TSTP Solution File: SWC407+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWC407+1 : TPTP v8.1.2. Released v2.4.0.
% 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 : Sun May 5 10:26:50 EDT 2024
% Result : Theorem 1.67s 0.59s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 206
% Syntax : Number of formulae : 994 ( 57 unt; 0 def)
% Number of atoms : 4314 ( 805 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 5378 (2058 ~;2121 |; 792 &)
% ( 113 <=>; 294 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 79 ( 77 usr; 41 prp; 0-2 aty)
% Number of functors : 58 ( 58 usr; 8 con; 0-2 aty)
% Number of variables : 1710 (1362 !; 348 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4977,plain,
$false,
inference(avatar_sat_refutation,[],[f666,f794,f797,f1102,f1106,f1138,f1390,f1394,f1407,f1411,f1491,f1495,f1508,f1512,f1584,f1588,f1713,f1717,f1823,f1829,f1839,f1887,f1914,f1918,f1928,f1943,f1947,f1981,f1985,f2452,f2456,f2505,f2509,f2578,f2582,f3343,f3358,f3369,f4970]) ).
fof(f4970,plain,
( ~ spl72_2
| ~ spl72_3 ),
inference(avatar_contradiction_clause,[],[f4969]) ).
fof(f4969,plain,
( $false
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f4943,f394]) ).
fof(f394,plain,
~ memberP(sK21,sK24),
inference(cnf_transformation,[],[f263]) ).
fof(f263,plain,
( ( ( nil = sK22
& nil = sK23 )
| sP0(sK23,sK22) )
& ~ memberP(sK21,sK24)
& memberP(sK20,sK24)
& ssItem(sK24)
& sK20 = sK22
& sK21 = sK23
& ssList(sK23)
& ssList(sK22)
& ssList(sK21)
& ssList(sK20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24])],[f257,f262,f261,f260,f259,f258]) ).
fof(f258,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP0(X3,X2) )
& ? [X4] :
( ~ memberP(X1,X4)
& memberP(X0,X4)
& ssItem(X4) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP0(X3,X2) )
& ? [X4] :
( ~ memberP(X1,X4)
& memberP(sK20,X4)
& ssItem(X4) )
& sK20 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f259,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP0(X3,X2) )
& ? [X4] :
( ~ memberP(X1,X4)
& memberP(sK20,X4)
& ssItem(X4) )
& sK20 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP0(X3,X2) )
& ? [X4] :
( ~ memberP(sK21,X4)
& memberP(sK20,X4)
& ssItem(X4) )
& sK20 = X2
& sK21 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f260,plain,
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP0(X3,X2) )
& ? [X4] :
( ~ memberP(sK21,X4)
& memberP(sK20,X4)
& ssItem(X4) )
& sK20 = X2
& sK21 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ( nil = sK22
& nil = X3 )
| sP0(X3,sK22) )
& ? [X4] :
( ~ memberP(sK21,X4)
& memberP(sK20,X4)
& ssItem(X4) )
& sK20 = sK22
& sK21 = X3
& ssList(X3) )
& ssList(sK22) ) ),
introduced(choice_axiom,[]) ).
fof(f261,plain,
( ? [X3] :
( ( ( nil = sK22
& nil = X3 )
| sP0(X3,sK22) )
& ? [X4] :
( ~ memberP(sK21,X4)
& memberP(sK20,X4)
& ssItem(X4) )
& sK20 = sK22
& sK21 = X3
& ssList(X3) )
=> ( ( ( nil = sK22
& nil = sK23 )
| sP0(sK23,sK22) )
& ? [X4] :
( ~ memberP(sK21,X4)
& memberP(sK20,X4)
& ssItem(X4) )
& sK20 = sK22
& sK21 = sK23
& ssList(sK23) ) ),
introduced(choice_axiom,[]) ).
fof(f262,plain,
( ? [X4] :
( ~ memberP(sK21,X4)
& memberP(sK20,X4)
& ssItem(X4) )
=> ( ~ memberP(sK21,sK24)
& memberP(sK20,sK24)
& ssItem(sK24) ) ),
introduced(choice_axiom,[]) ).
fof(f257,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP0(X3,X2) )
& ? [X4] :
( ~ memberP(X1,X4)
& memberP(X0,X4)
& ssItem(X4) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(rectify,[],[f225]) ).
fof(f225,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP0(X3,X2) )
& ? [X5] :
( ~ memberP(X1,X5)
& memberP(X0,X5)
& ssItem(X5) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f100,f224]) ).
fof(f224,plain,
! [X3,X2] :
( ? [X4] :
( memberP(X3,X4)
& cons(X4,nil) = X2
& ssItem(X4) )
| ~ sP0(X3,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f100,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| ? [X4] :
( memberP(X3,X4)
& cons(X4,nil) = X2
& ssItem(X4) ) )
& ? [X5] :
( ~ memberP(X1,X5)
& memberP(X0,X5)
& ssItem(X5) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| ? [X4] :
( memberP(X3,X4)
& cons(X4,nil) = X2
& ssItem(X4) ) )
& ? [X5] :
( ~ memberP(X1,X5)
& memberP(X0,X5)
& ssItem(X5) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X4] :
( ssItem(X4)
=> ( ~ memberP(X3,X4)
| cons(X4,nil) != X2 ) ) )
| ! [X5] :
( ssItem(X5)
=> ( memberP(X1,X5)
| ~ memberP(X0,X5) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X3,X5)
| cons(X5,nil) != X2 ) ) )
| ! [X4] :
( ssItem(X4)
=> ( memberP(X1,X4)
| ~ memberP(X0,X4) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X3,X5)
| cons(X5,nil) != X2 ) ) )
| ! [X4] :
( ssItem(X4)
=> ( memberP(X1,X4)
| ~ memberP(X0,X4) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f4943,plain,
( memberP(sK21,sK24)
| ~ spl72_2
| ~ spl72_3 ),
inference(superposition,[],[f2312,f4921]) ).
fof(f4921,plain,
( sK24 = hd(sK20)
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f4917,f392]) ).
fof(f392,plain,
ssItem(sK24),
inference(cnf_transformation,[],[f263]) ).
fof(f4917,plain,
( sK24 = hd(sK20)
| ~ ssItem(sK24)
| ~ spl72_2
| ~ spl72_3 ),
inference(resolution,[],[f4884,f393]) ).
fof(f393,plain,
memberP(sK20,sK24),
inference(cnf_transformation,[],[f263]) ).
fof(f4884,plain,
( ! [X0] :
( ~ memberP(sK20,X0)
| hd(sK20) = X0
| ~ ssItem(X0) )
| ~ spl72_2
| ~ spl72_3 ),
inference(forward_demodulation,[],[f4883,f2298]) ).
fof(f2298,plain,
( sK19(sK21,sK20) = hd(sK20)
| ~ spl72_2
| ~ spl72_3 ),
inference(forward_demodulation,[],[f2274,f1143]) ).
fof(f1143,plain,
( sK20 = cons(sK19(sK21,sK20),nil)
| ~ spl72_2 ),
inference(resolution,[],[f665,f384]) ).
fof(f384,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| cons(sK19(X0,X1),nil) = X1 ),
inference(cnf_transformation,[],[f256]) ).
fof(f256,plain,
! [X0,X1] :
( ( memberP(X0,sK19(X0,X1))
& cons(sK19(X0,X1),nil) = X1
& ssItem(sK19(X0,X1)) )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f254,f255]) ).
fof(f255,plain,
! [X0,X1] :
( ? [X2] :
( memberP(X0,X2)
& cons(X2,nil) = X1
& ssItem(X2) )
=> ( memberP(X0,sK19(X0,X1))
& cons(sK19(X0,X1),nil) = X1
& ssItem(sK19(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f254,plain,
! [X0,X1] :
( ? [X2] :
( memberP(X0,X2)
& cons(X2,nil) = X1
& ssItem(X2) )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f253]) ).
fof(f253,plain,
! [X3,X2] :
( ? [X4] :
( memberP(X3,X4)
& cons(X4,nil) = X2
& ssItem(X4) )
| ~ sP0(X3,X2) ),
inference(nnf_transformation,[],[f224]) ).
fof(f665,plain,
( sP0(sK21,sK20)
| ~ spl72_2 ),
inference(avatar_component_clause,[],[f663]) ).
fof(f663,plain,
( spl72_2
<=> sP0(sK21,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_2])]) ).
fof(f2274,plain,
( sK19(sK21,sK20) = hd(cons(sK19(sK21,sK20),nil))
| ~ spl72_3 ),
inference(resolution,[],[f955,f788]) ).
fof(f788,plain,
( ssItem(sK19(sK21,sK20))
| ~ spl72_3 ),
inference(avatar_component_clause,[],[f787]) ).
fof(f787,plain,
( spl72_3
<=> ssItem(sK19(sK21,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_3])]) ).
fof(f955,plain,
! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,nil)) = X0 ),
inference(resolution,[],[f571,f405]) ).
fof(f405,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f571,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| hd(cons(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f183]) ).
fof(f183,plain,
! [X0] :
( ! [X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> hd(cons(X1,X0)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23) ).
fof(f4883,plain,
( ! [X0] :
( ~ memberP(sK20,X0)
| sK19(sK21,sK20) = X0
| ~ ssItem(X0) )
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f4882,f406]) ).
fof(f406,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
fof(f4882,plain,
( ! [X0] :
( ~ memberP(sK20,X0)
| sK19(sK21,sK20) = X0
| memberP(nil,X0)
| ~ ssItem(X0) )
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f4881,f788]) ).
fof(f4881,plain,
( ! [X0] :
( ~ memberP(sK20,X0)
| sK19(sK21,sK20) = X0
| memberP(nil,X0)
| ~ ssItem(sK19(sK21,sK20))
| ~ ssItem(X0) )
| ~ spl72_2 ),
inference(subsumption_resolution,[],[f4861,f405]) ).
fof(f4861,plain,
( ! [X0] :
( ~ memberP(sK20,X0)
| sK19(sK21,sK20) = X0
| memberP(nil,X0)
| ~ ssList(nil)
| ~ ssItem(sK19(sK21,sK20))
| ~ ssItem(X0) )
| ~ spl72_2 ),
inference(superposition,[],[f436,f1143]) ).
fof(f436,plain,
! [X2,X0,X1] :
( ~ memberP(cons(X1,X2),X0)
| X0 = X1
| memberP(X2,X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f270]) ).
fof(f270,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( ~ memberP(X2,X0)
& X0 != X1 ) )
& ( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f269]) ).
fof(f269,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( ~ memberP(X2,X0)
& X0 != X1 ) )
& ( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).
fof(f2312,plain,
( memberP(sK21,hd(sK20))
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f2310,f665]) ).
fof(f2310,plain,
( memberP(sK21,hd(sK20))
| ~ sP0(sK21,sK20)
| ~ spl72_2
| ~ spl72_3 ),
inference(superposition,[],[f385,f2298]) ).
fof(f385,plain,
! [X0,X1] :
( memberP(X0,sK19(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f256]) ).
fof(f3369,plain,
( ~ spl72_39
| spl72_40
| ~ spl72_33
| ~ spl72_34 ),
inference(avatar_split_clause,[],[f2648,f2575,f2571,f3366,f3362]) ).
fof(f3362,plain,
( spl72_39
<=> rearsegP(sK20,cons(sK71,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_39])]) ).
fof(f3366,plain,
( spl72_40
<=> sK20 = cons(sK71,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_40])]) ).
fof(f2571,plain,
( spl72_33
<=> ssList(cons(sK71,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_33])]) ).
fof(f2575,plain,
( spl72_34
<=> ssList(cons(sK71,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_34])]) ).
fof(f2648,plain,
( sK20 = cons(sK71,sK20)
| ~ rearsegP(sK20,cons(sK71,sK20))
| ~ spl72_33
| ~ spl72_34 ),
inference(subsumption_resolution,[],[f2647,f386]) ).
fof(f386,plain,
ssList(sK20),
inference(cnf_transformation,[],[f263]) ).
fof(f2647,plain,
( sK20 = cons(sK71,sK20)
| ~ rearsegP(sK20,cons(sK71,sK20))
| ~ ssList(sK20)
| ~ spl72_33
| ~ spl72_34 ),
inference(subsumption_resolution,[],[f2646,f2577]) ).
fof(f2577,plain,
( ssList(cons(sK71,sK20))
| ~ spl72_34 ),
inference(avatar_component_clause,[],[f2575]) ).
fof(f2646,plain,
( sK20 = cons(sK71,sK20)
| ~ rearsegP(sK20,cons(sK71,sK20))
| ~ ssList(cons(sK71,sK20))
| ~ ssList(sK20)
| ~ spl72_33 ),
inference(resolution,[],[f2645,f581]) ).
fof(f581,plain,
! [X0,X1] :
( ~ rearsegP(X1,X0)
| X0 = X1
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f194]) ).
fof(f194,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f193]) ).
fof(f193,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( rearsegP(X1,X0)
& rearsegP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax48) ).
fof(f2645,plain,
( rearsegP(cons(sK71,sK20),sK20)
| ~ spl72_33 ),
inference(subsumption_resolution,[],[f2565,f2572]) ).
fof(f2572,plain,
( ssList(cons(sK71,nil))
| ~ spl72_33 ),
inference(avatar_component_clause,[],[f2571]) ).
fof(f2565,plain,
( rearsegP(cons(sK71,sK20),sK20)
| ~ ssList(cons(sK71,nil)) ),
inference(subsumption_resolution,[],[f2559,f386]) ).
fof(f2559,plain,
( rearsegP(cons(sK71,sK20),sK20)
| ~ ssList(cons(sK71,nil))
| ~ ssList(sK20) ),
inference(superposition,[],[f2117,f2340]) ).
fof(f2340,plain,
cons(sK71,sK20) = app(cons(sK71,nil),sK20),
inference(resolution,[],[f1844,f612]) ).
fof(f612,plain,
ssItem(sK71),
inference(cnf_transformation,[],[f382]) ).
fof(f382,plain,
( sK70 != sK71
& ssItem(sK71)
& ssItem(sK70) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK70,sK71])],[f2,f381,f380]) ).
fof(f380,plain,
( ? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) )
=> ( ? [X1] :
( sK70 != X1
& ssItem(X1) )
& ssItem(sK70) ) ),
introduced(choice_axiom,[]) ).
fof(f381,plain,
( ? [X1] :
( sK70 != X1
& ssItem(X1) )
=> ( sK70 != sK71
& ssItem(sK71) ) ),
introduced(choice_axiom,[]) ).
fof(f2,axiom,
? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(f1844,plain,
! [X0] :
( ~ ssItem(X0)
| cons(X0,sK20) = app(cons(X0,nil),sK20) ),
inference(resolution,[],[f572,f386]) ).
fof(f572,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f184]) ).
fof(f184,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).
fof(f2117,plain,
! [X2,X1] :
( rearsegP(app(X2,X1),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(subsumption_resolution,[],[f636,f577]) ).
fof(f577,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f186]) ).
fof(f186,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f636,plain,
! [X2,X1] :
( rearsegP(app(X2,X1),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X2,X1)) ),
inference(equality_resolution,[],[f588]) ).
fof(f588,plain,
! [X2,X0,X1] :
( rearsegP(X0,X1)
| app(X2,X1) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f368]) ).
fof(f368,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ( app(sK66(X0,X1),X1) = X0
& ssList(sK66(X0,X1)) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK66])],[f366,f367]) ).
fof(f367,plain,
! [X0,X1] :
( ? [X3] :
( app(X3,X1) = X0
& ssList(X3) )
=> ( app(sK66(X0,X1),X1) = X0
& ssList(sK66(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f366,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ? [X3] :
( app(X3,X1) = X0
& ssList(X3) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f365]) ).
fof(f365,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ? [X2] :
( app(X2,X1) = X0
& ssList(X2) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f200]) ).
fof(f200,plain,
! [X0] :
( ! [X1] :
( ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
fof(f3358,plain,
( ~ spl72_37
| spl72_38
| ~ spl72_31
| ~ spl72_32 ),
inference(avatar_split_clause,[],[f2643,f2502,f2498,f3355,f3351]) ).
fof(f3351,plain,
( spl72_37
<=> rearsegP(sK20,cons(sK70,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_37])]) ).
fof(f3355,plain,
( spl72_38
<=> sK20 = cons(sK70,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_38])]) ).
fof(f2498,plain,
( spl72_31
<=> ssList(cons(sK70,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_31])]) ).
fof(f2502,plain,
( spl72_32
<=> ssList(cons(sK70,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_32])]) ).
fof(f2643,plain,
( sK20 = cons(sK70,sK20)
| ~ rearsegP(sK20,cons(sK70,sK20))
| ~ spl72_31
| ~ spl72_32 ),
inference(subsumption_resolution,[],[f2642,f386]) ).
fof(f2642,plain,
( sK20 = cons(sK70,sK20)
| ~ rearsegP(sK20,cons(sK70,sK20))
| ~ ssList(sK20)
| ~ spl72_31
| ~ spl72_32 ),
inference(subsumption_resolution,[],[f2641,f2504]) ).
fof(f2504,plain,
( ssList(cons(sK70,sK20))
| ~ spl72_32 ),
inference(avatar_component_clause,[],[f2502]) ).
fof(f2641,plain,
( sK20 = cons(sK70,sK20)
| ~ rearsegP(sK20,cons(sK70,sK20))
| ~ ssList(cons(sK70,sK20))
| ~ ssList(sK20)
| ~ spl72_31 ),
inference(resolution,[],[f2640,f581]) ).
fof(f2640,plain,
( rearsegP(cons(sK70,sK20),sK20)
| ~ spl72_31 ),
inference(subsumption_resolution,[],[f2492,f2499]) ).
fof(f2499,plain,
( ssList(cons(sK70,nil))
| ~ spl72_31 ),
inference(avatar_component_clause,[],[f2498]) ).
fof(f2492,plain,
( rearsegP(cons(sK70,sK20),sK20)
| ~ ssList(cons(sK70,nil)) ),
inference(subsumption_resolution,[],[f2487,f386]) ).
fof(f2487,plain,
( rearsegP(cons(sK70,sK20),sK20)
| ~ ssList(cons(sK70,nil))
| ~ ssList(sK20) ),
inference(superposition,[],[f2117,f2339]) ).
fof(f2339,plain,
cons(sK70,sK20) = app(cons(sK70,nil),sK20),
inference(resolution,[],[f1844,f611]) ).
fof(f611,plain,
ssItem(sK70),
inference(cnf_transformation,[],[f382]) ).
fof(f3343,plain,
( ~ spl72_35
| spl72_36
| ~ spl72_29
| ~ spl72_30 ),
inference(avatar_split_clause,[],[f2638,f2449,f2445,f3340,f3336]) ).
fof(f3336,plain,
( spl72_35
<=> rearsegP(sK20,cons(sK24,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_35])]) ).
fof(f3340,plain,
( spl72_36
<=> sK20 = cons(sK24,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_36])]) ).
fof(f2445,plain,
( spl72_29
<=> ssList(cons(sK24,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_29])]) ).
fof(f2449,plain,
( spl72_30
<=> ssList(cons(sK24,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_30])]) ).
fof(f2638,plain,
( sK20 = cons(sK24,sK20)
| ~ rearsegP(sK20,cons(sK24,sK20))
| ~ spl72_29
| ~ spl72_30 ),
inference(subsumption_resolution,[],[f2637,f386]) ).
fof(f2637,plain,
( sK20 = cons(sK24,sK20)
| ~ rearsegP(sK20,cons(sK24,sK20))
| ~ ssList(sK20)
| ~ spl72_29
| ~ spl72_30 ),
inference(subsumption_resolution,[],[f2636,f2451]) ).
fof(f2451,plain,
( ssList(cons(sK24,sK20))
| ~ spl72_30 ),
inference(avatar_component_clause,[],[f2449]) ).
fof(f2636,plain,
( sK20 = cons(sK24,sK20)
| ~ rearsegP(sK20,cons(sK24,sK20))
| ~ ssList(cons(sK24,sK20))
| ~ ssList(sK20)
| ~ spl72_29 ),
inference(resolution,[],[f2635,f581]) ).
fof(f2635,plain,
( rearsegP(cons(sK24,sK20),sK20)
| ~ spl72_29 ),
inference(subsumption_resolution,[],[f2411,f2446]) ).
fof(f2446,plain,
( ssList(cons(sK24,nil))
| ~ spl72_29 ),
inference(avatar_component_clause,[],[f2445]) ).
fof(f2411,plain,
( rearsegP(cons(sK24,sK20),sK20)
| ~ ssList(cons(sK24,nil)) ),
inference(subsumption_resolution,[],[f2406,f386]) ).
fof(f2406,plain,
( rearsegP(cons(sK24,sK20),sK20)
| ~ ssList(cons(sK24,nil))
| ~ ssList(sK20) ),
inference(superposition,[],[f2117,f2318]) ).
fof(f2318,plain,
cons(sK24,sK20) = app(cons(sK24,nil),sK20),
inference(resolution,[],[f1844,f392]) ).
fof(f2582,plain,
spl72_33,
inference(avatar_contradiction_clause,[],[f2581]) ).
fof(f2581,plain,
( $false
| spl72_33 ),
inference(subsumption_resolution,[],[f2580,f405]) ).
fof(f2580,plain,
( ~ ssList(nil)
| spl72_33 ),
inference(subsumption_resolution,[],[f2579,f612]) ).
fof(f2579,plain,
( ~ ssItem(sK71)
| ~ ssList(nil)
| spl72_33 ),
inference(resolution,[],[f2573,f567]) ).
fof(f567,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f179]) ).
fof(f179,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
fof(f2573,plain,
( ~ ssList(cons(sK71,nil))
| spl72_33 ),
inference(avatar_component_clause,[],[f2571]) ).
fof(f2578,plain,
( ~ spl72_33
| spl72_34 ),
inference(avatar_split_clause,[],[f2569,f2575,f2571]) ).
fof(f2569,plain,
( ssList(cons(sK71,sK20))
| ~ ssList(cons(sK71,nil)) ),
inference(subsumption_resolution,[],[f2562,f386]) ).
fof(f2562,plain,
( ssList(cons(sK71,sK20))
| ~ ssList(sK20)
| ~ ssList(cons(sK71,nil)) ),
inference(superposition,[],[f577,f2340]) ).
fof(f2509,plain,
spl72_31,
inference(avatar_contradiction_clause,[],[f2508]) ).
fof(f2508,plain,
( $false
| spl72_31 ),
inference(subsumption_resolution,[],[f2507,f405]) ).
fof(f2507,plain,
( ~ ssList(nil)
| spl72_31 ),
inference(subsumption_resolution,[],[f2506,f611]) ).
fof(f2506,plain,
( ~ ssItem(sK70)
| ~ ssList(nil)
| spl72_31 ),
inference(resolution,[],[f2500,f567]) ).
fof(f2500,plain,
( ~ ssList(cons(sK70,nil))
| spl72_31 ),
inference(avatar_component_clause,[],[f2498]) ).
fof(f2505,plain,
( ~ spl72_31
| spl72_32 ),
inference(avatar_split_clause,[],[f2496,f2502,f2498]) ).
fof(f2496,plain,
( ssList(cons(sK70,sK20))
| ~ ssList(cons(sK70,nil)) ),
inference(subsumption_resolution,[],[f2490,f386]) ).
fof(f2490,plain,
( ssList(cons(sK70,sK20))
| ~ ssList(sK20)
| ~ ssList(cons(sK70,nil)) ),
inference(superposition,[],[f577,f2339]) ).
fof(f2456,plain,
spl72_29,
inference(avatar_contradiction_clause,[],[f2455]) ).
fof(f2455,plain,
( $false
| spl72_29 ),
inference(subsumption_resolution,[],[f2454,f405]) ).
fof(f2454,plain,
( ~ ssList(nil)
| spl72_29 ),
inference(subsumption_resolution,[],[f2453,f392]) ).
fof(f2453,plain,
( ~ ssItem(sK24)
| ~ ssList(nil)
| spl72_29 ),
inference(resolution,[],[f2447,f567]) ).
fof(f2447,plain,
( ~ ssList(cons(sK24,nil))
| spl72_29 ),
inference(avatar_component_clause,[],[f2445]) ).
fof(f2452,plain,
( ~ spl72_29
| spl72_30 ),
inference(avatar_split_clause,[],[f2415,f2449,f2445]) ).
fof(f2415,plain,
( ssList(cons(sK24,sK20))
| ~ ssList(cons(sK24,nil)) ),
inference(subsumption_resolution,[],[f2409,f386]) ).
fof(f2409,plain,
( ssList(cons(sK24,sK20))
| ~ ssList(sK20)
| ~ ssList(cons(sK24,nil)) ),
inference(superposition,[],[f577,f2318]) ).
fof(f1985,plain,
( ~ spl72_2
| ~ spl72_3
| ~ spl72_7
| ~ spl72_15
| ~ spl72_22
| spl72_26 ),
inference(avatar_contradiction_clause,[],[f1984]) ).
fof(f1984,plain,
( $false
| ~ spl72_2
| ~ spl72_3
| ~ spl72_7
| ~ spl72_15
| ~ spl72_22
| spl72_26 ),
inference(subsumption_resolution,[],[f1983,f1926]) ).
fof(f1926,plain,
( nil != sK25(sK20)
| spl72_26 ),
inference(avatar_component_clause,[],[f1925]) ).
fof(f1925,plain,
( spl72_26
<=> nil = sK25(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_26])]) ).
fof(f1983,plain,
( nil = sK25(sK20)
| ~ spl72_2
| ~ spl72_3
| ~ spl72_7
| ~ spl72_15
| ~ spl72_22 ),
inference(forward_demodulation,[],[f1982,f1838]) ).
fof(f1838,plain,
( nil = tl(sK20)
| ~ spl72_22 ),
inference(avatar_component_clause,[],[f1836]) ).
fof(f1836,plain,
( spl72_22
<=> nil = tl(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_22])]) ).
fof(f1982,plain,
( tl(sK20) = sK25(sK20)
| ~ spl72_2
| ~ spl72_3
| ~ spl72_7
| ~ spl72_15 ),
inference(forward_demodulation,[],[f1957,f1352]) ).
fof(f1352,plain,
( sK20 = cons(sK26(sK20),sK25(sK20))
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f1319,f804]) ).
fof(f804,plain,
( nil != sK20
| ~ spl72_2
| ~ spl72_3 ),
inference(global_subsumption,[],[f396,f395,f418,f419,f420,f421,f425,f424,f427,f426,f430,f429,f645,f431,f432,f433,f434,f435,f438,f436,f643,f440,f439,f443,f442,f448,f446,f451,f450,f456,f454,f460,f459,f458,f471,f474,f476,f478,f622,f480,f489,f623,f500,f642,f511,f626,f523,f627,f535,f628,f547,f629,f558,f630,f631,f632,f633,f570,f571,f572,f634,f575,f574,f573,f578,f579,f580,f581,f582,f583,f636,f587,f586,f637,f591,f590,f589,f638,f594,f593,f641,f597,f596,f599,f601,f600,f602,f603,f604,f605,f606,f607,f608,f609,f610,f386,f387,f388,f389,f392,f397,f398,f399,f400,f401,f402,f403,f404,f405,f611,f612,f390,f391,f393,f394,f613,f618,f620,f646,f647,f648,f491,f502,f514,f526,f538,f549,f560,f657,f654,f665,f406,f407,f408,f409,f461,f462,f463,f464,f465,f466,f485,f486,f487,f488,f495,f496,f497,f498,f499,f506,f507,f508,f509,f510,f518,f519,f520,f521,f522,f530,f531,f532,f533,f534,f542,f543,f544,f545,f546,f553,f554,f555,f556,f557,f649,f410,f411,f412,f413,f414,f415,f416,f482,f492,f503,f515,f527,f539,f540,f550,f551,f667,f668,f669,f670,f671,f672,f673,f674,f383,f675,f449,f457,f467,f705,f706,f690,f691,f692,f693,f694,f695,f696,f697,f698,f699,f700,f701,f702,f703,f704,f681,f682,f468,f732,f733,f712,f713,f714,f715,f716,f717,f718,f719,f720,f721,f722,f723,f724,f725,f726,f727,f728,f729,f730,f731,f708,f709,f479,f490,f501,f512,f513,f524,f525,f536,f537,f548,f559,f385,f735,f445,f453,f469,f738,f739,f470,f472,f473,f740,f741,f475,f477,f742,f743,f561,f563,f565,f567,f759,f760,f577,f761,f762,f568,f569,f644,f685,f686,f687,f688,f689,f384,f769,f771,f772,f773,f774,f775,f776,f781,f782,f784,f785,f770,f788,f798,f799,f417,f800,f801,f802,f803,f783]) ).
fof(f783,plain,
( nil != sK20
| ~ ssItem(sK19(sK21,nil))
| ~ spl72_2 ),
inference(inner_rewriting,[],[f782]) ).
fof(f803,plain,
( totalorderedP(sK20)
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f776,f788]) ).
fof(f802,plain,
( strictorderedP(sK20)
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f775,f788]) ).
fof(f801,plain,
( strictorderP(sK20)
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f774,f788]) ).
fof(f800,plain,
( totalorderP(sK20)
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f773,f788]) ).
fof(f417,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0] :
( ! [X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f112]) ).
fof(f112,plain,
! [X0] :
( ! [X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f94]) ).
fof(f94,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( gt(X0,X1)
=> ~ gt(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax94) ).
fof(f799,plain,
( cyclefreeP(sK20)
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f772,f788]) ).
fof(f798,plain,
( duplicatefreeP(sK20)
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f771,f788]) ).
fof(f770,plain,
( equalelemsP(sK20)
| ~ ssItem(sK19(sK21,sK20))
| ~ spl72_2 ),
inference(superposition,[],[f410,f769]) ).
fof(f785,plain,
( nil != sK20
| ~ ssItem(sK19(sK21,nil))
| ~ spl72_2 ),
inference(inner_rewriting,[],[f784]) ).
fof(f784,plain,
( nil != sK20
| ~ ssItem(sK19(sK21,sK20))
| ~ spl72_2 ),
inference(subsumption_resolution,[],[f779,f405]) ).
fof(f779,plain,
( nil != sK20
| ~ ssItem(sK19(sK21,sK20))
| ~ ssList(nil)
| ~ spl72_2 ),
inference(superposition,[],[f568,f769]) ).
fof(f782,plain,
( nil != sK20
| ~ ssItem(sK19(sK21,sK20))
| ~ spl72_2 ),
inference(subsumption_resolution,[],[f778,f405]) ).
fof(f778,plain,
( nil != sK20
| ~ ssItem(sK19(sK21,sK20))
| ~ ssList(nil)
| ~ spl72_2 ),
inference(superposition,[],[f569,f769]) ).
fof(f781,plain,
( memberP(sK20,sK19(sK21,sK20))
| ~ ssItem(sK19(sK21,sK20))
| ~ spl72_2 ),
inference(subsumption_resolution,[],[f777,f405]) ).
fof(f777,plain,
( memberP(sK20,sK19(sK21,sK20))
| ~ ssList(nil)
| ~ ssItem(sK19(sK21,sK20))
| ~ spl72_2 ),
inference(superposition,[],[f644,f769]) ).
fof(f776,plain,
( totalorderedP(sK20)
| ~ ssItem(sK19(sK21,sK20))
| ~ spl72_2 ),
inference(superposition,[],[f416,f769]) ).
fof(f775,plain,
( strictorderedP(sK20)
| ~ ssItem(sK19(sK21,sK20))
| ~ spl72_2 ),
inference(superposition,[],[f415,f769]) ).
fof(f774,plain,
( strictorderP(sK20)
| ~ ssItem(sK19(sK21,sK20))
| ~ spl72_2 ),
inference(superposition,[],[f414,f769]) ).
fof(f773,plain,
( totalorderP(sK20)
| ~ ssItem(sK19(sK21,sK20))
| ~ spl72_2 ),
inference(superposition,[],[f413,f769]) ).
fof(f772,plain,
( cyclefreeP(sK20)
| ~ ssItem(sK19(sK21,sK20))
| ~ spl72_2 ),
inference(superposition,[],[f412,f769]) ).
fof(f771,plain,
( duplicatefreeP(sK20)
| ~ ssItem(sK19(sK21,sK20))
| ~ spl72_2 ),
inference(superposition,[],[f411,f769]) ).
fof(f769,plain,
( sK20 = cons(sK19(sK21,sK20),nil)
| ~ spl72_2 ),
inference(resolution,[],[f384,f665]) ).
fof(f689,plain,
! [X0] :
( sP7(X0)
| sK38(X0) = app(sK38(X0),nil) ),
inference(resolution,[],[f467,f499]) ).
fof(f688,plain,
! [X0] :
( sP7(X0)
| sK37(X0) = app(sK37(X0),nil) ),
inference(resolution,[],[f467,f498]) ).
fof(f687,plain,
! [X0] :
( sP7(X0)
| sK36(X0) = app(sK36(X0),nil) ),
inference(resolution,[],[f467,f497]) ).
fof(f686,plain,
! [X0] :
( sP5(X0)
| sK33(X0) = app(sK33(X0),nil) ),
inference(resolution,[],[f467,f488]) ).
fof(f685,plain,
! [X0] :
( sP5(X0)
| sK32(X0) = app(sK32(X0),nil) ),
inference(resolution,[],[f467,f487]) ).
fof(f644,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f616]) ).
fof(f616,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f437]) ).
fof(f437,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| X0 != X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f270]) ).
fof(f569,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f181]) ).
fof(f181,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
fof(f568,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f180]) ).
fof(f180,plain,
! [X0] :
( ! [X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).
fof(f762,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X1,X0) = app(app(X1,X0),nil) ),
inference(resolution,[],[f577,f467]) ).
fof(f761,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X1,X0) = app(nil,app(X1,X0)) ),
inference(resolution,[],[f577,f468]) ).
fof(f760,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) = app(cons(X0,X1),nil) ),
inference(resolution,[],[f567,f467]) ).
fof(f759,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) = app(nil,cons(X0,X1)) ),
inference(resolution,[],[f567,f468]) ).
fof(f565,plain,
! [X0] :
( ~ frontsegP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f358]) ).
fof(f358,plain,
! [X0] :
( ( ( frontsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ frontsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f178]) ).
fof(f178,plain,
! [X0] :
( ( frontsegP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0] :
( ssList(X0)
=> ( frontsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46) ).
fof(f563,plain,
! [X0] :
( ~ rearsegP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f357,plain,
! [X0] :
( ( ( rearsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ rearsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f177]) ).
fof(f177,plain,
! [X0] :
( ( rearsegP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0] :
( ssList(X0)
=> ( rearsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).
fof(f561,plain,
! [X0] :
( ~ segmentP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f356]) ).
fof(f356,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f176]) ).
fof(f176,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
fof(f743,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| sK28(X0) = app(sK28(X0),nil) ),
inference(resolution,[],[f477,f467]) ).
fof(f742,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| sK28(X0) = app(nil,sK28(X0)) ),
inference(resolution,[],[f477,f468]) ).
fof(f477,plain,
! [X0] :
( ssList(sK28(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f289]) ).
fof(f289,plain,
! [X0] :
( ( tl(X0) = sK28(X0)
& ssList(sK28(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f160,f288]) ).
fof(f288,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
=> ( tl(X0) = sK28(X0)
& ssList(sK28(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f160,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f159]) ).
fof(f159,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax76) ).
fof(f475,plain,
! [X0] :
( ssItem(sK27(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f287]) ).
fof(f287,plain,
! [X0] :
( ( hd(X0) = sK27(X0)
& ssItem(sK27(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f158,f286]) ).
fof(f286,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
=> ( hd(X0) = sK27(X0)
& ssItem(sK27(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f158,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f157]) ).
fof(f157,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax75) ).
fof(f741,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| tl(X0) = app(tl(X0),nil) ),
inference(resolution,[],[f473,f467]) ).
fof(f740,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| tl(X0) = app(nil,tl(X0)) ),
inference(resolution,[],[f473,f468]) ).
fof(f473,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f153]) ).
fof(f153,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
fof(f472,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f152,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f151]) ).
fof(f151,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
fof(f470,plain,
! [X0] :
( ssItem(sK26(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f285]) ).
fof(f285,plain,
! [X0] :
( ( cons(sK26(X0),sK25(X0)) = X0
& ssItem(sK26(X0))
& ssList(sK25(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26])],[f150,f284,f283]) ).
fof(f283,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
=> ( ? [X2] :
( cons(X2,sK25(X0)) = X0
& ssItem(X2) )
& ssList(sK25(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f284,plain,
! [X0] :
( ? [X2] :
( cons(X2,sK25(X0)) = X0
& ssItem(X2) )
=> ( cons(sK26(X0),sK25(X0)) = X0
& ssItem(sK26(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f150,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f149]) ).
fof(f149,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ssList(X0)
=> ( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).
fof(f739,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| sK25(X0) = app(sK25(X0),nil) ),
inference(resolution,[],[f469,f467]) ).
fof(f738,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| sK25(X0) = app(nil,sK25(X0)) ),
inference(resolution,[],[f469,f468]) ).
fof(f469,plain,
! [X0] :
( ssList(sK25(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f285]) ).
fof(f453,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| nil = X0
| strictorderedP(X0) ),
inference(cnf_transformation,[],[f280]) ).
fof(f280,plain,
! [X0,X1] :
( ( sP3(X0,X1)
| ( ( ~ lt(X1,hd(X0))
| ~ strictorderedP(X0)
| nil = X0 )
& nil != X0 ) )
& ( ( lt(X1,hd(X0))
& strictorderedP(X0)
& nil != X0 )
| nil = X0
| ~ sP3(X0,X1) ) ),
inference(rectify,[],[f279]) ).
fof(f279,plain,
! [X1,X0] :
( ( sP3(X1,X0)
| ( ( ~ lt(X0,hd(X1))
| ~ strictorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP3(X1,X0) ) ),
inference(flattening,[],[f278]) ).
fof(f278,plain,
! [X1,X0] :
( ( sP3(X1,X0)
| ( ( ~ lt(X0,hd(X1))
| ~ strictorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP3(X1,X0) ) ),
inference(nnf_transformation,[],[f229]) ).
fof(f229,plain,
! [X1,X0] :
( sP3(X1,X0)
<=> ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f445,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| nil = X0
| totalorderedP(X0) ),
inference(cnf_transformation,[],[f276]) ).
fof(f276,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ( ( ~ leq(X1,hd(X0))
| ~ totalorderedP(X0)
| nil = X0 )
& nil != X0 ) )
& ( ( leq(X1,hd(X0))
& totalorderedP(X0)
& nil != X0 )
| nil = X0
| ~ sP1(X0,X1) ) ),
inference(rectify,[],[f275]) ).
fof(f275,plain,
! [X1,X0] :
( ( sP1(X1,X0)
| ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP1(X1,X0) ) ),
inference(flattening,[],[f274]) ).
fof(f274,plain,
! [X1,X0] :
( ( sP1(X1,X0)
| ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP1(X1,X0) ) ),
inference(nnf_transformation,[],[f226]) ).
fof(f226,plain,
! [X1,X0] :
( sP1(X1,X0)
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f735,plain,
! [X0] : ~ sP0(nil,X0),
inference(subsumption_resolution,[],[f734,f383]) ).
fof(f734,plain,
! [X0] :
( ~ sP0(nil,X0)
| ~ ssItem(sK19(nil,X0)) ),
inference(resolution,[],[f385,f406]) ).
fof(f559,plain,
! [X0] :
( ~ lt(sK59(X0),sK60(X0))
| sP17(X0) ),
inference(cnf_transformation,[],[f355]) ).
fof(f355,plain,
! [X0] :
( ( sP17(X0)
| ( ~ lt(sK59(X0),sK60(X0))
& app(app(sK61(X0),cons(sK59(X0),sK62(X0))),cons(sK60(X0),sK63(X0))) = X0
& ssList(sK63(X0))
& ssList(sK62(X0))
& ssList(sK61(X0))
& ssItem(sK60(X0))
& ssItem(sK59(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP17(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK59,sK60,sK61,sK62,sK63])],[f349,f354,f353,f352,f351,f350]) ).
fof(f350,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK59(X0),X2)
& app(app(X3,cons(sK59(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK59(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f351,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK59(X0),X2)
& app(app(X3,cons(sK59(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK59(X0),sK60(X0))
& app(app(X3,cons(sK59(X0),X4)),cons(sK60(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK60(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f352,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK59(X0),sK60(X0))
& app(app(X3,cons(sK59(X0),X4)),cons(sK60(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ lt(sK59(X0),sK60(X0))
& app(app(sK61(X0),cons(sK59(X0),X4)),cons(sK60(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK61(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f353,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK59(X0),sK60(X0))
& app(app(sK61(X0),cons(sK59(X0),X4)),cons(sK60(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ lt(sK59(X0),sK60(X0))
& app(app(sK61(X0),cons(sK59(X0),sK62(X0))),cons(sK60(X0),X5)) = X0
& ssList(X5) )
& ssList(sK62(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f354,plain,
! [X0] :
( ? [X5] :
( ~ lt(sK59(X0),sK60(X0))
& app(app(sK61(X0),cons(sK59(X0),sK62(X0))),cons(sK60(X0),X5)) = X0
& ssList(X5) )
=> ( ~ lt(sK59(X0),sK60(X0))
& app(app(sK61(X0),cons(sK59(X0),sK62(X0))),cons(sK60(X0),sK63(X0))) = X0
& ssList(sK63(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f349,plain,
! [X0] :
( ( sP17(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP17(X0) ) ),
inference(rectify,[],[f348]) ).
fof(f348,plain,
! [X0] :
( ( sP17(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP17(X0) ) ),
inference(nnf_transformation,[],[f250]) ).
fof(f250,plain,
! [X0] :
( sP17(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
fof(f548,plain,
! [X0] :
( ~ leq(sK54(X0),sK55(X0))
| sP15(X0) ),
inference(cnf_transformation,[],[f346]) ).
fof(f346,plain,
! [X0] :
( ( sP15(X0)
| ( ~ leq(sK54(X0),sK55(X0))
& app(app(sK56(X0),cons(sK54(X0),sK57(X0))),cons(sK55(X0),sK58(X0))) = X0
& ssList(sK58(X0))
& ssList(sK57(X0))
& ssList(sK56(X0))
& ssItem(sK55(X0))
& ssItem(sK54(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP15(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK54,sK55,sK56,sK57,sK58])],[f340,f345,f344,f343,f342,f341]) ).
fof(f341,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK54(X0),X2)
& app(app(X3,cons(sK54(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK54(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f342,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK54(X0),X2)
& app(app(X3,cons(sK54(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK54(X0),sK55(X0))
& app(app(X3,cons(sK54(X0),X4)),cons(sK55(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK55(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f343,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK54(X0),sK55(X0))
& app(app(X3,cons(sK54(X0),X4)),cons(sK55(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ leq(sK54(X0),sK55(X0))
& app(app(sK56(X0),cons(sK54(X0),X4)),cons(sK55(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK56(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f344,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK54(X0),sK55(X0))
& app(app(sK56(X0),cons(sK54(X0),X4)),cons(sK55(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ leq(sK54(X0),sK55(X0))
& app(app(sK56(X0),cons(sK54(X0),sK57(X0))),cons(sK55(X0),X5)) = X0
& ssList(X5) )
& ssList(sK57(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
! [X0] :
( ? [X5] :
( ~ leq(sK54(X0),sK55(X0))
& app(app(sK56(X0),cons(sK54(X0),sK57(X0))),cons(sK55(X0),X5)) = X0
& ssList(X5) )
=> ( ~ leq(sK54(X0),sK55(X0))
& app(app(sK56(X0),cons(sK54(X0),sK57(X0))),cons(sK55(X0),sK58(X0))) = X0
& ssList(sK58(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f340,plain,
! [X0] :
( ( sP15(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP15(X0) ) ),
inference(rectify,[],[f339]) ).
fof(f339,plain,
! [X0] :
( ( sP15(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP15(X0) ) ),
inference(nnf_transformation,[],[f247]) ).
fof(f247,plain,
! [X0] :
( sP15(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
fof(f537,plain,
! [X0] :
( leq(sK50(X0),sK49(X0))
| sP13(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f337,plain,
! [X0] :
( ( sP13(X0)
| ( leq(sK50(X0),sK49(X0))
& leq(sK49(X0),sK50(X0))
& app(app(sK51(X0),cons(sK49(X0),sK52(X0))),cons(sK50(X0),sK53(X0))) = X0
& ssList(sK53(X0))
& ssList(sK52(X0))
& ssList(sK51(X0))
& ssItem(sK50(X0))
& ssItem(sK49(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP13(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK49,sK50,sK51,sK52,sK53])],[f331,f336,f335,f334,f333,f332]) ).
fof(f332,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,X1)
& leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,sK49(X0))
& leq(sK49(X0),X2)
& app(app(X3,cons(sK49(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK49(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f333,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,sK49(X0))
& leq(sK49(X0),X2)
& app(app(X3,cons(sK49(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(sK50(X0),sK49(X0))
& leq(sK49(X0),sK50(X0))
& app(app(X3,cons(sK49(X0),X4)),cons(sK50(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK50(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f334,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(sK50(X0),sK49(X0))
& leq(sK49(X0),sK50(X0))
& app(app(X3,cons(sK49(X0),X4)),cons(sK50(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( leq(sK50(X0),sK49(X0))
& leq(sK49(X0),sK50(X0))
& app(app(sK51(X0),cons(sK49(X0),X4)),cons(sK50(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK51(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f335,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( leq(sK50(X0),sK49(X0))
& leq(sK49(X0),sK50(X0))
& app(app(sK51(X0),cons(sK49(X0),X4)),cons(sK50(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( leq(sK50(X0),sK49(X0))
& leq(sK49(X0),sK50(X0))
& app(app(sK51(X0),cons(sK49(X0),sK52(X0))),cons(sK50(X0),X5)) = X0
& ssList(X5) )
& ssList(sK52(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f336,plain,
! [X0] :
( ? [X5] :
( leq(sK50(X0),sK49(X0))
& leq(sK49(X0),sK50(X0))
& app(app(sK51(X0),cons(sK49(X0),sK52(X0))),cons(sK50(X0),X5)) = X0
& ssList(X5) )
=> ( leq(sK50(X0),sK49(X0))
& leq(sK49(X0),sK50(X0))
& app(app(sK51(X0),cons(sK49(X0),sK52(X0))),cons(sK50(X0),sK53(X0))) = X0
& ssList(sK53(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f331,plain,
! [X0] :
( ( sP13(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,X1)
& leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP13(X0) ) ),
inference(rectify,[],[f330]) ).
fof(f330,plain,
! [X0] :
( ( sP13(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,X1)
& leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP13(X0) ) ),
inference(nnf_transformation,[],[f244]) ).
fof(f244,plain,
! [X0] :
( sP13(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f536,plain,
! [X0] :
( leq(sK49(X0),sK50(X0))
| sP13(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f525,plain,
! [X0] :
( ~ lt(sK45(X0),sK44(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f328,plain,
! [X0] :
( ( sP11(X0)
| ( ~ lt(sK45(X0),sK44(X0))
& ~ lt(sK44(X0),sK45(X0))
& app(app(sK46(X0),cons(sK44(X0),sK47(X0))),cons(sK45(X0),sK48(X0))) = X0
& ssList(sK48(X0))
& ssList(sK47(X0))
& ssList(sK46(X0))
& ssItem(sK45(X0))
& ssItem(sK44(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X7,X6)
| lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP11(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK44,sK45,sK46,sK47,sK48])],[f322,f327,f326,f325,f324,f323]) ).
fof(f323,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,X1)
& ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,sK44(X0))
& ~ lt(sK44(X0),X2)
& app(app(X3,cons(sK44(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK44(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f324,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,sK44(X0))
& ~ lt(sK44(X0),X2)
& app(app(X3,cons(sK44(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK45(X0),sK44(X0))
& ~ lt(sK44(X0),sK45(X0))
& app(app(X3,cons(sK44(X0),X4)),cons(sK45(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK45(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f325,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK45(X0),sK44(X0))
& ~ lt(sK44(X0),sK45(X0))
& app(app(X3,cons(sK44(X0),X4)),cons(sK45(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ lt(sK45(X0),sK44(X0))
& ~ lt(sK44(X0),sK45(X0))
& app(app(sK46(X0),cons(sK44(X0),X4)),cons(sK45(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK46(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f326,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK45(X0),sK44(X0))
& ~ lt(sK44(X0),sK45(X0))
& app(app(sK46(X0),cons(sK44(X0),X4)),cons(sK45(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ lt(sK45(X0),sK44(X0))
& ~ lt(sK44(X0),sK45(X0))
& app(app(sK46(X0),cons(sK44(X0),sK47(X0))),cons(sK45(X0),X5)) = X0
& ssList(X5) )
& ssList(sK47(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f327,plain,
! [X0] :
( ? [X5] :
( ~ lt(sK45(X0),sK44(X0))
& ~ lt(sK44(X0),sK45(X0))
& app(app(sK46(X0),cons(sK44(X0),sK47(X0))),cons(sK45(X0),X5)) = X0
& ssList(X5) )
=> ( ~ lt(sK45(X0),sK44(X0))
& ~ lt(sK44(X0),sK45(X0))
& app(app(sK46(X0),cons(sK44(X0),sK47(X0))),cons(sK45(X0),sK48(X0))) = X0
& ssList(sK48(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f322,plain,
! [X0] :
( ( sP11(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,X1)
& ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X7,X6)
| lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP11(X0) ) ),
inference(rectify,[],[f321]) ).
fof(f321,plain,
! [X0] :
( ( sP11(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,X1)
& ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP11(X0) ) ),
inference(nnf_transformation,[],[f241]) ).
fof(f241,plain,
! [X0] :
( sP11(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f524,plain,
! [X0] :
( ~ lt(sK44(X0),sK45(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f513,plain,
! [X0] :
( ~ leq(sK40(X0),sK39(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f319,plain,
! [X0] :
( ( sP9(X0)
| ( ~ leq(sK40(X0),sK39(X0))
& ~ leq(sK39(X0),sK40(X0))
& app(app(sK41(X0),cons(sK39(X0),sK42(X0))),cons(sK40(X0),sK43(X0))) = X0
& ssList(sK43(X0))
& ssList(sK42(X0))
& ssList(sK41(X0))
& ssItem(sK40(X0))
& ssItem(sK39(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X7,X6)
| leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP9(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK39,sK40,sK41,sK42,sK43])],[f313,f318,f317,f316,f315,f314]) ).
fof(f314,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,X1)
& ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,sK39(X0))
& ~ leq(sK39(X0),X2)
& app(app(X3,cons(sK39(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK39(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f315,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,sK39(X0))
& ~ leq(sK39(X0),X2)
& app(app(X3,cons(sK39(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK40(X0),sK39(X0))
& ~ leq(sK39(X0),sK40(X0))
& app(app(X3,cons(sK39(X0),X4)),cons(sK40(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK40(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f316,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK40(X0),sK39(X0))
& ~ leq(sK39(X0),sK40(X0))
& app(app(X3,cons(sK39(X0),X4)),cons(sK40(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ leq(sK40(X0),sK39(X0))
& ~ leq(sK39(X0),sK40(X0))
& app(app(sK41(X0),cons(sK39(X0),X4)),cons(sK40(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK41(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f317,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK40(X0),sK39(X0))
& ~ leq(sK39(X0),sK40(X0))
& app(app(sK41(X0),cons(sK39(X0),X4)),cons(sK40(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ leq(sK40(X0),sK39(X0))
& ~ leq(sK39(X0),sK40(X0))
& app(app(sK41(X0),cons(sK39(X0),sK42(X0))),cons(sK40(X0),X5)) = X0
& ssList(X5) )
& ssList(sK42(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f318,plain,
! [X0] :
( ? [X5] :
( ~ leq(sK40(X0),sK39(X0))
& ~ leq(sK39(X0),sK40(X0))
& app(app(sK41(X0),cons(sK39(X0),sK42(X0))),cons(sK40(X0),X5)) = X0
& ssList(X5) )
=> ( ~ leq(sK40(X0),sK39(X0))
& ~ leq(sK39(X0),sK40(X0))
& app(app(sK41(X0),cons(sK39(X0),sK42(X0))),cons(sK40(X0),sK43(X0))) = X0
& ssList(sK43(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f313,plain,
! [X0] :
( ( sP9(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,X1)
& ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X7,X6)
| leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP9(X0) ) ),
inference(rectify,[],[f312]) ).
fof(f312,plain,
! [X0] :
( ( sP9(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,X1)
& ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP9(X0) ) ),
inference(nnf_transformation,[],[f238]) ).
fof(f238,plain,
! [X0] :
( sP9(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f512,plain,
! [X0] :
( ~ leq(sK39(X0),sK40(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f501,plain,
! [X0] :
( sP7(X0)
| sK34(X0) = sK35(X0) ),
inference(cnf_transformation,[],[f310]) ).
fof(f310,plain,
! [X0] :
( ( sP7(X0)
| ( sK34(X0) = sK35(X0)
& app(app(sK36(X0),cons(sK34(X0),sK37(X0))),cons(sK35(X0),sK38(X0))) = X0
& ssList(sK38(X0))
& ssList(sK37(X0))
& ssList(sK36(X0))
& ssItem(sK35(X0))
& ssItem(sK34(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( X6 != X7
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP7(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK34,sK35,sK36,sK37,sK38])],[f304,f309,f308,f307,f306,f305]) ).
fof(f305,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( X1 = X2
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK34(X0) = X2
& app(app(X3,cons(sK34(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK34(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f306,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK34(X0) = X2
& app(app(X3,cons(sK34(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK34(X0) = sK35(X0)
& app(app(X3,cons(sK34(X0),X4)),cons(sK35(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK35(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f307,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK34(X0) = sK35(X0)
& app(app(X3,cons(sK34(X0),X4)),cons(sK35(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( sK34(X0) = sK35(X0)
& app(app(sK36(X0),cons(sK34(X0),X4)),cons(sK35(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK36(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f308,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( sK34(X0) = sK35(X0)
& app(app(sK36(X0),cons(sK34(X0),X4)),cons(sK35(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( sK34(X0) = sK35(X0)
& app(app(sK36(X0),cons(sK34(X0),sK37(X0))),cons(sK35(X0),X5)) = X0
& ssList(X5) )
& ssList(sK37(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f309,plain,
! [X0] :
( ? [X5] :
( sK34(X0) = sK35(X0)
& app(app(sK36(X0),cons(sK34(X0),sK37(X0))),cons(sK35(X0),X5)) = X0
& ssList(X5) )
=> ( sK34(X0) = sK35(X0)
& app(app(sK36(X0),cons(sK34(X0),sK37(X0))),cons(sK35(X0),sK38(X0))) = X0
& ssList(sK38(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f304,plain,
! [X0] :
( ( sP7(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( X1 = X2
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( X6 != X7
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP7(X0) ) ),
inference(rectify,[],[f303]) ).
fof(f303,plain,
! [X0] :
( ( sP7(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( X1 = X2
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP7(X0) ) ),
inference(nnf_transformation,[],[f235]) ).
fof(f235,plain,
! [X0] :
( sP7(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f490,plain,
! [X0] :
( sK30(X0) != sK31(X0)
| sP5(X0) ),
inference(cnf_transformation,[],[f301]) ).
fof(f301,plain,
! [X0] :
( ( sP5(X0)
| ( sK30(X0) != sK31(X0)
& app(sK32(X0),cons(sK30(X0),cons(sK31(X0),sK33(X0)))) = X0
& ssList(sK33(X0))
& ssList(sK32(X0))
& ssItem(sK31(X0))
& ssItem(sK30(X0)) ) )
& ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( X5 = X6
| app(X7,cons(X5,cons(X6,X8))) != X0
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
| ~ ssItem(X5) )
| ~ sP5(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30,sK31,sK32,sK33])],[f296,f300,f299,f298,f297]) ).
fof(f297,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( X1 != X2
& app(X3,cons(X1,cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( sK30(X0) != X2
& app(X3,cons(sK30(X0),cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK30(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f298,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( sK30(X0) != X2
& app(X3,cons(sK30(X0),cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( sK30(X0) != sK31(X0)
& app(X3,cons(sK30(X0),cons(sK31(X0),X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(sK31(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f299,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( sK30(X0) != sK31(X0)
& app(X3,cons(sK30(X0),cons(sK31(X0),X4))) = X0
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( sK30(X0) != sK31(X0)
& app(sK32(X0),cons(sK30(X0),cons(sK31(X0),X4))) = X0
& ssList(X4) )
& ssList(sK32(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f300,plain,
! [X0] :
( ? [X4] :
( sK30(X0) != sK31(X0)
& app(sK32(X0),cons(sK30(X0),cons(sK31(X0),X4))) = X0
& ssList(X4) )
=> ( sK30(X0) != sK31(X0)
& app(sK32(X0),cons(sK30(X0),cons(sK31(X0),sK33(X0)))) = X0
& ssList(sK33(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f296,plain,
! [X0] :
( ( sP5(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( X1 != X2
& app(X3,cons(X1,cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( X5 = X6
| app(X7,cons(X5,cons(X6,X8))) != X0
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
| ~ ssItem(X5) )
| ~ sP5(X0) ) ),
inference(rectify,[],[f295]) ).
fof(f295,plain,
! [X0] :
( ( sP5(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( X1 != X2
& app(X3,cons(X1,cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP5(X0) ) ),
inference(nnf_transformation,[],[f232]) ).
fof(f232,plain,
! [X0] :
( sP5(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f479,plain,
! [X0] :
( ssItem(sK29(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f293]) ).
fof(f293,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ( cons(sK29(X0),nil) = X0
& ssItem(sK29(X0)) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f291,f292]) ).
fof(f292,plain,
! [X0] :
( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
=> ( cons(sK29(X0),nil) = X0
& ssItem(sK29(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f291,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f290]) ).
fof(f290,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f161]) ).
fof(f161,plain,
! [X0] :
( ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f709,plain,
sK21 = app(nil,sK21),
inference(resolution,[],[f468,f387]) ).
fof(f708,plain,
sK20 = app(nil,sK20),
inference(resolution,[],[f468,f386]) ).
fof(f731,plain,
! [X0] :
( sP17(X0)
| sK63(X0) = app(nil,sK63(X0)) ),
inference(resolution,[],[f468,f557]) ).
fof(f730,plain,
! [X0] :
( sP17(X0)
| sK62(X0) = app(nil,sK62(X0)) ),
inference(resolution,[],[f468,f556]) ).
fof(f729,plain,
! [X0] :
( sP17(X0)
| sK61(X0) = app(nil,sK61(X0)) ),
inference(resolution,[],[f468,f555]) ).
fof(f728,plain,
! [X0] :
( sP15(X0)
| sK58(X0) = app(nil,sK58(X0)) ),
inference(resolution,[],[f468,f546]) ).
fof(f727,plain,
! [X0] :
( sP15(X0)
| sK57(X0) = app(nil,sK57(X0)) ),
inference(resolution,[],[f468,f545]) ).
fof(f726,plain,
! [X0] :
( sP15(X0)
| sK56(X0) = app(nil,sK56(X0)) ),
inference(resolution,[],[f468,f544]) ).
fof(f725,plain,
! [X0] :
( sP13(X0)
| sK53(X0) = app(nil,sK53(X0)) ),
inference(resolution,[],[f468,f534]) ).
fof(f724,plain,
! [X0] :
( sP13(X0)
| sK52(X0) = app(nil,sK52(X0)) ),
inference(resolution,[],[f468,f533]) ).
fof(f723,plain,
! [X0] :
( sP13(X0)
| sK51(X0) = app(nil,sK51(X0)) ),
inference(resolution,[],[f468,f532]) ).
fof(f722,plain,
! [X0] :
( sP11(X0)
| sK48(X0) = app(nil,sK48(X0)) ),
inference(resolution,[],[f468,f522]) ).
fof(f721,plain,
! [X0] :
( sP11(X0)
| sK47(X0) = app(nil,sK47(X0)) ),
inference(resolution,[],[f468,f521]) ).
fof(f720,plain,
! [X0] :
( sP11(X0)
| sK46(X0) = app(nil,sK46(X0)) ),
inference(resolution,[],[f468,f520]) ).
fof(f719,plain,
! [X0] :
( sP9(X0)
| sK43(X0) = app(nil,sK43(X0)) ),
inference(resolution,[],[f468,f510]) ).
fof(f718,plain,
! [X0] :
( sP9(X0)
| sK42(X0) = app(nil,sK42(X0)) ),
inference(resolution,[],[f468,f509]) ).
fof(f717,plain,
! [X0] :
( sP9(X0)
| sK41(X0) = app(nil,sK41(X0)) ),
inference(resolution,[],[f468,f508]) ).
fof(f716,plain,
! [X0] :
( sP7(X0)
| sK38(X0) = app(nil,sK38(X0)) ),
inference(resolution,[],[f468,f499]) ).
fof(f715,plain,
! [X0] :
( sP7(X0)
| sK37(X0) = app(nil,sK37(X0)) ),
inference(resolution,[],[f468,f498]) ).
fof(f714,plain,
! [X0] :
( sP7(X0)
| sK36(X0) = app(nil,sK36(X0)) ),
inference(resolution,[],[f468,f497]) ).
fof(f713,plain,
! [X0] :
( sP5(X0)
| sK33(X0) = app(nil,sK33(X0)) ),
inference(resolution,[],[f468,f488]) ).
fof(f712,plain,
! [X0] :
( sP5(X0)
| sK32(X0) = app(nil,sK32(X0)) ),
inference(resolution,[],[f468,f487]) ).
fof(f733,plain,
sK21 = app(nil,sK21),
inference(forward_demodulation,[],[f711,f390]) ).
fof(f711,plain,
sK23 = app(nil,sK23),
inference(resolution,[],[f468,f389]) ).
fof(f732,plain,
sK20 = app(nil,sK20),
inference(forward_demodulation,[],[f710,f391]) ).
fof(f710,plain,
sK22 = app(nil,sK22),
inference(resolution,[],[f468,f388]) ).
fof(f468,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
fof(f682,plain,
sK21 = app(sK21,nil),
inference(resolution,[],[f467,f387]) ).
fof(f681,plain,
sK20 = app(sK20,nil),
inference(resolution,[],[f467,f386]) ).
fof(f704,plain,
! [X0] :
( sP17(X0)
| sK63(X0) = app(sK63(X0),nil) ),
inference(resolution,[],[f467,f557]) ).
fof(f703,plain,
! [X0] :
( sP17(X0)
| sK62(X0) = app(sK62(X0),nil) ),
inference(resolution,[],[f467,f556]) ).
fof(f702,plain,
! [X0] :
( sP17(X0)
| sK61(X0) = app(sK61(X0),nil) ),
inference(resolution,[],[f467,f555]) ).
fof(f701,plain,
! [X0] :
( sP15(X0)
| sK58(X0) = app(sK58(X0),nil) ),
inference(resolution,[],[f467,f546]) ).
fof(f700,plain,
! [X0] :
( sP15(X0)
| sK57(X0) = app(sK57(X0),nil) ),
inference(resolution,[],[f467,f545]) ).
fof(f699,plain,
! [X0] :
( sP15(X0)
| sK56(X0) = app(sK56(X0),nil) ),
inference(resolution,[],[f467,f544]) ).
fof(f698,plain,
! [X0] :
( sP13(X0)
| sK53(X0) = app(sK53(X0),nil) ),
inference(resolution,[],[f467,f534]) ).
fof(f697,plain,
! [X0] :
( sP13(X0)
| sK52(X0) = app(sK52(X0),nil) ),
inference(resolution,[],[f467,f533]) ).
fof(f696,plain,
! [X0] :
( sP13(X0)
| sK51(X0) = app(sK51(X0),nil) ),
inference(resolution,[],[f467,f532]) ).
fof(f695,plain,
! [X0] :
( sP11(X0)
| sK48(X0) = app(sK48(X0),nil) ),
inference(resolution,[],[f467,f522]) ).
fof(f694,plain,
! [X0] :
( sP11(X0)
| sK47(X0) = app(sK47(X0),nil) ),
inference(resolution,[],[f467,f521]) ).
fof(f693,plain,
! [X0] :
( sP11(X0)
| sK46(X0) = app(sK46(X0),nil) ),
inference(resolution,[],[f467,f520]) ).
fof(f692,plain,
! [X0] :
( sP9(X0)
| sK43(X0) = app(sK43(X0),nil) ),
inference(resolution,[],[f467,f510]) ).
fof(f691,plain,
! [X0] :
( sP9(X0)
| sK42(X0) = app(sK42(X0),nil) ),
inference(resolution,[],[f467,f509]) ).
fof(f690,plain,
! [X0] :
( sP9(X0)
| sK41(X0) = app(sK41(X0),nil) ),
inference(resolution,[],[f467,f508]) ).
fof(f706,plain,
sK21 = app(sK21,nil),
inference(forward_demodulation,[],[f684,f390]) ).
fof(f684,plain,
sK23 = app(sK23,nil),
inference(resolution,[],[f467,f389]) ).
fof(f705,plain,
sK20 = app(sK20,nil),
inference(forward_demodulation,[],[f683,f391]) ).
fof(f683,plain,
sK22 = app(sK22,nil),
inference(resolution,[],[f467,f388]) ).
fof(f467,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
fof(f457,plain,
! [X0,X1] :
( sP4(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f231]) ).
fof(f231,plain,
! [X0] :
( ! [X1] :
( sP4(X0,X1)
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(definition_folding,[],[f139,f230,f229]) ).
fof(f230,plain,
! [X0,X1] :
( ( strictorderedP(cons(X0,X1))
<=> sP3(X1,X0) )
| ~ sP4(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f139,plain,
! [X0] :
( ! [X1] :
( ( strictorderedP(cons(X0,X1))
<=> ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1 ) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ( strictorderedP(cons(X0,X1))
<=> ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax70) ).
fof(f449,plain,
! [X0,X1] :
( sP2(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f228]) ).
fof(f228,plain,
! [X0] :
( ! [X1] :
( sP2(X0,X1)
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(definition_folding,[],[f138,f227,f226]) ).
fof(f227,plain,
! [X0,X1] :
( ( totalorderedP(cons(X0,X1))
<=> sP1(X1,X0) )
| ~ sP2(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f138,plain,
! [X0] :
( ! [X1] :
( ( totalorderedP(cons(X0,X1))
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ( totalorderedP(cons(X0,X1))
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax67) ).
fof(f675,plain,
! [X0] :
( ~ sP17(X0)
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f551,f560]) ).
fof(f383,plain,
! [X0,X1] :
( ssItem(sK19(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f256]) ).
fof(f674,plain,
! [X0] :
( sP17(X0)
| ~ strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f550,f560]) ).
fof(f673,plain,
! [X0] :
( ~ sP15(X0)
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f540,f549]) ).
fof(f672,plain,
! [X0] :
( sP15(X0)
| ~ totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f539,f549]) ).
fof(f671,plain,
! [X0] :
( sP13(X0)
| ~ cyclefreeP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f527,f538]) ).
fof(f670,plain,
! [X0] :
( sP11(X0)
| ~ strictorderP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f515,f526]) ).
fof(f669,plain,
! [X0] :
( sP9(X0)
| ~ totalorderP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f503,f514]) ).
fof(f668,plain,
! [X0] :
( sP7(X0)
| ~ duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f492,f502]) ).
fof(f667,plain,
! [X0] :
( sP5(X0)
| ~ equalelemsP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f482,f491]) ).
fof(f551,plain,
! [X0] :
( ~ sP18(X0)
| ~ sP17(X0)
| strictorderedP(X0) ),
inference(cnf_transformation,[],[f347]) ).
fof(f347,plain,
! [X0] :
( ( ( strictorderedP(X0)
| ~ sP17(X0) )
& ( sP17(X0)
| ~ strictorderedP(X0) ) )
| ~ sP18(X0) ),
inference(nnf_transformation,[],[f251]) ).
fof(f251,plain,
! [X0] :
( ( strictorderedP(X0)
<=> sP17(X0) )
| ~ sP18(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP18])]) ).
fof(f550,plain,
! [X0] :
( ~ sP18(X0)
| ~ strictorderedP(X0)
| sP17(X0) ),
inference(cnf_transformation,[],[f347]) ).
fof(f540,plain,
! [X0] :
( ~ sP16(X0)
| ~ sP15(X0)
| totalorderedP(X0) ),
inference(cnf_transformation,[],[f338]) ).
fof(f338,plain,
! [X0] :
( ( ( totalorderedP(X0)
| ~ sP15(X0) )
& ( sP15(X0)
| ~ totalorderedP(X0) ) )
| ~ sP16(X0) ),
inference(nnf_transformation,[],[f248]) ).
fof(f248,plain,
! [X0] :
( ( totalorderedP(X0)
<=> sP15(X0) )
| ~ sP16(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
fof(f539,plain,
! [X0] :
( ~ sP16(X0)
| ~ totalorderedP(X0)
| sP15(X0) ),
inference(cnf_transformation,[],[f338]) ).
fof(f527,plain,
! [X0] :
( ~ sP14(X0)
| ~ cyclefreeP(X0)
| sP13(X0) ),
inference(cnf_transformation,[],[f329]) ).
fof(f329,plain,
! [X0] :
( ( ( cyclefreeP(X0)
| ~ sP13(X0) )
& ( sP13(X0)
| ~ cyclefreeP(X0) ) )
| ~ sP14(X0) ),
inference(nnf_transformation,[],[f245]) ).
fof(f245,plain,
! [X0] :
( ( cyclefreeP(X0)
<=> sP13(X0) )
| ~ sP14(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f515,plain,
! [X0] :
( ~ sP12(X0)
| ~ strictorderP(X0)
| sP11(X0) ),
inference(cnf_transformation,[],[f320]) ).
fof(f320,plain,
! [X0] :
( ( ( strictorderP(X0)
| ~ sP11(X0) )
& ( sP11(X0)
| ~ strictorderP(X0) ) )
| ~ sP12(X0) ),
inference(nnf_transformation,[],[f242]) ).
fof(f242,plain,
! [X0] :
( ( strictorderP(X0)
<=> sP11(X0) )
| ~ sP12(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f503,plain,
! [X0] :
( ~ sP10(X0)
| ~ totalorderP(X0)
| sP9(X0) ),
inference(cnf_transformation,[],[f311]) ).
fof(f311,plain,
! [X0] :
( ( ( totalorderP(X0)
| ~ sP9(X0) )
& ( sP9(X0)
| ~ totalorderP(X0) ) )
| ~ sP10(X0) ),
inference(nnf_transformation,[],[f239]) ).
fof(f239,plain,
! [X0] :
( ( totalorderP(X0)
<=> sP9(X0) )
| ~ sP10(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f492,plain,
! [X0] :
( ~ sP8(X0)
| ~ duplicatefreeP(X0)
| sP7(X0) ),
inference(cnf_transformation,[],[f302]) ).
fof(f302,plain,
! [X0] :
( ( ( duplicatefreeP(X0)
| ~ sP7(X0) )
& ( sP7(X0)
| ~ duplicatefreeP(X0) ) )
| ~ sP8(X0) ),
inference(nnf_transformation,[],[f236]) ).
fof(f236,plain,
! [X0] :
( ( duplicatefreeP(X0)
<=> sP7(X0) )
| ~ sP8(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f482,plain,
! [X0] :
( ~ sP6(X0)
| ~ equalelemsP(X0)
| sP5(X0) ),
inference(cnf_transformation,[],[f294]) ).
fof(f294,plain,
! [X0] :
( ( ( equalelemsP(X0)
| ~ sP5(X0) )
& ( sP5(X0)
| ~ equalelemsP(X0) ) )
| ~ sP6(X0) ),
inference(nnf_transformation,[],[f233]) ).
fof(f233,plain,
! [X0] :
( ( equalelemsP(X0)
<=> sP5(X0) )
| ~ sP6(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f416,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f65]) ).
fof(f65,axiom,
! [X0] :
( ssItem(X0)
=> totalorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax65) ).
fof(f415,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f68,axiom,
! [X0] :
( ssItem(X0)
=> strictorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax68) ).
fof(f414,plain,
! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f63]) ).
fof(f63,axiom,
! [X0] :
( ssItem(X0)
=> strictorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax63) ).
fof(f413,plain,
! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,axiom,
! [X0] :
( ssItem(X0)
=> totalorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax61) ).
fof(f412,plain,
! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,axiom,
! [X0] :
( ssItem(X0)
=> cyclefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax59) ).
fof(f411,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f71]) ).
fof(f71,axiom,
! [X0] :
( ssItem(X0)
=> duplicatefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax71) ).
fof(f410,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,axiom,
! [X0] :
( ssItem(X0)
=> equalelemsP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax73) ).
fof(f649,plain,
nil = app(nil,nil),
inference(global_subsumption,[],[f385,f384,f383,f396,f395,f394,f393,f392,f391,f390,f389,f388,f387,f386,f397,f398,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f417,f418,f419,f420,f421,f425,f424,f427,f426,f430,f429,f645,f431,f432,f433,f434,f435,f438,f644,f436,f643,f440,f439,f443,f442,f448,f618,f446,f445,f449,f451,f450,f456,f620,f454,f453,f457,f460,f459,f458,f461,f462,f463,f464,f465,f466,f467,f468,f471,f470,f469,f472,f473,f474,f476,f475,f478,f477,f622,f480,f479,f482,f490,f489,f488,f487,f486,f485,f623,f491,f492,f501,f500,f499,f498,f497,f496,f495,f642,f502,f503,f513,f512,f511,f510,f509,f508,f507,f506,f626,f514,f515,f525,f524,f523,f522,f521,f520,f519,f518,f627,f526,f527,f537,f536,f535,f534,f533,f532,f531,f530,f628,f538,f540,f539,f548,f547,f546,f545,f544,f543,f542,f629,f549,f551,f550,f559,f558,f557,f556,f555,f554,f553,f630,f560,f631,f646,f561,f632,f647,f563,f633,f648,f565,f567,f568,f569,f570,f571,f572,f634,f575,f574,f573,f577,f578,f579,f580,f581,f582,f583,f636,f587,f586,f637,f591,f590,f589,f638,f594,f593,f641]) ).
fof(f557,plain,
! [X0] :
( ssList(sK63(X0))
| sP17(X0) ),
inference(cnf_transformation,[],[f355]) ).
fof(f556,plain,
! [X0] :
( ssList(sK62(X0))
| sP17(X0) ),
inference(cnf_transformation,[],[f355]) ).
fof(f555,plain,
! [X0] :
( ssList(sK61(X0))
| sP17(X0) ),
inference(cnf_transformation,[],[f355]) ).
fof(f554,plain,
! [X0] :
( ssItem(sK60(X0))
| sP17(X0) ),
inference(cnf_transformation,[],[f355]) ).
fof(f553,plain,
! [X0] :
( ssItem(sK59(X0))
| sP17(X0) ),
inference(cnf_transformation,[],[f355]) ).
fof(f546,plain,
! [X0] :
( ssList(sK58(X0))
| sP15(X0) ),
inference(cnf_transformation,[],[f346]) ).
fof(f545,plain,
! [X0] :
( ssList(sK57(X0))
| sP15(X0) ),
inference(cnf_transformation,[],[f346]) ).
fof(f544,plain,
! [X0] :
( ssList(sK56(X0))
| sP15(X0) ),
inference(cnf_transformation,[],[f346]) ).
fof(f543,plain,
! [X0] :
( ssItem(sK55(X0))
| sP15(X0) ),
inference(cnf_transformation,[],[f346]) ).
fof(f542,plain,
! [X0] :
( ssItem(sK54(X0))
| sP15(X0) ),
inference(cnf_transformation,[],[f346]) ).
fof(f534,plain,
! [X0] :
( ssList(sK53(X0))
| sP13(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f533,plain,
! [X0] :
( ssList(sK52(X0))
| sP13(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f532,plain,
! [X0] :
( ssList(sK51(X0))
| sP13(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f531,plain,
! [X0] :
( ssItem(sK50(X0))
| sP13(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f530,plain,
! [X0] :
( ssItem(sK49(X0))
| sP13(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f522,plain,
! [X0] :
( ssList(sK48(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f521,plain,
! [X0] :
( ssList(sK47(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f520,plain,
! [X0] :
( ssList(sK46(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f519,plain,
! [X0] :
( ssItem(sK45(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f518,plain,
! [X0] :
( ssItem(sK44(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f510,plain,
! [X0] :
( ssList(sK43(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f509,plain,
! [X0] :
( ssList(sK42(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f508,plain,
! [X0] :
( ssList(sK41(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f507,plain,
! [X0] :
( ssItem(sK40(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f506,plain,
! [X0] :
( ssItem(sK39(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f499,plain,
! [X0] :
( ssList(sK38(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f310]) ).
fof(f498,plain,
! [X0] :
( ssList(sK37(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f310]) ).
fof(f497,plain,
! [X0] :
( ssList(sK36(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f310]) ).
fof(f496,plain,
! [X0] :
( ssItem(sK35(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f310]) ).
fof(f495,plain,
! [X0] :
( ssItem(sK34(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f310]) ).
fof(f488,plain,
! [X0] :
( ssList(sK33(X0))
| sP5(X0) ),
inference(cnf_transformation,[],[f301]) ).
fof(f487,plain,
! [X0] :
( ssList(sK32(X0))
| sP5(X0) ),
inference(cnf_transformation,[],[f301]) ).
fof(f486,plain,
! [X0] :
( ssItem(sK31(X0))
| sP5(X0) ),
inference(cnf_transformation,[],[f301]) ).
fof(f485,plain,
! [X0] :
( ssItem(sK30(X0))
| sP5(X0) ),
inference(cnf_transformation,[],[f301]) ).
fof(f466,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,axiom,
! [X0] :
( ssList(X0)
=> rearsegP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax49) ).
fof(f465,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f145,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
fof(f464,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45) ).
fof(f463,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax42) ).
fof(f462,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0] :
( ssList(X0)
=> rearsegP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51) ).
fof(f461,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f141,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).
fof(f409,plain,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0] :
( ssItem(X0)
=> leq(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax31) ).
fof(f408,plain,
! [X0] :
( geq(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0] :
( geq(X0,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f89]) ).
fof(f89,axiom,
! [X0] :
( ssItem(X0)
=> geq(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax89) ).
fof(f407,plain,
! [X0] :
( ~ lt(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0] :
( ~ lt(X0,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f90]) ).
fof(f90,axiom,
! [X0] :
( ssItem(X0)
=> ~ lt(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax90) ).
fof(f654,plain,
( sP0(sK21,sK20)
| nil = sK21 ),
inference(forward_demodulation,[],[f653,f390]) ).
fof(f653,plain,
( sP0(sK23,sK20)
| nil = sK21 ),
inference(forward_demodulation,[],[f652,f391]) ).
fof(f652,plain,
( nil = sK21
| sP0(sK23,sK22) ),
inference(forward_demodulation,[],[f395,f390]) ).
fof(f657,plain,
( sP0(sK21,sK20)
| nil = sK20 ),
inference(forward_demodulation,[],[f656,f390]) ).
fof(f656,plain,
( sP0(sK23,sK20)
| nil = sK20 ),
inference(forward_demodulation,[],[f655,f391]) ).
fof(f655,plain,
( nil = sK20
| sP0(sK23,sK22) ),
inference(forward_demodulation,[],[f396,f391]) ).
fof(f560,plain,
! [X0] :
( sP18(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f252]) ).
fof(f252,plain,
! [X0] :
( sP18(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f175,f251,f250]) ).
fof(f175,plain,
! [X0] :
( ( strictorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f174]) ).
fof(f174,plain,
! [X0] :
( ( strictorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( ssList(X0)
=> ( strictorderedP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> lt(X1,X2) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax12) ).
fof(f549,plain,
! [X0] :
( sP16(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f249]) ).
fof(f249,plain,
! [X0] :
( sP16(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f173,f248,f247]) ).
fof(f173,plain,
! [X0] :
( ( totalorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f172]) ).
fof(f172,plain,
! [X0] :
( ( totalorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( ssList(X0)
=> ( totalorderedP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> leq(X1,X2) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax11) ).
fof(f538,plain,
! [X0] :
( sP14(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f246]) ).
fof(f246,plain,
! [X0] :
( sP14(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f171,f245,f244]) ).
fof(f171,plain,
! [X0] :
( ( cyclefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f170]) ).
fof(f170,plain,
! [X0] :
( ( cyclefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( ssList(X0)
=> ( cyclefreeP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> ~ ( leq(X2,X1)
& leq(X1,X2) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax8) ).
fof(f526,plain,
! [X0] :
( sP12(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f243]) ).
fof(f243,plain,
! [X0] :
( sP12(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f169,f242,f241]) ).
fof(f169,plain,
! [X0] :
( ( strictorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f168]) ).
fof(f168,plain,
! [X0] :
( ( strictorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( ssList(X0)
=> ( strictorderP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> ( lt(X2,X1)
| lt(X1,X2) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax10) ).
fof(f514,plain,
! [X0] :
( sP10(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f240]) ).
fof(f240,plain,
! [X0] :
( sP10(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f167,f239,f238]) ).
fof(f167,plain,
! [X0] :
( ( totalorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f166]) ).
fof(f166,plain,
! [X0] :
( ( totalorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( ssList(X0)
=> ( totalorderP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> ( leq(X2,X1)
| leq(X1,X2) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax9) ).
fof(f502,plain,
! [X0] :
( sP8(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f237]) ).
fof(f237,plain,
! [X0] :
( sP8(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f165,f236,f235]) ).
fof(f165,plain,
! [X0] :
( ( duplicatefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f164]) ).
fof(f164,plain,
! [X0] :
( ( duplicatefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( ssList(X0)
=> ( duplicatefreeP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> X1 != X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax13) ).
fof(f491,plain,
! [X0] :
( sP6(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f234]) ).
fof(f234,plain,
! [X0] :
( sP6(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f163,f233,f232]) ).
fof(f163,plain,
! [X0] :
( ( equalelemsP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f162]) ).
fof(f162,plain,
! [X0] :
( ( equalelemsP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ssList(X0)
=> ( equalelemsP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( app(X3,cons(X1,cons(X2,X4))) = X0
=> X1 = X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax14) ).
fof(f648,plain,
frontsegP(nil,nil),
inference(global_subsumption,[],[f385,f384,f383,f396,f395,f394,f393,f392,f391,f390,f389,f388,f387,f386,f397,f398,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f417,f418,f419,f420,f421,f425,f424,f427,f426,f430,f429,f645,f431,f432,f433,f434,f435,f438,f644,f436,f643,f440,f439,f443,f442,f448,f618,f446,f445,f449,f451,f450,f456,f620,f454,f453,f457,f460,f459,f458,f461,f462,f463,f464,f465,f466,f467,f468,f471,f470,f469,f472,f473,f474,f476,f475,f478,f477,f622,f480,f479,f482,f490,f489,f488,f487,f486,f485,f623,f491,f492,f501,f500,f499,f498,f497,f496,f495,f642,f502,f503,f513,f512,f511,f510,f509,f508,f507,f506,f626,f514,f515,f525,f524,f523,f522,f521,f520,f519,f518,f627,f526,f527,f537,f536,f535,f534,f533,f532,f531,f530,f628,f538,f540,f539,f548,f547,f546,f545,f544,f543,f542,f629,f549,f551,f550,f559,f558,f557,f556,f555,f554,f553,f630,f560,f631,f646,f561,f632,f647,f563,f633]) ).
fof(f647,plain,
rearsegP(nil,nil),
inference(global_subsumption,[],[f385,f384,f383,f396,f395,f394,f393,f392,f391,f390,f389,f388,f387,f386,f397,f398,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f417,f418,f419,f420,f421,f425,f424,f427,f426,f430,f429,f645,f431,f432,f433,f434,f435,f438,f644,f436,f643,f440,f439,f443,f442,f448,f618,f446,f445,f449,f451,f450,f456,f620,f454,f453,f457,f460,f459,f458,f461,f462,f463,f464,f465,f466,f467,f468,f471,f470,f469,f472,f473,f474,f476,f475,f478,f477,f622,f480,f479,f482,f490,f489,f488,f487,f486,f485,f623,f491,f492,f501,f500,f499,f498,f497,f496,f495,f642,f502,f503,f513,f512,f511,f510,f509,f508,f507,f506,f626,f514,f515,f525,f524,f523,f522,f521,f520,f519,f518,f627,f526,f527,f537,f536,f535,f534,f533,f532,f531,f530,f628,f538,f540,f539,f548,f547,f546,f545,f544,f543,f542,f629,f549,f551,f550,f559,f558,f557,f556,f555,f554,f553,f630,f560,f631,f646,f561,f632]) ).
fof(f646,plain,
segmentP(nil,nil),
inference(global_subsumption,[],[f385,f384,f383,f396,f395,f394,f393,f392,f391,f390,f389,f388,f387,f386,f397,f398,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f417,f418,f419,f420,f421,f425,f424,f427,f426,f430,f429,f645,f431,f432,f433,f434,f435,f438,f644,f436,f643,f440,f439,f443,f442,f448,f618,f446,f445,f449,f451,f450,f456,f620,f454,f453,f457,f460,f459,f458,f461,f462,f463,f464,f465,f466,f467,f468,f471,f470,f469,f472,f473,f474,f476,f475,f478,f477,f622,f480,f479,f482,f490,f489,f488,f487,f486,f485,f623,f491,f492,f501,f500,f499,f498,f497,f496,f495,f642,f502,f503,f513,f512,f511,f510,f509,f508,f507,f506,f626,f514,f515,f525,f524,f523,f522,f521,f520,f519,f518,f627,f526,f527,f537,f536,f535,f534,f533,f532,f531,f530,f628,f538,f540,f539,f548,f547,f546,f545,f544,f543,f542,f629,f549,f551,f550,f559,f558,f557,f556,f555,f554,f553,f630,f560,f631]) ).
fof(f620,plain,
! [X1] : sP3(nil,X1),
inference(equality_resolution,[],[f455]) ).
fof(f455,plain,
! [X0,X1] :
( sP3(X0,X1)
| nil != X0 ),
inference(cnf_transformation,[],[f280]) ).
fof(f618,plain,
! [X1] : sP1(nil,X1),
inference(equality_resolution,[],[f447]) ).
fof(f447,plain,
! [X0,X1] :
( sP1(X0,X1)
| nil != X0 ),
inference(cnf_transformation,[],[f276]) ).
fof(f613,plain,
sK70 != sK71,
inference(cnf_transformation,[],[f382]) ).
fof(f391,plain,
sK20 = sK22,
inference(cnf_transformation,[],[f263]) ).
fof(f390,plain,
sK21 = sK23,
inference(cnf_transformation,[],[f263]) ).
fof(f404,plain,
totalorderedP(nil),
inference(cnf_transformation,[],[f66]) ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax66) ).
fof(f403,plain,
strictorderedP(nil),
inference(cnf_transformation,[],[f69]) ).
fof(f69,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax69) ).
fof(f402,plain,
totalorderP(nil),
inference(cnf_transformation,[],[f62]) ).
fof(f62,axiom,
totalorderP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax62) ).
fof(f401,plain,
strictorderP(nil),
inference(cnf_transformation,[],[f64]) ).
fof(f64,axiom,
strictorderP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax64) ).
fof(f400,plain,
cyclefreeP(nil),
inference(cnf_transformation,[],[f60]) ).
fof(f60,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax60) ).
fof(f399,plain,
duplicatefreeP(nil),
inference(cnf_transformation,[],[f72]) ).
fof(f72,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).
fof(f398,plain,
equalelemsP(nil),
inference(cnf_transformation,[],[f74]) ).
fof(f74,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax74) ).
fof(f397,plain,
~ singletonP(nil),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).
fof(f389,plain,
ssList(sK23),
inference(cnf_transformation,[],[f263]) ).
fof(f388,plain,
ssList(sK22),
inference(cnf_transformation,[],[f263]) ).
fof(f387,plain,
ssList(sK21),
inference(cnf_transformation,[],[f263]) ).
fof(f610,plain,
! [X2,X3,X0,X1] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f223]) ).
fof(f223,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f222]) ).
fof(f222,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f56]) ).
fof(f56,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( segmentP(X0,X1)
=> segmentP(app(app(X2,X0),X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax56) ).
fof(f609,plain,
! [X2,X0,X1] :
( ~ frontsegP(X1,X2)
| frontsegP(X0,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f221]) ).
fof(f221,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f220]) ).
fof(f220,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( frontsegP(X1,X2)
& frontsegP(X0,X1) )
=> frontsegP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax40) ).
fof(f608,plain,
! [X2,X0,X1] :
( ~ rearsegP(X1,X2)
| rearsegP(X0,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f219]) ).
fof(f219,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f218]) ).
fof(f218,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( rearsegP(X1,X2)
& rearsegP(X0,X1) )
=> rearsegP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax47) ).
fof(f607,plain,
! [X2,X0,X1] :
( ~ segmentP(X1,X2)
| segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f217]) ).
fof(f217,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f216]) ).
fof(f216,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X1,X2)
& segmentP(X0,X1) )
=> segmentP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax53) ).
fof(f606,plain,
! [X2,X0,X1] :
( app(X1,X2) != app(X1,X0)
| X0 = X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f215]) ).
fof(f215,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f214]) ).
fof(f214,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f80]) ).
fof(f80,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X1,X2) = app(X1,X0)
=> X0 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax80) ).
fof(f605,plain,
! [X2,X0,X1] :
( app(X2,X1) != app(X0,X1)
| X0 = X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f213]) ).
fof(f213,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f212]) ).
fof(f212,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f79]) ).
fof(f79,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X2,X1) = app(X0,X1)
=> X0 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax79) ).
fof(f604,plain,
! [X2,X0,X1] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f211]) ).
fof(f211,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f210]) ).
fof(f210,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X0,X1)
=> frontsegP(app(X0,X2),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax43) ).
fof(f603,plain,
! [X2,X0,X1] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f209]) ).
fof(f209,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f208]) ).
fof(f208,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X0,X1)
=> rearsegP(app(X2,X0),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax50) ).
fof(f602,plain,
! [X2,X0,X1] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f207]) ).
fof(f207,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f82,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> app(app(X0,X1),X2) = app(X0,app(X1,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax82) ).
fof(f600,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f206]) ).
fof(f206,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( X0 = X1
& X2 = X3 )
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3) )
| ~ ssItem(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f205]) ).
fof(f205,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( X0 = X1
& X2 = X3 )
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3) )
| ~ ssItem(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ( cons(X2,X0) = cons(X3,X1)
=> ( X0 = X1
& X2 = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax19) ).
fof(f601,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f206]) ).
fof(f599,plain,
! [X2,X0,X1] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f204]) ).
fof(f204,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,app(X1,X0)) = app(cons(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax27) ).
fof(f596,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f379]) ).
fof(f379,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f378]) ).
fof(f378,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f203]) ).
fof(f203,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax83) ).
fof(f597,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f379]) ).
fof(f641,plain,
( nil = app(nil,nil)
| ~ ssList(nil) ),
inference(duplicate_literal_removal,[],[f640]) ).
fof(f640,plain,
( nil = app(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f639]) ).
fof(f639,plain,
! [X1] :
( nil = app(nil,X1)
| nil != X1
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f598]) ).
fof(f598,plain,
! [X0,X1] :
( nil = app(X0,X1)
| nil != X0
| nil != X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f379]) ).
fof(f593,plain,
! [X0,X1] :
( ssList(sK69(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f377]) ).
fof(f377,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ( app(X1,sK69(X0,X1)) = X0
& ssList(sK69(X0,X1)) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK69])],[f375,f376]) ).
fof(f376,plain,
! [X0,X1] :
( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
=> ( app(X1,sK69(X0,X1)) = X0
& ssList(sK69(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f375,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f374]) ).
fof(f374,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ? [X2] :
( app(X1,X2) = X0
& ssList(X2) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f202]) ).
fof(f202,plain,
! [X0] :
( ! [X1] :
( ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
fof(f594,plain,
! [X0,X1] :
( ~ frontsegP(X0,X1)
| app(X1,sK69(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f377]) ).
fof(f638,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(equality_resolution,[],[f595]) ).
fof(f595,plain,
! [X2,X0,X1] :
( frontsegP(X0,X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f377]) ).
fof(f589,plain,
! [X0,X1] :
( ssList(sK67(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f373]) ).
fof(f373,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(app(sK67(X0,X1),X1),sK68(X0,X1)) = X0
& ssList(sK68(X0,X1))
& ssList(sK67(X0,X1)) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK67,sK68])],[f370,f372,f371]) ).
fof(f371,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(app(sK67(X0,X1),X1),X5) = X0
& ssList(X5) )
& ssList(sK67(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f372,plain,
! [X0,X1] :
( ? [X5] :
( app(app(sK67(X0,X1),X1),X5) = X0
& ssList(X5) )
=> ( app(app(sK67(X0,X1),X1),sK68(X0,X1)) = X0
& ssList(sK68(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f370,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f369]) ).
fof(f369,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f201]) ).
fof(f201,plain,
! [X0] :
( ! [X1] :
( ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
fof(f590,plain,
! [X0,X1] :
( ssList(sK68(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f373]) ).
fof(f591,plain,
! [X0,X1] :
( app(app(sK67(X0,X1),X1),sK68(X0,X1)) = X0
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f373]) ).
fof(f637,plain,
! [X2,X3,X1] :
( segmentP(app(app(X2,X1),X3),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(app(X2,X1),X3)) ),
inference(equality_resolution,[],[f592]) ).
fof(f592,plain,
! [X2,X3,X0,X1] :
( segmentP(X0,X1)
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f373]) ).
fof(f586,plain,
! [X0,X1] :
( ssList(sK66(X0,X1))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f368]) ).
fof(f587,plain,
! [X0,X1] :
( ~ rearsegP(X0,X1)
| app(sK66(X0,X1),X1) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f368]) ).
fof(f583,plain,
! [X0,X1] :
( ~ frontsegP(X1,X0)
| X0 = X1
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f198,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f197]) ).
fof(f197,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( frontsegP(X1,X0)
& frontsegP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).
fof(f582,plain,
! [X0,X1] :
( ~ segmentP(X1,X0)
| X0 = X1
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f196]) ).
fof(f196,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f195]) ).
fof(f195,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( segmentP(X1,X0)
& segmentP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax54) ).
fof(f580,plain,
! [X0,X1] :
( X0 = X1
| tl(X0) != tl(X1)
| hd(X0) != hd(X1)
| nil = X0
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f192]) ).
fof(f192,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| tl(X0) != tl(X1)
| hd(X0) != hd(X1)
| nil = X0
| nil = X1
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f191]) ).
fof(f191,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| tl(X0) != tl(X1)
| hd(X0) != hd(X1)
| nil = X0
| nil = X1
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f77]) ).
fof(f77,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( tl(X0) = tl(X1)
& hd(X0) = hd(X1)
& nil != X0
& nil != X1 )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax77) ).
fof(f579,plain,
! [X0,X1] :
( ~ ssList(X1)
| nil = X0
| tl(app(X0,X1)) = app(tl(X0),X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f190]) ).
fof(f190,plain,
! [X0] :
( ! [X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f189]) ).
fof(f189,plain,
! [X0] :
( ! [X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f86]) ).
fof(f86,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil != X0
=> tl(app(X0,X1)) = app(tl(X0),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax86) ).
fof(f578,plain,
! [X0,X1] :
( ~ ssList(X1)
| nil = X0
| hd(X0) = hd(app(X0,X1))
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f188]) ).
fof(f188,plain,
! [X0] :
( ! [X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f187]) ).
fof(f187,plain,
! [X0] :
( ! [X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f85]) ).
fof(f85,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil != X0
=> hd(X0) = hd(app(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax85) ).
fof(f573,plain,
! [X0,X1] :
( ssList(sK64(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f363]) ).
fof(f363,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(sK64(X0,X1),cons(X1,sK65(X0,X1))) = X0
& ssList(sK65(X0,X1))
& ssList(sK64(X0,X1)) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK64,sK65])],[f360,f362,f361]) ).
fof(f361,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(sK64(X0,X1),cons(X1,X5)) = X0
& ssList(X5) )
& ssList(sK64(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f362,plain,
! [X0,X1] :
( ? [X5] :
( app(sK64(X0,X1),cons(X1,X5)) = X0
& ssList(X5) )
=> ( app(sK64(X0,X1),cons(X1,sK65(X0,X1))) = X0
& ssList(sK65(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f360,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f359]) ).
fof(f359,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f185]) ).
fof(f185,plain,
! [X0] :
( ! [X1] :
( ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f574,plain,
! [X0,X1] :
( ssList(sK65(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f363]) ).
fof(f575,plain,
! [X0,X1] :
( app(sK64(X0,X1),cons(X1,sK65(X0,X1))) = X0
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f363]) ).
fof(f634,plain,
! [X2,X3,X1] :
( memberP(app(X2,cons(X1,X3)),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssList(app(X2,cons(X1,X3))) ),
inference(equality_resolution,[],[f576]) ).
fof(f576,plain,
! [X2,X3,X0,X1] :
( memberP(X0,X1)
| app(X2,cons(X1,X3)) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f363]) ).
fof(f570,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| tl(cons(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f182]) ).
fof(f182,plain,
! [X0] :
( ! [X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> tl(cons(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax25) ).
fof(f633,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f566]) ).
fof(f566,plain,
! [X0] :
( frontsegP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f358]) ).
fof(f632,plain,
( rearsegP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f564]) ).
fof(f564,plain,
! [X0] :
( rearsegP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f631,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f562]) ).
fof(f562,plain,
! [X0] :
( segmentP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f356]) ).
fof(f630,plain,
! [X10,X8,X6,X9,X7] :
( lt(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP17(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f552]) ).
fof(f552,plain,
! [X10,X0,X8,X6,X9,X7] :
( lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP17(X0) ),
inference(cnf_transformation,[],[f355]) ).
fof(f558,plain,
! [X0] :
( sP17(X0)
| app(app(sK61(X0),cons(sK59(X0),sK62(X0))),cons(sK60(X0),sK63(X0))) = X0 ),
inference(cnf_transformation,[],[f355]) ).
fof(f629,plain,
! [X10,X8,X6,X9,X7] :
( leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP15(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f541]) ).
fof(f541,plain,
! [X10,X0,X8,X6,X9,X7] :
( leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP15(X0) ),
inference(cnf_transformation,[],[f346]) ).
fof(f547,plain,
! [X0] :
( sP15(X0)
| app(app(sK56(X0),cons(sK54(X0),sK57(X0))),cons(sK55(X0),sK58(X0))) = X0 ),
inference(cnf_transformation,[],[f346]) ).
fof(f628,plain,
! [X10,X8,X6,X9,X7] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP13(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f529]) ).
fof(f529,plain,
! [X10,X0,X8,X6,X9,X7] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP13(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f535,plain,
! [X0] :
( sP13(X0)
| app(app(sK51(X0),cons(sK49(X0),sK52(X0))),cons(sK50(X0),sK53(X0))) = X0 ),
inference(cnf_transformation,[],[f337]) ).
fof(f627,plain,
! [X10,X8,X6,X9,X7] :
( lt(X7,X6)
| lt(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP11(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f517]) ).
fof(f517,plain,
! [X10,X0,X8,X6,X9,X7] :
( lt(X7,X6)
| lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP11(X0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f523,plain,
! [X0] :
( sP11(X0)
| app(app(sK46(X0),cons(sK44(X0),sK47(X0))),cons(sK45(X0),sK48(X0))) = X0 ),
inference(cnf_transformation,[],[f328]) ).
fof(f626,plain,
! [X10,X8,X6,X9,X7] :
( leq(X7,X6)
| leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP9(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f505]) ).
fof(f505,plain,
! [X10,X0,X8,X6,X9,X7] :
( leq(X7,X6)
| leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f511,plain,
! [X0] :
( sP9(X0)
| app(app(sK41(X0),cons(sK39(X0),sK42(X0))),cons(sK40(X0),sK43(X0))) = X0 ),
inference(cnf_transformation,[],[f319]) ).
fof(f642,plain,
! [X10,X8,X9,X7] :
( ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ sP7(app(app(X8,cons(X7,X9)),cons(X7,X10))) ),
inference(duplicate_literal_removal,[],[f625]) ).
fof(f625,plain,
! [X10,X8,X9,X7] :
( ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X7)
| ~ sP7(app(app(X8,cons(X7,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f624]) ).
fof(f624,plain,
! [X10,X0,X8,X9,X7] :
( app(app(X8,cons(X7,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X7)
| ~ sP7(X0) ),
inference(equality_resolution,[],[f494]) ).
fof(f494,plain,
! [X10,X0,X8,X6,X9,X7] :
( X6 != X7
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f310]) ).
fof(f500,plain,
! [X0] :
( sP7(X0)
| app(app(sK36(X0),cons(sK34(X0),sK37(X0))),cons(sK35(X0),sK38(X0))) = X0 ),
inference(cnf_transformation,[],[f310]) ).
fof(f623,plain,
! [X8,X6,X7,X5] :
( X5 = X6
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ ssItem(X5)
| ~ sP5(app(X7,cons(X5,cons(X6,X8)))) ),
inference(equality_resolution,[],[f484]) ).
fof(f484,plain,
! [X0,X8,X6,X7,X5] :
( X5 = X6
| app(X7,cons(X5,cons(X6,X8))) != X0
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ ssItem(X5)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f301]) ).
fof(f489,plain,
! [X0] :
( sP5(X0)
| app(sK32(X0),cons(sK30(X0),cons(sK31(X0),sK33(X0)))) = X0 ),
inference(cnf_transformation,[],[f301]) ).
fof(f480,plain,
! [X0] :
( ~ singletonP(X0)
| cons(sK29(X0),nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f293]) ).
fof(f622,plain,
! [X1] :
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(equality_resolution,[],[f481]) ).
fof(f481,plain,
! [X0,X1] :
( singletonP(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f293]) ).
fof(f478,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| tl(X0) = sK28(X0) ),
inference(cnf_transformation,[],[f289]) ).
fof(f476,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| hd(X0) = sK27(X0) ),
inference(cnf_transformation,[],[f287]) ).
fof(f474,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f155]) ).
fof(f155,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax78) ).
fof(f471,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(sK26(X0),sK25(X0)) = X0 ),
inference(cnf_transformation,[],[f285]) ).
fof(f458,plain,
! [X2,X0,X1] :
( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f282]) ).
fof(f282,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) ) )
& ( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f281]) ).
fof(f281,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) ) )
& ( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f140]) ).
fof(f140,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax36) ).
fof(f459,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f282]) ).
fof(f460,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f282]) ).
fof(f454,plain,
! [X0,X1] :
( lt(X1,hd(X0))
| nil = X0
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f280]) ).
fof(f456,plain,
! [X0,X1] :
( ~ lt(X1,hd(X0))
| sP3(X0,X1)
| ~ strictorderedP(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f280]) ).
fof(f450,plain,
! [X0,X1] :
( ~ strictorderedP(cons(X0,X1))
| sP3(X1,X0)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f277]) ).
fof(f277,plain,
! [X0,X1] :
( ( ( strictorderedP(cons(X0,X1))
| ~ sP3(X1,X0) )
& ( sP3(X1,X0)
| ~ strictorderedP(cons(X0,X1)) ) )
| ~ sP4(X0,X1) ),
inference(nnf_transformation,[],[f230]) ).
fof(f451,plain,
! [X0,X1] :
( strictorderedP(cons(X0,X1))
| ~ sP3(X1,X0)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f277]) ).
fof(f446,plain,
! [X0,X1] :
( leq(X1,hd(X0))
| nil = X0
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f276]) ).
fof(f448,plain,
! [X0,X1] :
( ~ leq(X1,hd(X0))
| sP1(X0,X1)
| ~ totalorderedP(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f276]) ).
fof(f442,plain,
! [X0,X1] :
( ~ totalorderedP(cons(X0,X1))
| sP1(X1,X0)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f273]) ).
fof(f273,plain,
! [X0,X1] :
( ( ( totalorderedP(cons(X0,X1))
| ~ sP1(X1,X0) )
& ( sP1(X1,X0)
| ~ totalorderedP(cons(X0,X1)) ) )
| ~ sP2(X0,X1) ),
inference(nnf_transformation,[],[f227]) ).
fof(f443,plain,
! [X0,X1] :
( totalorderedP(cons(X0,X1))
| ~ sP1(X1,X0)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f273]) ).
fof(f439,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| ~ frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f272]) ).
fof(f272,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( frontsegP(cons(X0,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| X0 != X1 )
& ( ( frontsegP(X2,X3)
& X0 = X1 )
| ~ frontsegP(cons(X0,X2),cons(X1,X3)) ) )
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f271]) ).
fof(f271,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( frontsegP(cons(X0,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| X0 != X1 )
& ( ( frontsegP(X2,X3)
& X0 = X1 )
| ~ frontsegP(cons(X0,X2),cons(X1,X3)) ) )
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f137]) ).
fof(f137,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( frontsegP(cons(X0,X2),cons(X1,X3))
<=> ( frontsegP(X2,X3)
& X0 = X1 ) )
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( frontsegP(cons(X0,X2),cons(X1,X3))
<=> ( frontsegP(X2,X3)
& X0 = X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax44) ).
fof(f440,plain,
! [X2,X3,X0,X1] :
( frontsegP(X2,X3)
| ~ frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f272]) ).
fof(f643,plain,
! [X2,X3,X1] :
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f617]) ).
fof(f617,plain,
! [X2,X3,X1] :
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f441]) ).
fof(f441,plain,
! [X2,X3,X0,X1] :
( frontsegP(cons(X0,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| X0 != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f272]) ).
fof(f438,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f270]) ).
fof(f435,plain,
! [X2,X0,X1] :
( ~ lt(X1,X2)
| lt(X0,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f134]) ).
fof(f134,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( lt(X1,X2)
& lt(X0,X1) )
=> lt(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax34) ).
fof(f434,plain,
! [X2,X0,X1] :
( ~ lt(X1,X2)
| lt(X0,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f132]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f91]) ).
fof(f91,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( lt(X1,X2)
& leq(X0,X1) )
=> lt(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax91) ).
fof(f433,plain,
! [X2,X0,X1] :
( ~ leq(X1,X2)
| leq(X0,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f130]) ).
fof(f130,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( leq(X1,X2)
& leq(X0,X1) )
=> leq(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax30) ).
fof(f432,plain,
! [X2,X0,X1] :
( ~ geq(X1,X2)
| geq(X0,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( geq(X0,X2)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f128]) ).
fof(f128,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( geq(X0,X2)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f88]) ).
fof(f88,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( geq(X1,X2)
& geq(X0,X1) )
=> geq(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax88) ).
fof(f431,plain,
! [X2,X0,X1] :
( ~ gt(X1,X2)
| gt(X0,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f126]) ).
fof(f126,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f95]) ).
fof(f95,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( gt(X1,X2)
& gt(X0,X1) )
=> gt(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax95) ).
fof(f645,plain,
! [X1] :
( ~ lt(X1,X1)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f615]) ).
fof(f615,plain,
! [X1] :
( ~ lt(X1,X1)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f428]) ).
fof(f428,plain,
! [X0,X1] :
( X0 != X1
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f268]) ).
fof(f268,plain,
! [X0] :
( ! [X1] :
( ( ( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1 )
& ( ( leq(X0,X1)
& X0 != X1 )
| ~ lt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f267]) ).
fof(f267,plain,
! [X0] :
( ! [X1] :
( ( ( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1 )
& ( ( leq(X0,X1)
& X0 != X1 )
| ~ lt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0] :
( ! [X1] :
( ( lt(X0,X1)
<=> ( leq(X0,X1)
& X0 != X1 ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f93]) ).
fof(f93,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( lt(X0,X1)
<=> ( leq(X0,X1)
& X0 != X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax93) ).
fof(f429,plain,
! [X0,X1] :
( ~ lt(X0,X1)
| leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f268]) ).
fof(f430,plain,
! [X0,X1] :
( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f268]) ).
fof(f426,plain,
! [X0,X1] :
( ~ geq(X0,X1)
| leq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f266]) ).
fof(f266,plain,
! [X0] :
( ! [X1] :
( ( ( geq(X0,X1)
| ~ leq(X1,X0) )
& ( leq(X1,X0)
| ~ geq(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f124]) ).
fof(f124,plain,
! [X0] :
( ! [X1] :
( ( geq(X0,X1)
<=> leq(X1,X0) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( geq(X0,X1)
<=> leq(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax32) ).
fof(f427,plain,
! [X0,X1] :
( geq(X0,X1)
| ~ leq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f266]) ).
fof(f424,plain,
! [X0,X1] :
( ~ gt(X0,X1)
| lt(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f265]) ).
fof(f265,plain,
! [X0] :
( ! [X1] :
( ( ( gt(X0,X1)
| ~ lt(X1,X0) )
& ( lt(X1,X0)
| ~ gt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f123]) ).
fof(f123,plain,
! [X0] :
( ! [X1] :
( ( gt(X0,X1)
<=> lt(X1,X0) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( gt(X0,X1)
<=> lt(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax35) ).
fof(f425,plain,
! [X0,X1] :
( gt(X0,X1)
| ~ lt(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f265]) ).
fof(f421,plain,
! [X0,X1] :
( ~ leq(X1,X0)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f120]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( ( leq(X1,X0)
& leq(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax29) ).
fof(f420,plain,
! [X0,X1] :
( ~ geq(X1,X0)
| X0 = X1
| ~ geq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f118]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f87]) ).
fof(f87,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( ( geq(X1,X0)
& geq(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax87) ).
fof(f419,plain,
! [X0,X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0] :
( ! [X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f116]) ).
fof(f116,plain,
! [X0] :
( ! [X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( lt(X0,X1)
=> ~ lt(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax33) ).
fof(f418,plain,
! [X0,X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0] :
( ! [X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f114]) ).
fof(f114,plain,
! [X0] :
( ! [X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f92]) ).
fof(f92,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( leq(X0,X1)
=> ( lt(X0,X1)
| X0 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax92) ).
fof(f395,plain,
( nil = sK23
| sP0(sK23,sK22) ),
inference(cnf_transformation,[],[f263]) ).
fof(f396,plain,
( nil = sK22
| sP0(sK23,sK22) ),
inference(cnf_transformation,[],[f263]) ).
fof(f1319,plain,
( nil = sK20
| sK20 = cons(sK26(sK20),sK25(sK20)) ),
inference(resolution,[],[f471,f386]) ).
fof(f1957,plain,
( sK25(sK20) = tl(cons(sK26(sK20),sK25(sK20)))
| ~ spl72_7
| ~ spl72_15 ),
inference(resolution,[],[f1595,f1384]) ).
fof(f1384,plain,
( ssItem(sK26(sK20))
| ~ spl72_7 ),
inference(avatar_component_clause,[],[f1383]) ).
fof(f1383,plain,
( spl72_7
<=> ssItem(sK26(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_7])]) ).
fof(f1595,plain,
( ! [X0] :
( ~ ssItem(X0)
| sK25(sK20) = tl(cons(X0,sK25(sK20))) )
| ~ spl72_15 ),
inference(resolution,[],[f1578,f570]) ).
fof(f1578,plain,
( ssList(sK25(sK20))
| ~ spl72_15 ),
inference(avatar_component_clause,[],[f1577]) ).
fof(f1577,plain,
( spl72_15
<=> ssList(sK25(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_15])]) ).
fof(f1981,plain,
( ~ spl72_2
| ~ spl72_3
| ~ spl72_7
| ~ spl72_11
| ~ spl72_15
| ~ spl72_22
| spl72_26 ),
inference(avatar_contradiction_clause,[],[f1980]) ).
fof(f1980,plain,
( $false
| ~ spl72_2
| ~ spl72_3
| ~ spl72_7
| ~ spl72_11
| ~ spl72_15
| ~ spl72_22
| spl72_26 ),
inference(subsumption_resolution,[],[f1979,f1926]) ).
fof(f1979,plain,
( nil = sK25(sK20)
| ~ spl72_2
| ~ spl72_3
| ~ spl72_7
| ~ spl72_11
| ~ spl72_15
| ~ spl72_22 ),
inference(forward_demodulation,[],[f1978,f1838]) ).
fof(f1978,plain,
( tl(sK20) = sK25(sK20)
| ~ spl72_2
| ~ spl72_3
| ~ spl72_7
| ~ spl72_11
| ~ spl72_15 ),
inference(forward_demodulation,[],[f1951,f1648]) ).
fof(f1648,plain,
( sK20 = cons(hd(sK20),sK25(sK20))
| ~ spl72_2
| ~ spl72_3
| ~ spl72_7
| ~ spl72_15 ),
inference(superposition,[],[f1352,f1647]) ).
fof(f1647,plain,
( hd(sK20) = sK26(sK20)
| ~ spl72_2
| ~ spl72_3
| ~ spl72_7
| ~ spl72_15 ),
inference(forward_demodulation,[],[f1626,f1352]) ).
fof(f1626,plain,
( sK26(sK20) = hd(cons(sK26(sK20),sK25(sK20)))
| ~ spl72_7
| ~ spl72_15 ),
inference(resolution,[],[f1596,f1384]) ).
fof(f1596,plain,
( ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK25(sK20))) = X0 )
| ~ spl72_15 ),
inference(resolution,[],[f1578,f571]) ).
fof(f1951,plain,
( sK25(sK20) = tl(cons(hd(sK20),sK25(sK20)))
| ~ spl72_11
| ~ spl72_15 ),
inference(resolution,[],[f1595,f1485]) ).
fof(f1485,plain,
( ssItem(hd(sK20))
| ~ spl72_11 ),
inference(avatar_component_clause,[],[f1484]) ).
fof(f1484,plain,
( spl72_11
<=> ssItem(hd(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_11])]) ).
fof(f1947,plain,
( ~ spl72_11
| ~ spl72_15
| spl72_28 ),
inference(avatar_contradiction_clause,[],[f1946]) ).
fof(f1946,plain,
( $false
| ~ spl72_11
| ~ spl72_15
| spl72_28 ),
inference(subsumption_resolution,[],[f1945,f1485]) ).
fof(f1945,plain,
( ~ ssItem(hd(sK20))
| ~ spl72_15
| spl72_28 ),
inference(subsumption_resolution,[],[f1944,f1578]) ).
fof(f1944,plain,
( ~ ssList(sK25(sK20))
| ~ ssItem(hd(sK20))
| spl72_28 ),
inference(resolution,[],[f1942,f457]) ).
fof(f1942,plain,
( ~ sP4(hd(sK20),sK25(sK20))
| spl72_28 ),
inference(avatar_component_clause,[],[f1940]) ).
fof(f1940,plain,
( spl72_28
<=> sP4(hd(sK20),sK25(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_28])]) ).
fof(f1943,plain,
( spl72_27
| ~ spl72_28
| ~ spl72_2
| ~ spl72_3
| ~ spl72_7
| ~ spl72_15 ),
inference(avatar_split_clause,[],[f1703,f1577,f1383,f787,f663,f1940,f1936]) ).
fof(f1936,plain,
( spl72_27
<=> sP3(sK25(sK20),hd(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_27])]) ).
fof(f1703,plain,
( ~ sP4(hd(sK20),sK25(sK20))
| sP3(sK25(sK20),hd(sK20))
| ~ spl72_2
| ~ spl72_3
| ~ spl72_7
| ~ spl72_15 ),
inference(forward_demodulation,[],[f1702,f1647]) ).
fof(f1702,plain,
( sP3(sK25(sK20),hd(sK20))
| ~ sP4(sK26(sK20),sK25(sK20))
| ~ spl72_2
| ~ spl72_3
| ~ spl72_7
| ~ spl72_15 ),
inference(forward_demodulation,[],[f1369,f1647]) ).
fof(f1369,plain,
( sP3(sK25(sK20),sK26(sK20))
| ~ sP4(sK26(sK20),sK25(sK20))
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f1362,f802]) ).
fof(f1362,plain,
( ~ strictorderedP(sK20)
| sP3(sK25(sK20),sK26(sK20))
| ~ sP4(sK26(sK20),sK25(sK20))
| ~ spl72_2
| ~ spl72_3 ),
inference(superposition,[],[f450,f1352]) ).
fof(f1928,plain,
( spl72_25
| spl72_26
| ~ spl72_23 ),
inference(avatar_split_clause,[],[f1919,f1907,f1925,f1921]) ).
fof(f1921,plain,
( spl72_25
<=> totalorderedP(sK25(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_25])]) ).
fof(f1907,plain,
( spl72_23
<=> sP1(sK25(sK20),hd(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_23])]) ).
fof(f1919,plain,
( nil = sK25(sK20)
| totalorderedP(sK25(sK20))
| ~ spl72_23 ),
inference(resolution,[],[f1909,f445]) ).
fof(f1909,plain,
( sP1(sK25(sK20),hd(sK20))
| ~ spl72_23 ),
inference(avatar_component_clause,[],[f1907]) ).
fof(f1918,plain,
( ~ spl72_11
| ~ spl72_15
| spl72_24 ),
inference(avatar_contradiction_clause,[],[f1917]) ).
fof(f1917,plain,
( $false
| ~ spl72_11
| ~ spl72_15
| spl72_24 ),
inference(subsumption_resolution,[],[f1916,f1485]) ).
fof(f1916,plain,
( ~ ssItem(hd(sK20))
| ~ spl72_15
| spl72_24 ),
inference(subsumption_resolution,[],[f1915,f1578]) ).
fof(f1915,plain,
( ~ ssList(sK25(sK20))
| ~ ssItem(hd(sK20))
| spl72_24 ),
inference(resolution,[],[f1913,f449]) ).
fof(f1913,plain,
( ~ sP2(hd(sK20),sK25(sK20))
| spl72_24 ),
inference(avatar_component_clause,[],[f1911]) ).
fof(f1911,plain,
( spl72_24
<=> sP2(hd(sK20),sK25(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_24])]) ).
fof(f1914,plain,
( spl72_23
| ~ spl72_24
| ~ spl72_2
| ~ spl72_3
| ~ spl72_7
| ~ spl72_15 ),
inference(avatar_split_clause,[],[f1701,f1577,f1383,f787,f663,f1911,f1907]) ).
fof(f1701,plain,
( ~ sP2(hd(sK20),sK25(sK20))
| sP1(sK25(sK20),hd(sK20))
| ~ spl72_2
| ~ spl72_3
| ~ spl72_7
| ~ spl72_15 ),
inference(forward_demodulation,[],[f1700,f1647]) ).
fof(f1700,plain,
( sP1(sK25(sK20),hd(sK20))
| ~ sP2(sK26(sK20),sK25(sK20))
| ~ spl72_2
| ~ spl72_3
| ~ spl72_7
| ~ spl72_15 ),
inference(forward_demodulation,[],[f1368,f1647]) ).
fof(f1368,plain,
( sP1(sK25(sK20),sK26(sK20))
| ~ sP2(sK26(sK20),sK25(sK20))
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f1360,f803]) ).
fof(f1360,plain,
( ~ totalorderedP(sK20)
| sP1(sK25(sK20),sK26(sK20))
| ~ sP2(sK26(sK20),sK25(sK20))
| ~ spl72_2
| ~ spl72_3 ),
inference(superposition,[],[f442,f1352]) ).
fof(f1887,plain,
( spl72_21
| ~ spl72_22 ),
inference(avatar_contradiction_clause,[],[f1886]) ).
fof(f1886,plain,
( $false
| spl72_21
| ~ spl72_22 ),
inference(subsumption_resolution,[],[f1880,f404]) ).
fof(f1880,plain,
( ~ totalorderedP(nil)
| spl72_21
| ~ spl72_22 ),
inference(superposition,[],[f1833,f1838]) ).
fof(f1833,plain,
( ~ totalorderedP(tl(sK20))
| spl72_21 ),
inference(avatar_component_clause,[],[f1832]) ).
fof(f1832,plain,
( spl72_21
<=> totalorderedP(tl(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_21])]) ).
fof(f1839,plain,
( spl72_21
| spl72_22
| ~ spl72_20 ),
inference(avatar_split_clause,[],[f1830,f1820,f1836,f1832]) ).
fof(f1820,plain,
( spl72_20
<=> sP1(tl(sK20),hd(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_20])]) ).
fof(f1830,plain,
( nil = tl(sK20)
| totalorderedP(tl(sK20))
| ~ spl72_20 ),
inference(resolution,[],[f1822,f445]) ).
fof(f1822,plain,
( sP1(tl(sK20),hd(sK20))
| ~ spl72_20 ),
inference(avatar_component_clause,[],[f1820]) ).
fof(f1829,plain,
( ~ spl72_2
| ~ spl72_3
| ~ spl72_11
| spl72_19 ),
inference(avatar_contradiction_clause,[],[f1828]) ).
fof(f1828,plain,
( $false
| ~ spl72_2
| ~ spl72_3
| ~ spl72_11
| spl72_19 ),
inference(subsumption_resolution,[],[f1827,f386]) ).
fof(f1827,plain,
( ~ ssList(sK20)
| ~ spl72_2
| ~ spl72_3
| ~ spl72_11
| spl72_19 ),
inference(subsumption_resolution,[],[f1826,f804]) ).
fof(f1826,plain,
( nil = sK20
| ~ ssList(sK20)
| ~ spl72_11
| spl72_19 ),
inference(resolution,[],[f1825,f473]) ).
fof(f1825,plain,
( ~ ssList(tl(sK20))
| ~ spl72_11
| spl72_19 ),
inference(subsumption_resolution,[],[f1824,f1485]) ).
fof(f1824,plain,
( ~ ssList(tl(sK20))
| ~ ssItem(hd(sK20))
| spl72_19 ),
inference(resolution,[],[f1818,f449]) ).
fof(f1818,plain,
( ~ sP2(hd(sK20),tl(sK20))
| spl72_19 ),
inference(avatar_component_clause,[],[f1816]) ).
fof(f1816,plain,
( spl72_19
<=> sP2(hd(sK20),tl(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_19])]) ).
fof(f1823,plain,
( ~ spl72_19
| spl72_20
| ~ spl72_2
| ~ spl72_3 ),
inference(avatar_split_clause,[],[f1469,f787,f663,f1820,f1816]) ).
fof(f1469,plain,
( sP1(tl(sK20),hd(sK20))
| ~ sP2(hd(sK20),tl(sK20))
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f1461,f803]) ).
fof(f1461,plain,
( ~ totalorderedP(sK20)
| sP1(tl(sK20),hd(sK20))
| ~ sP2(hd(sK20),tl(sK20))
| ~ spl72_2
| ~ spl72_3 ),
inference(superposition,[],[f442,f1453]) ).
fof(f1453,plain,
( sK20 = cons(hd(sK20),tl(sK20))
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f1420,f804]) ).
fof(f1420,plain,
( nil = sK20
| sK20 = cons(hd(sK20),tl(sK20)) ),
inference(resolution,[],[f474,f386]) ).
fof(f1717,plain,
( spl72_1
| spl72_17 ),
inference(avatar_contradiction_clause,[],[f1716]) ).
fof(f1716,plain,
( $false
| spl72_1
| spl72_17 ),
inference(subsumption_resolution,[],[f1715,f387]) ).
fof(f1715,plain,
( ~ ssList(sK21)
| spl72_1
| spl72_17 ),
inference(subsumption_resolution,[],[f1714,f660]) ).
fof(f660,plain,
( nil != sK21
| spl72_1 ),
inference(avatar_component_clause,[],[f659]) ).
fof(f659,plain,
( spl72_1
<=> nil = sK21 ),
introduced(avatar_definition,[new_symbols(naming,[spl72_1])]) ).
fof(f1714,plain,
( nil = sK21
| ~ ssList(sK21)
| spl72_17 ),
inference(resolution,[],[f1708,f469]) ).
fof(f1708,plain,
( ~ ssList(sK25(sK21))
| spl72_17 ),
inference(avatar_component_clause,[],[f1706]) ).
fof(f1706,plain,
( spl72_17
<=> ssList(sK25(sK21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_17])]) ).
fof(f1713,plain,
( ~ spl72_17
| spl72_18
| spl72_1
| ~ spl72_9 ),
inference(avatar_split_clause,[],[f1704,f1400,f659,f1710,f1706]) ).
fof(f1710,plain,
( spl72_18
<=> memberP(sK21,sK26(sK21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_18])]) ).
fof(f1400,plain,
( spl72_9
<=> ssItem(sK26(sK21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_9])]) ).
fof(f1704,plain,
( memberP(sK21,sK26(sK21))
| ~ ssList(sK25(sK21))
| spl72_1
| ~ spl72_9 ),
inference(subsumption_resolution,[],[f1379,f1401]) ).
fof(f1401,plain,
( ssItem(sK26(sK21))
| ~ spl72_9 ),
inference(avatar_component_clause,[],[f1400]) ).
fof(f1379,plain,
( memberP(sK21,sK26(sK21))
| ~ ssList(sK25(sK21))
| ~ ssItem(sK26(sK21))
| spl72_1 ),
inference(superposition,[],[f644,f1353]) ).
fof(f1353,plain,
( sK21 = cons(sK26(sK21),sK25(sK21))
| spl72_1 ),
inference(subsumption_resolution,[],[f1320,f660]) ).
fof(f1320,plain,
( nil = sK21
| sK21 = cons(sK26(sK21),sK25(sK21)) ),
inference(resolution,[],[f471,f387]) ).
fof(f1588,plain,
( ~ spl72_2
| ~ spl72_3
| spl72_15 ),
inference(avatar_contradiction_clause,[],[f1587]) ).
fof(f1587,plain,
( $false
| ~ spl72_2
| ~ spl72_3
| spl72_15 ),
inference(subsumption_resolution,[],[f1586,f386]) ).
fof(f1586,plain,
( ~ ssList(sK20)
| ~ spl72_2
| ~ spl72_3
| spl72_15 ),
inference(subsumption_resolution,[],[f1585,f804]) ).
fof(f1585,plain,
( nil = sK20
| ~ ssList(sK20)
| spl72_15 ),
inference(resolution,[],[f1579,f469]) ).
fof(f1579,plain,
( ~ ssList(sK25(sK20))
| spl72_15 ),
inference(avatar_component_clause,[],[f1577]) ).
fof(f1584,plain,
( ~ spl72_15
| spl72_16
| ~ spl72_2
| ~ spl72_3
| ~ spl72_7 ),
inference(avatar_split_clause,[],[f1575,f1383,f787,f663,f1581,f1577]) ).
fof(f1581,plain,
( spl72_16
<=> memberP(sK20,sK26(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_16])]) ).
fof(f1575,plain,
( memberP(sK20,sK26(sK20))
| ~ ssList(sK25(sK20))
| ~ spl72_2
| ~ spl72_3
| ~ spl72_7 ),
inference(subsumption_resolution,[],[f1367,f1384]) ).
fof(f1367,plain,
( memberP(sK20,sK26(sK20))
| ~ ssList(sK25(sK20))
| ~ ssItem(sK26(sK20))
| ~ spl72_2
| ~ spl72_3 ),
inference(superposition,[],[f644,f1352]) ).
fof(f1512,plain,
( spl72_1
| spl72_13 ),
inference(avatar_contradiction_clause,[],[f1511]) ).
fof(f1511,plain,
( $false
| spl72_1
| spl72_13 ),
inference(subsumption_resolution,[],[f1510,f387]) ).
fof(f1510,plain,
( ~ ssList(sK21)
| spl72_1
| spl72_13 ),
inference(subsumption_resolution,[],[f1509,f660]) ).
fof(f1509,plain,
( nil = sK21
| ~ ssList(sK21)
| spl72_13 ),
inference(resolution,[],[f1503,f472]) ).
fof(f1503,plain,
( ~ ssItem(hd(sK21))
| spl72_13 ),
inference(avatar_component_clause,[],[f1501]) ).
fof(f1501,plain,
( spl72_13
<=> ssItem(hd(sK21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_13])]) ).
fof(f1508,plain,
( ~ spl72_13
| ~ spl72_14
| spl72_1 ),
inference(avatar_split_clause,[],[f1482,f659,f1505,f1501]) ).
fof(f1505,plain,
( spl72_14
<=> sK21 = tl(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_14])]) ).
fof(f1482,plain,
( sK21 != tl(sK21)
| ~ ssItem(hd(sK21))
| spl72_1 ),
inference(subsumption_resolution,[],[f1481,f387]) ).
fof(f1481,plain,
( sK21 != tl(sK21)
| ~ ssItem(hd(sK21))
| ~ ssList(sK21)
| spl72_1 ),
inference(inner_rewriting,[],[f1479]) ).
fof(f1479,plain,
( sK21 != tl(sK21)
| ~ ssItem(hd(sK21))
| ~ ssList(tl(sK21))
| spl72_1 ),
inference(superposition,[],[f569,f1454]) ).
fof(f1454,plain,
( sK21 = cons(hd(sK21),tl(sK21))
| spl72_1 ),
inference(subsumption_resolution,[],[f1421,f660]) ).
fof(f1421,plain,
( nil = sK21
| sK21 = cons(hd(sK21),tl(sK21)) ),
inference(resolution,[],[f474,f387]) ).
fof(f1495,plain,
( ~ spl72_2
| ~ spl72_3
| spl72_11 ),
inference(avatar_contradiction_clause,[],[f1494]) ).
fof(f1494,plain,
( $false
| ~ spl72_2
| ~ spl72_3
| spl72_11 ),
inference(subsumption_resolution,[],[f1493,f386]) ).
fof(f1493,plain,
( ~ ssList(sK20)
| ~ spl72_2
| ~ spl72_3
| spl72_11 ),
inference(subsumption_resolution,[],[f1492,f804]) ).
fof(f1492,plain,
( nil = sK20
| ~ ssList(sK20)
| spl72_11 ),
inference(resolution,[],[f1486,f472]) ).
fof(f1486,plain,
( ~ ssItem(hd(sK20))
| spl72_11 ),
inference(avatar_component_clause,[],[f1484]) ).
fof(f1491,plain,
( ~ spl72_11
| ~ spl72_12
| ~ spl72_2
| ~ spl72_3 ),
inference(avatar_split_clause,[],[f1472,f787,f663,f1488,f1484]) ).
fof(f1488,plain,
( spl72_12
<=> sK20 = tl(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_12])]) ).
fof(f1472,plain,
( sK20 != tl(sK20)
| ~ ssItem(hd(sK20))
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f1471,f386]) ).
fof(f1471,plain,
( sK20 != tl(sK20)
| ~ ssItem(hd(sK20))
| ~ ssList(sK20)
| ~ spl72_2
| ~ spl72_3 ),
inference(inner_rewriting,[],[f1467]) ).
fof(f1467,plain,
( sK20 != tl(sK20)
| ~ ssItem(hd(sK20))
| ~ ssList(tl(sK20))
| ~ spl72_2
| ~ spl72_3 ),
inference(superposition,[],[f569,f1453]) ).
fof(f1411,plain,
( spl72_1
| spl72_9 ),
inference(avatar_contradiction_clause,[],[f1410]) ).
fof(f1410,plain,
( $false
| spl72_1
| spl72_9 ),
inference(subsumption_resolution,[],[f1409,f387]) ).
fof(f1409,plain,
( ~ ssList(sK21)
| spl72_1
| spl72_9 ),
inference(subsumption_resolution,[],[f1408,f660]) ).
fof(f1408,plain,
( nil = sK21
| ~ ssList(sK21)
| spl72_9 ),
inference(resolution,[],[f1402,f470]) ).
fof(f1402,plain,
( ~ ssItem(sK26(sK21))
| spl72_9 ),
inference(avatar_component_clause,[],[f1400]) ).
fof(f1407,plain,
( ~ spl72_9
| ~ spl72_10
| spl72_1 ),
inference(avatar_split_clause,[],[f1381,f659,f1404,f1400]) ).
fof(f1404,plain,
( spl72_10
<=> sK21 = sK25(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_10])]) ).
fof(f1381,plain,
( sK21 != sK25(sK21)
| ~ ssItem(sK26(sK21))
| spl72_1 ),
inference(subsumption_resolution,[],[f1380,f387]) ).
fof(f1380,plain,
( sK21 != sK25(sK21)
| ~ ssItem(sK26(sK21))
| ~ ssList(sK21)
| spl72_1 ),
inference(inner_rewriting,[],[f1378]) ).
fof(f1378,plain,
( sK21 != sK25(sK21)
| ~ ssItem(sK26(sK21))
| ~ ssList(sK25(sK21))
| spl72_1 ),
inference(superposition,[],[f569,f1353]) ).
fof(f1394,plain,
( ~ spl72_2
| ~ spl72_3
| spl72_7 ),
inference(avatar_contradiction_clause,[],[f1393]) ).
fof(f1393,plain,
( $false
| ~ spl72_2
| ~ spl72_3
| spl72_7 ),
inference(subsumption_resolution,[],[f1392,f386]) ).
fof(f1392,plain,
( ~ ssList(sK20)
| ~ spl72_2
| ~ spl72_3
| spl72_7 ),
inference(subsumption_resolution,[],[f1391,f804]) ).
fof(f1391,plain,
( nil = sK20
| ~ ssList(sK20)
| spl72_7 ),
inference(resolution,[],[f1385,f470]) ).
fof(f1385,plain,
( ~ ssItem(sK26(sK20))
| spl72_7 ),
inference(avatar_component_clause,[],[f1383]) ).
fof(f1390,plain,
( ~ spl72_7
| ~ spl72_8
| ~ spl72_2
| ~ spl72_3 ),
inference(avatar_split_clause,[],[f1371,f787,f663,f1387,f1383]) ).
fof(f1387,plain,
( spl72_8
<=> sK20 = sK25(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_8])]) ).
fof(f1371,plain,
( sK20 != sK25(sK20)
| ~ ssItem(sK26(sK20))
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f1370,f386]) ).
fof(f1370,plain,
( sK20 != sK25(sK20)
| ~ ssItem(sK26(sK20))
| ~ ssList(sK20)
| ~ spl72_2
| ~ spl72_3 ),
inference(inner_rewriting,[],[f1366]) ).
fof(f1366,plain,
( sK20 != sK25(sK20)
| ~ ssItem(sK26(sK20))
| ~ ssList(sK25(sK20))
| ~ spl72_2
| ~ spl72_3 ),
inference(superposition,[],[f569,f1352]) ).
fof(f1138,plain,
~ spl72_1,
inference(avatar_contradiction_clause,[],[f1137]) ).
fof(f1137,plain,
( $false
| ~ spl72_1 ),
inference(subsumption_resolution,[],[f1124,f1113]) ).
fof(f1113,plain,
( ~ memberP(nil,sK24)
| ~ spl72_1 ),
inference(superposition,[],[f394,f661]) ).
fof(f661,plain,
( nil = sK21
| ~ spl72_1 ),
inference(avatar_component_clause,[],[f659]) ).
fof(f1124,plain,
( memberP(nil,sK24)
| ~ spl72_1 ),
inference(superposition,[],[f393,f1122]) ).
fof(f1122,plain,
( nil = sK20
| ~ spl72_1 ),
inference(subsumption_resolution,[],[f1121,f735]) ).
fof(f1121,plain,
( sP0(nil,sK20)
| nil = sK20
| ~ spl72_1 ),
inference(forward_demodulation,[],[f657,f661]) ).
fof(f1106,plain,
( ~ spl72_2
| ~ spl72_3
| spl72_5 ),
inference(avatar_contradiction_clause,[],[f1105]) ).
fof(f1105,plain,
( $false
| ~ spl72_2
| ~ spl72_3
| spl72_5 ),
inference(subsumption_resolution,[],[f1104,f386]) ).
fof(f1104,plain,
( ~ ssList(sK20)
| ~ spl72_2
| ~ spl72_3
| spl72_5 ),
inference(subsumption_resolution,[],[f1103,f1065]) ).
fof(f1065,plain,
( singletonP(sK20)
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f1064,f386]) ).
fof(f1064,plain,
( ~ ssList(sK20)
| singletonP(sK20)
| ~ spl72_2
| ~ spl72_3 ),
inference(forward_demodulation,[],[f1063,f769]) ).
fof(f1063,plain,
( singletonP(sK20)
| ~ ssList(cons(sK19(sK21,sK20),nil))
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f1061,f788]) ).
fof(f1061,plain,
( singletonP(sK20)
| ~ ssItem(sK19(sK21,sK20))
| ~ ssList(cons(sK19(sK21,sK20),nil))
| ~ spl72_2 ),
inference(superposition,[],[f622,f769]) ).
fof(f1103,plain,
( ~ singletonP(sK20)
| ~ ssList(sK20)
| spl72_5 ),
inference(resolution,[],[f1097,f479]) ).
fof(f1097,plain,
( ~ ssItem(sK29(sK20))
| spl72_5 ),
inference(avatar_component_clause,[],[f1095]) ).
fof(f1095,plain,
( spl72_5
<=> ssItem(sK29(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_5])]) ).
fof(f1102,plain,
( ~ spl72_5
| spl72_6
| ~ spl72_2
| ~ spl72_3 ),
inference(avatar_split_clause,[],[f1093,f787,f663,f1099,f1095]) ).
fof(f1099,plain,
( spl72_6
<=> memberP(sK20,sK29(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_6])]) ).
fof(f1093,plain,
( memberP(sK20,sK29(sK20))
| ~ ssItem(sK29(sK20))
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f1092,f405]) ).
fof(f1092,plain,
( memberP(sK20,sK29(sK20))
| ~ ssList(nil)
| ~ ssItem(sK29(sK20))
| ~ spl72_2
| ~ spl72_3 ),
inference(superposition,[],[f644,f1067]) ).
fof(f1067,plain,
( sK20 = cons(sK29(sK20),nil)
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f1066,f386]) ).
fof(f1066,plain,
( sK20 = cons(sK29(sK20),nil)
| ~ ssList(sK20)
| ~ spl72_2
| ~ spl72_3 ),
inference(resolution,[],[f1065,f480]) ).
fof(f797,plain,
( ~ spl72_2
| spl72_3 ),
inference(avatar_contradiction_clause,[],[f796]) ).
fof(f796,plain,
( $false
| ~ spl72_2
| spl72_3 ),
inference(subsumption_resolution,[],[f795,f665]) ).
fof(f795,plain,
( ~ sP0(sK21,sK20)
| spl72_3 ),
inference(resolution,[],[f789,f383]) ).
fof(f789,plain,
( ~ ssItem(sK19(sK21,sK20))
| spl72_3 ),
inference(avatar_component_clause,[],[f787]) ).
fof(f794,plain,
( ~ spl72_3
| spl72_4
| ~ spl72_2 ),
inference(avatar_split_clause,[],[f770,f663,f791,f787]) ).
fof(f791,plain,
( spl72_4
<=> equalelemsP(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_4])]) ).
fof(f666,plain,
( spl72_1
| spl72_2 ),
inference(avatar_split_clause,[],[f654,f663,f659]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC407+1 : TPTP v8.1.2. Released v2.4.0.
% 0.13/0.14 % 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 : Fri May 3 20:25:38 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (31609)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (31610)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.39 % (31612)WARNING: value z3 for option sas not known
% 0.14/0.39 % (31613)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.39 % (31616)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)
% 0.14/0.39 % (31611)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.39 % (31614)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)
% 0.14/0.39 % (31615)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)
% 0.14/0.39 % (31612)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)
% 0.14/0.40 TRYING [1]
% 0.14/0.40 TRYING [2]
% 0.14/0.41 TRYING [3]
% 0.14/0.42 TRYING [1]
% 0.14/0.42 TRYING [2]
% 0.22/0.43 TRYING [3]
% 0.22/0.48 TRYING [4]
% 0.22/0.48 TRYING [4]
% 0.22/0.54 TRYING [1]
% 0.22/0.54 TRYING [2]
% 0.22/0.56 TRYING [3]
% 1.54/0.57 % (31612)First to succeed.
% 1.67/0.58 % (31612)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-31609"
% 1.67/0.59 % (31612)Refutation found. Thanks to Tanya!
% 1.67/0.59 % SZS status Theorem for theBenchmark
% 1.67/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 1.67/0.59 % (31612)------------------------------
% 1.67/0.59 % (31612)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.67/0.59 % (31612)Termination reason: Refutation
% 1.67/0.59
% 1.67/0.59 % (31612)Memory used [KB]: 3727
% 1.67/0.59 % (31612)Time elapsed: 0.194 s
% 1.67/0.59 % (31612)Instructions burned: 406 (million)
% 1.67/0.59 % (31609)Success in time 0.232 s
%------------------------------------------------------------------------------