],[f90]) ).
fof(f267,plain,
spl6_26,
inference(avatar_split_clause,[],[f125,f265]) ).
fof(f125,plain,
! [X2,X0,X1] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1,X2] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ),
inference(flattening,[],[f65]) ).
fof(f65,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/sandbox/benchmark/theBenchmark.p',transitivity) ).
fof(f263,plain,
spl6_25,
inference(avatar_split_clause,[],[f121,f261]) ).
fof(f261,plain,
( spl6_25
<=> ! [X2,X0,X1] : lookup_slb(insert_slb(X0,pair(X1,X2)),X1) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl6_25])]) ).
fof(f121,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/sandbox/benchmark/theBenchmark.p',ax26) ).
fof(f259,plain,
spl6_24,
inference(avatar_split_clause,[],[f120,f257]) ).
fof(f257,plain,
( spl6_24
<=> ! [X2,X0,X1] : remove_slb(insert_slb(X0,pair(X1,X2)),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl6_24])]) ).
fof(f120,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/sandbox/benchmark/theBenchmark.p',ax24) ).
fof(f255,plain,
spl6_23,
inference(avatar_split_clause,[],[f117,f253]) ).
fof(f117,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(flattening,[],[f60]) ).
fof(f60,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,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/sandbox/benchmark/theBenchmark.p',stricly_smaller_definition) ).
fof(f250,plain,
spl6_22,
inference(avatar_split_clause,[],[f156,f248]) ).
fof(f248,plain,
( spl6_22
<=> ! [X4,X0,X2] : pair_in_list(insert_slb(X0,pair(X2,X4)),X2,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_22])]) ).
fof(f156,plain,
! [X2,X0,X4] : pair_in_list(insert_slb(X0,pair(X2,X4)),X2,X4),
inference(equality_resolution,[],[f155]) ).
fof(f155,plain,
! [X2,X0,X1,X4] :
( pair_in_list(insert_slb(X0,pair(X1,X4)),X2,X4)
| X1 != X2 ),
inference(equality_resolution,[],[f149]) ).
fof(f149,plain,
! [X2,X3,X0,X1,X4] :
( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| X3 != X4
| X1 != X2 ),
inference(cnf_transformation,[],[f95]) ).
fof(f246,plain,
spl6_21,
inference(avatar_split_clause,[],[f124,f244]) ).
fof(f244,plain,
( spl6_21
<=> ! [X2,X0,X1] :
( bad = X2
| ok(triple(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_21])]) ).
fof(f124,plain,
! [X2,X0,X1] :
( bad = X2
| ok(triple(X0,X1,X2)) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,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/sandbox/benchmark/theBenchmark.p',ax41) ).
fof(f242,plain,
spl6_20,
inference(avatar_split_clause,[],[f123,f240]) ).
fof(f240,plain,
( spl6_20
<=> ! [X2,X0,X1] :
( succ_cpq(X0,remove_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_20])]) ).
fof(f123,plain,
! [X2,X0,X1] :
( succ_cpq(X0,remove_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,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/sandbox/benchmark/theBenchmark.p',ax33) ).
fof(f238,plain,
spl6_19,
inference(avatar_split_clause,[],[f122,f236]) ).
fof(f236,plain,
( spl6_19
<=> ! [X2,X0,X1] :
( succ_cpq(X0,insert_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_19])]) ).
fof(f122,plain,
! [X2,X0,X1] :
( succ_cpq(X0,insert_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,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/sandbox/benchmark/theBenchmark.p',ax32) ).
fof(f234,plain,
spl6_18,
inference(avatar_split_clause,[],[f154,f232]) ).
fof(f232,plain,
( spl6_18
<=> ! [X2,X0,X3] : contains_slb(insert_slb(X0,pair(X2,X3)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_18])]) ).
fof(f154,plain,
! [X2,X3,X0] : contains_slb(insert_slb(X0,pair(X2,X3)),X2),
inference(equality_resolution,[],[f142]) ).
fof(f142,plain,
! [X2,X3,X0,X1] :
( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| X1 != X2 ),
inference(cnf_transformation,[],[f92]) ).
fof(f230,plain,
spl6_17,
inference(avatar_split_clause,[],[f151,f228]) ).
fof(f228,plain,
( spl6_17
<=> ! [X0,X1] : bottom = removemin_cpq_res(triple(X0,create_slb,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_17])]) ).
fof(f151,plain,
! [X0,X1] : bottom = removemin_cpq_res(triple(X0,create_slb,X1)),
inference(definition_unfolding,[],[f112,f108]) ).
fof(f112,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/sandbox/benchmark/theBenchmark.p',ax50) ).
fof(f226,plain,
spl6_16,
inference(avatar_split_clause,[],[f116,f224]) ).
fof(f224,plain,
( spl6_16
<=> ! [X0,X1] :
( succ_cpq(X0,findmin_cpq_eff(X1))
| ~ succ_cpq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_16])]) ).
fof(f116,plain,
! [X0,X1] :
( succ_cpq(X0,findmin_cpq_eff(X1))
| ~ succ_cpq(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,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/sandbox/benchmark/theBenchmark.p',ax34) ).
fof(f221,plain,
spl6_15,
inference(avatar_split_clause,[],[f119,f219]) ).
fof(f219,plain,
( spl6_15
<=> ! [X2,X0,X1] : isnonempty_slb(insert_slb(X0,pair(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_15])]) ).
fof(f119,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/sandbox/benchmark/theBenchmark.p',ax19) ).
fof(f217,plain,
spl6_14,
inference(avatar_split_clause,[],[f114,f215]) ).
fof(f114,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/sandbox/benchmark/theBenchmark.p',totality) ).
fof(f213,plain,
spl6_13,
inference(avatar_split_clause,[],[f118,f211]) ).
fof(f211,plain,
( spl6_13
<=> ! [X0,X1] : ~ ok(triple(X0,X1,bad)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_13])]) ).
fof(f118,plain,
! [X0,X1] : ~ ok(triple(X0,X1,bad)),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1] : ~ ok(triple(X0,X1,bad)),
inference(flattening,[],[f45]) ).
fof(f45,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/sandbox/benchmark/theBenchmark.p',ax40) ).
fof(f209,plain,
spl6_12,
inference(avatar_split_clause,[],[f111,f207]) ).
fof(f207,plain,
( spl6_12
<=> ! [X0,X1] : check_cpq(triple(X0,create_slb,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_12])]) ).
fof(f111,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/sandbox/benchmark/theBenchmark.p',ax36) ).
fof(f205,plain,
spl6_11,
inference(avatar_split_clause,[],[f107,f203]) ).
fof(f203,plain,
( spl6_11
<=> ! [X0] : create_slb = update_slb(create_slb,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_11])]) ).
fof(f107,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/sandbox/benchmark/theBenchmark.p',ax28) ).
fof(f201,plain,
spl6_10,
inference(avatar_split_clause,[],[f110,f199]) ).
fof(f199,plain,
( spl6_10
<=> ! [X0,X1] : ~ pair_in_list(create_slb,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_10])]) ).
fof(f110,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/sandbox/benchmark/theBenchmark.p',ax22) ).
fof(f197,plain,
spl6_9,
inference(avatar_split_clause,[],[f106,f195]) ).
fof(f195,plain,
( spl6_9
<=> ! [X0] : succ_cpq(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_9])]) ).
fof(f106,plain,
! [X0] : succ_cpq(X0,X0),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] : succ_cpq(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax31) ).
fof(f193,plain,
spl6_8,
inference(avatar_split_clause,[],[f105,f191]) ).
fof(f105,plain,
! [X0] : less_than(bottom,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] : less_than(bottom,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bottom_smallest) ).
fof(f189,plain,
spl6_7,
inference(avatar_split_clause,[],[f104,f187]) ).
fof(f187,plain,
( spl6_7
<=> ! [X0] : less_than(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_7])]) ).
fof(f104,plain,
! [X0] : less_than(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : less_than(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
fof(f185,plain,
spl6_6,
inference(avatar_split_clause,[],[f103,f183]) ).
fof(f183,plain,
( spl6_6
<=> ! [X0] : ~ contains_slb(create_slb,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_6])]) ).
fof(f103,plain,
! [X0] : ~ contains_slb(create_slb,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] : ~ contains_slb(create_slb,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
fof(f181,plain,
spl6_5,
inference(avatar_split_clause,[],[f97,f178]) ).
fof(f97,plain,
succ_cpq(triple(sK0,sK1,sK2),triple(sK3,sK4,sK5)),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
( check_cpq(triple(sK3,sK4,sK5))
& ok(triple(sK3,sK4,sK5))
& succ_cpq(triple(sK0,sK1,sK2),triple(sK3,sK4,sK5))
& ~ check_cpq(triple(sK0,sK1,sK2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f55,f88,f87]) ).
fof(f87,plain,
( ? [X0,X1,X2] :
( ? [X3,X4,X5] :
( check_cpq(triple(X3,X4,X5))
& ok(triple(X3,X4,X5))
& succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) )
& ~ check_cpq(triple(X0,X1,X2)) )
=> ( ? [X5,X4,X3] :
( check_cpq(triple(X3,X4,X5))
& ok(triple(X3,X4,X5))
& succ_cpq(triple(sK0,sK1,sK2),triple(X3,X4,X5)) )
& ~ check_cpq(triple(sK0,sK1,sK2)) ) ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
( ? [X5,X4,X3] :
( check_cpq(triple(X3,X4,X5))
& ok(triple(X3,X4,X5))
& succ_cpq(triple(sK0,sK1,sK2),triple(X3,X4,X5)) )
=> ( check_cpq(triple(sK3,sK4,sK5))
& 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] :
( check_cpq(triple(X3,X4,X5))
& ok(triple(X3,X4,X5))
& succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) )
& ~ check_cpq(triple(X0,X1,X2)) ),
inference(flattening,[],[f54]) ).
fof(f54,plain,
? [X0,X1,X2] :
( ? [X3,X4,X5] :
( check_cpq(triple(X3,X4,X5))
& ok(triple(X3,X4,X5))
& succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) )
& ~ check_cpq(triple(X0,X1,X2)) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,negated_conjecture,
~ ! [X0,X1,X2] :
( ~ check_cpq(triple(X0,X1,X2))
=> ! [X3,X4,X5] :
( succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
=> ( ~ check_cpq(triple(X3,X4,X5))
| ~ ok(triple(X3,X4,X5)) ) ) ),
inference(negated_conjecture,[],[f43]) ).
fof(f43,conjecture,
! [X0,X1,X2] :
( ~ check_cpq(triple(X0,X1,X2))
=> ! [X3,X4,X5] :
( succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
=> ( ~ check_cpq(triple(X3,X4,X5))
| ~ ok(triple(X3,X4,X5)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l19_co) ).
fof(f176,plain,
~ spl6_4,
inference(avatar_split_clause,[],[f102,f173]) ).
fof(f173,plain,
( spl6_4
<=> isnonempty_slb(create_slb) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_4])]) ).
fof(f102,plain,
~ isnonempty_slb(create_slb),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
~ isnonempty_slb(create_slb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
fof(f171,plain,
spl6_3,
inference(avatar_split_clause,[],[f99,f168]) ).
fof(f99,plain,
check_cpq(triple(sK3,sK4,sK5)),
inference(cnf_transformation,[],[f89]) ).
fof(f166,plain,
spl6_2,
inference(avatar_split_clause,[],[f98,f163]) ).
fof(f98,plain,
ok(triple(sK3,sK4,sK5)),
inference(cnf_transformation,[],[f89]) ).
fof(f161,plain,
~ spl6_1,
inference(avatar_split_clause,[],[f96,f158]) ).
fof(f96,plain,
~ check_cpq(triple(sK0,sK1,sK2)),
inference(cnf_transformation,[],[f89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV383+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n003.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 05:02:18 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (11346)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (11348)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (11349)WARNING: value z3 for option sas not known
% 0.14/0.38 % (11347)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (11350)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (11349)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)
% 0.14/0.38 % (11351)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)
% 0.14/0.38 % (11352)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)
% 0.14/0.38 % (11353)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)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 TRYING [2]
% 0.14/0.39 % (11351)First to succeed.
% 0.14/0.39 % (11351)Refutation found. Thanks to Tanya!
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.40 % (11351)------------------------------
% 0.14/0.40 % (11351)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.40 % (11351)Termination reason: Refutation
% 0.14/0.40
% 0.14/0.40 % (11351)Memory used [KB]: 1046
% 0.14/0.40 % (11351)Time elapsed: 0.018 s
% 0.14/0.40 % (11351)Instructions burned: 23 (million)
% 0.14/0.40 % (11351)------------------------------
% 0.14/0.40 % (11351)------------------------------
% 0.14/0.40 % (11346)Success in time 0.035 s
%------------------------------------------------------------------------------