TSTP Solution File: NUM845+2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM845+2 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -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 : Fri Sep 1 20:40:39 EDT 2023
% Result : Theorem 0.21s 0.44s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 32
% Syntax : Number of formulae : 120 ( 30 unt; 0 def)
% Number of atoms : 290 ( 152 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 306 ( 136 ~; 129 |; 8 &)
% ( 20 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 22 ( 20 usr; 21 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 105 (; 103 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f272,plain,
$false,
inference(avatar_sat_refutation,[],[f64,f69,f73,f77,f81,f85,f104,f108,f120,f135,f168,f172,f179,f203,f213,f239,f248,f261,f266,f270,f271]) ).
fof(f271,plain,
( spl1_19
| ~ spl1_6
| ~ spl1_7
| ~ spl1_13
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f235,f211,f177,f101,f83,f263]) ).
fof(f263,plain,
( spl1_19
<=> vmul(vsucc(vd411),vsucc(sK0)) = vsucc(vplus(sK0,vmul(vd411,vsucc(sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_19])]) ).
fof(f83,plain,
( spl1_6
<=> ! [X0,X1] : vplus(X1,X0) = vplus(X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).
fof(f101,plain,
( spl1_7
<=> vmul(vsucc(vd411),sK0) = vplus(sK0,vmul(vd411,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_7])]) ).
fof(f177,plain,
( spl1_13
<=> ! [X0] :
( vmul(vsucc(vd411),X0) != vplus(X0,vmul(vd411,X0))
| vmul(vsucc(vd411),vsucc(X0)) = vplus(vmul(vd411,X0),vsucc(vplus(X0,vd411))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_13])]) ).
fof(f211,plain,
( spl1_15
<=> ! [X0] :
( vmul(vsucc(vd411),X0) != vplus(X0,vmul(vd411,X0))
| vplus(vmul(vd411,X0),vsucc(vplus(vd411,X0))) = vsucc(vplus(X0,vmul(vd411,vsucc(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_15])]) ).
fof(f235,plain,
( vmul(vsucc(vd411),vsucc(sK0)) = vsucc(vplus(sK0,vmul(vd411,vsucc(sK0))))
| ~ spl1_6
| ~ spl1_7
| ~ spl1_13
| ~ spl1_15 ),
inference(forward_demodulation,[],[f234,f199]) ).
fof(f199,plain,
( vmul(vsucc(vd411),vsucc(sK0)) = vplus(vmul(vd411,sK0),vsucc(vplus(sK0,vd411)))
| ~ spl1_7
| ~ spl1_13 ),
inference(trivial_inequality_removal,[],[f197]) ).
fof(f197,plain,
( vmul(vsucc(vd411),sK0) != vmul(vsucc(vd411),sK0)
| vmul(vsucc(vd411),vsucc(sK0)) = vplus(vmul(vd411,sK0),vsucc(vplus(sK0,vd411)))
| ~ spl1_7
| ~ spl1_13 ),
inference(superposition,[],[f178,f103]) ).
fof(f103,plain,
( vmul(vsucc(vd411),sK0) = vplus(sK0,vmul(vd411,sK0))
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f178,plain,
( ! [X0] :
( vmul(vsucc(vd411),X0) != vplus(X0,vmul(vd411,X0))
| vmul(vsucc(vd411),vsucc(X0)) = vplus(vmul(vd411,X0),vsucc(vplus(X0,vd411))) )
| ~ spl1_13 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f234,plain,
( vsucc(vplus(sK0,vmul(vd411,vsucc(sK0)))) = vplus(vmul(vd411,sK0),vsucc(vplus(sK0,vd411)))
| ~ spl1_6
| ~ spl1_7
| ~ spl1_15 ),
inference(forward_demodulation,[],[f218,f84]) ).
fof(f84,plain,
( ! [X0,X1] : vplus(X1,X0) = vplus(X0,X1)
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f218,plain,
( vsucc(vplus(sK0,vmul(vd411,vsucc(sK0)))) = vplus(vmul(vd411,sK0),vsucc(vplus(vd411,sK0)))
| ~ spl1_7
| ~ spl1_15 ),
inference(trivial_inequality_removal,[],[f217]) ).
fof(f217,plain,
( vmul(vsucc(vd411),sK0) != vmul(vsucc(vd411),sK0)
| vsucc(vplus(sK0,vmul(vd411,vsucc(sK0)))) = vplus(vmul(vd411,sK0),vsucc(vplus(vd411,sK0)))
| ~ spl1_7
| ~ spl1_15 ),
inference(superposition,[],[f212,f103]) ).
fof(f212,plain,
( ! [X0] :
( vmul(vsucc(vd411),X0) != vplus(X0,vmul(vd411,X0))
| vplus(vmul(vd411,X0),vsucc(vplus(vd411,X0))) = vsucc(vplus(X0,vmul(vd411,vsucc(X0)))) )
| ~ spl1_15 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f270,plain,
( spl1_20
| ~ spl1_1
| ~ spl1_10 ),
inference(avatar_split_clause,[],[f140,f133,f61,f268]) ).
fof(f268,plain,
( spl1_20
<=> ! [X11] : vplus(vmul(vd411,sK0),vplus(sK0,X11)) = vplus(vmul(vsucc(vd411),sK0),X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_20])]) ).
fof(f61,plain,
( spl1_1
<=> vmul(vsucc(vd411),sK0) = vplus(vmul(vd411,sK0),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).
fof(f133,plain,
( spl1_10
<=> ! [X2,X0,X1] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_10])]) ).
fof(f140,plain,
( ! [X11] : vplus(vmul(vd411,sK0),vplus(sK0,X11)) = vplus(vmul(vsucc(vd411),sK0),X11)
| ~ spl1_1
| ~ spl1_10 ),
inference(superposition,[],[f134,f63]) ).
fof(f63,plain,
( vmul(vsucc(vd411),sK0) = vplus(vmul(vd411,sK0),sK0)
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f134,plain,
( ! [X2,X0,X1] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2))
| ~ spl1_10 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f266,plain,
( ~ spl1_19
| spl1_2
| ~ spl1_6
| ~ spl1_8 ),
inference(avatar_split_clause,[],[f116,f106,f83,f66,f263]) ).
fof(f66,plain,
( spl1_2
<=> vmul(vsucc(vd411),vsucc(sK0)) = vplus(vmul(vd411,vsucc(sK0)),vsucc(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).
fof(f106,plain,
( spl1_8
<=> ! [X0,X1] : vplus(X0,vsucc(X1)) = vsucc(vplus(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_8])]) ).
fof(f116,plain,
( vmul(vsucc(vd411),vsucc(sK0)) != vsucc(vplus(sK0,vmul(vd411,vsucc(sK0))))
| spl1_2
| ~ spl1_6
| ~ spl1_8 ),
inference(forward_demodulation,[],[f112,f84]) ).
fof(f112,plain,
( vmul(vsucc(vd411),vsucc(sK0)) != vsucc(vplus(vmul(vd411,vsucc(sK0)),sK0))
| spl1_2
| ~ spl1_8 ),
inference(superposition,[],[f68,f107]) ).
fof(f107,plain,
( ! [X0,X1] : vplus(X0,vsucc(X1)) = vsucc(vplus(X0,X1))
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f68,plain,
( vmul(vsucc(vd411),vsucc(sK0)) != vplus(vmul(vd411,vsucc(sK0)),vsucc(sK0))
| spl1_2 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f261,plain,
( ~ spl1_18
| spl1_2
| ~ spl1_6 ),
inference(avatar_split_clause,[],[f93,f83,f66,f258]) ).
fof(f258,plain,
( spl1_18
<=> vmul(vsucc(vd411),vsucc(sK0)) = vplus(vsucc(sK0),vmul(vd411,vsucc(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_18])]) ).
fof(f93,plain,
( vmul(vsucc(vd411),vsucc(sK0)) != vplus(vsucc(sK0),vmul(vd411,vsucc(sK0)))
| spl1_2
| ~ spl1_6 ),
inference(superposition,[],[f68,f84]) ).
fof(f248,plain,
spl1_17,
inference(avatar_split_clause,[],[f51,f246]) ).
fof(f246,plain,
( spl1_17
<=> ! [X0] :
( vplus(vmul(vd411,X0),vplus(vsucc(vd411),X0)) = vplus(vmul(vd411,X0),vplus(X0,vsucc(vd411)))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_17])]) ).
fof(f51,plain,
! [X0] :
( vplus(vmul(vd411,X0),vplus(vsucc(vd411),X0)) = vplus(vmul(vd411,X0),vplus(X0,vsucc(vd411)))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0] :
( vplus(vmul(vd411,X0),vplus(vsucc(vd411),X0)) = vplus(vmul(vd411,X0),vplus(X0,vsucc(vd411)))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0] :
( vmul(vsucc(vd411),X0) = vplus(vmul(vd411,X0),X0)
=> vplus(vmul(vd411,X0),vplus(vsucc(vd411),X0)) = vplus(vmul(vd411,X0),vplus(X0,vsucc(vd411))) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1] :
( vmul(vsucc(vd411),X1) = vplus(vmul(vd411,X1),X1)
=> vplus(vmul(vd411,X1),vplus(vsucc(vd411),X1)) = vplus(vmul(vd411,X1),vplus(X1,vsucc(vd411))) ),
file('/export/starexec/sandbox2/tmp/tmp.oNnbrs1EEg/Vampire---4.8_15442','ass(cond(conseq(263), 1), 4)') ).
fof(f239,plain,
spl1_16,
inference(avatar_split_clause,[],[f50,f237]) ).
fof(f237,plain,
( spl1_16
<=> ! [X0] :
( vplus(vmul(vd411,X0),vsucc(vplus(vd411,X0))) = vplus(vmul(vd411,X0),vplus(vd411,vsucc(X0)))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_16])]) ).
fof(f50,plain,
! [X0] :
( vplus(vmul(vd411,X0),vsucc(vplus(vd411,X0))) = vplus(vmul(vd411,X0),vplus(vd411,vsucc(X0)))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0] :
( vplus(vmul(vd411,X0),vsucc(vplus(vd411,X0))) = vplus(vmul(vd411,X0),vplus(vd411,vsucc(X0)))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0] :
( vmul(vsucc(vd411),X0) = vplus(vmul(vd411,X0),X0)
=> vplus(vmul(vd411,X0),vsucc(vplus(vd411,X0))) = vplus(vmul(vd411,X0),vplus(vd411,vsucc(X0))) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1] :
( vmul(vsucc(vd411),X1) = vplus(vmul(vd411,X1),X1)
=> vplus(vmul(vd411,X1),vplus(vd411,vsucc(X1))) = vplus(vmul(vd411,X1),vsucc(vplus(vd411,X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.oNnbrs1EEg/Vampire---4.8_15442','ass(cond(conseq(263), 1), 2)') ).
fof(f213,plain,
( spl1_15
| ~ spl1_6
| ~ spl1_8
| ~ spl1_9
| ~ spl1_10
| ~ spl1_14 ),
inference(avatar_split_clause,[],[f209,f201,f133,f118,f106,f83,f211]) ).
fof(f118,plain,
( spl1_9
<=> ! [X0,X1] : vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_9])]) ).
fof(f201,plain,
( spl1_14
<=> ! [X0] :
( vplus(vmul(vd411,X0),vsucc(vplus(vd411,X0))) = vplus(vmul(vd411,X0),vplus(vsucc(vd411),X0))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_14])]) ).
fof(f209,plain,
( ! [X0] :
( vmul(vsucc(vd411),X0) != vplus(X0,vmul(vd411,X0))
| vplus(vmul(vd411,X0),vsucc(vplus(vd411,X0))) = vsucc(vplus(X0,vmul(vd411,vsucc(X0)))) )
| ~ spl1_6
| ~ spl1_8
| ~ spl1_9
| ~ spl1_10
| ~ spl1_14 ),
inference(forward_demodulation,[],[f208,f84]) ).
fof(f208,plain,
( ! [X0] :
( vplus(vmul(vd411,X0),vsucc(vplus(vd411,X0))) = vsucc(vplus(X0,vmul(vd411,vsucc(X0))))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) )
| ~ spl1_6
| ~ spl1_8
| ~ spl1_9
| ~ spl1_10
| ~ spl1_14 ),
inference(forward_demodulation,[],[f207,f119]) ).
fof(f119,plain,
( ! [X0,X1] : vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0)
| ~ spl1_9 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f207,plain,
( ! [X0] :
( vplus(vmul(vd411,X0),vsucc(vplus(vd411,X0))) = vsucc(vplus(X0,vplus(vmul(vd411,X0),vd411)))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) )
| ~ spl1_6
| ~ spl1_8
| ~ spl1_10
| ~ spl1_14 ),
inference(forward_demodulation,[],[f206,f107]) ).
fof(f206,plain,
( ! [X0] :
( vplus(vmul(vd411,X0),vsucc(vplus(vd411,X0))) = vplus(X0,vsucc(vplus(vmul(vd411,X0),vd411)))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) )
| ~ spl1_6
| ~ spl1_8
| ~ spl1_10
| ~ spl1_14 ),
inference(forward_demodulation,[],[f205,f110]) ).
fof(f110,plain,
( ! [X3,X4] : vplus(vsucc(X4),X3) = vsucc(vplus(X3,X4))
| ~ spl1_6
| ~ spl1_8 ),
inference(superposition,[],[f107,f84]) ).
fof(f205,plain,
( ! [X0] :
( vplus(vmul(vd411,X0),vsucc(vplus(vd411,X0))) = vplus(X0,vplus(vsucc(vd411),vmul(vd411,X0)))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) )
| ~ spl1_6
| ~ spl1_10
| ~ spl1_14 ),
inference(forward_demodulation,[],[f204,f84]) ).
fof(f204,plain,
( ! [X0] :
( vplus(vmul(vd411,X0),vsucc(vplus(vd411,X0))) = vplus(X0,vplus(vmul(vd411,X0),vsucc(vd411)))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) )
| ~ spl1_6
| ~ spl1_10
| ~ spl1_14 ),
inference(forward_demodulation,[],[f202,f145]) ).
fof(f145,plain,
( ! [X6,X7,X5] : vplus(X5,vplus(X6,X7)) = vplus(X7,vplus(X5,X6))
| ~ spl1_6
| ~ spl1_10 ),
inference(superposition,[],[f134,f84]) ).
fof(f202,plain,
( ! [X0] :
( vplus(vmul(vd411,X0),vsucc(vplus(vd411,X0))) = vplus(vmul(vd411,X0),vplus(vsucc(vd411),X0))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) )
| ~ spl1_14 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f203,plain,
spl1_14,
inference(avatar_split_clause,[],[f48,f201]) ).
fof(f48,plain,
! [X0] :
( vplus(vmul(vd411,X0),vsucc(vplus(vd411,X0))) = vplus(vmul(vd411,X0),vplus(vsucc(vd411),X0))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0] :
( vplus(vmul(vd411,X0),vsucc(vplus(vd411,X0))) = vplus(vmul(vd411,X0),vplus(vsucc(vd411),X0))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0] :
( vmul(vsucc(vd411),X0) = vplus(vmul(vd411,X0),X0)
=> vplus(vmul(vd411,X0),vsucc(vplus(vd411,X0))) = vplus(vmul(vd411,X0),vplus(vsucc(vd411),X0)) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X1] :
( vmul(vsucc(vd411),X1) = vplus(vmul(vd411,X1),X1)
=> vplus(vmul(vd411,X1),vsucc(vplus(vd411,X1))) = vplus(vmul(vd411,X1),vplus(vsucc(vd411),X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.oNnbrs1EEg/Vampire---4.8_15442','ass(cond(conseq(263), 1), 3)') ).
fof(f179,plain,
( spl1_13
| ~ spl1_6
| ~ spl1_8
| ~ spl1_9
| ~ spl1_12 ),
inference(avatar_split_clause,[],[f175,f170,f118,f106,f83,f177]) ).
fof(f170,plain,
( spl1_12
<=> ! [X0] :
( vplus(vmul(vsucc(vd411),X0),vsucc(vd411)) = vplus(vmul(vd411,X0),vplus(X0,vsucc(vd411)))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_12])]) ).
fof(f175,plain,
( ! [X0] :
( vmul(vsucc(vd411),X0) != vplus(X0,vmul(vd411,X0))
| vmul(vsucc(vd411),vsucc(X0)) = vplus(vmul(vd411,X0),vsucc(vplus(X0,vd411))) )
| ~ spl1_6
| ~ spl1_8
| ~ spl1_9
| ~ spl1_12 ),
inference(forward_demodulation,[],[f174,f84]) ).
fof(f174,plain,
( ! [X0] :
( vmul(vsucc(vd411),vsucc(X0)) = vplus(vmul(vd411,X0),vsucc(vplus(X0,vd411)))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) )
| ~ spl1_8
| ~ spl1_9
| ~ spl1_12 ),
inference(forward_demodulation,[],[f173,f119]) ).
fof(f173,plain,
( ! [X0] :
( vplus(vmul(vsucc(vd411),X0),vsucc(vd411)) = vplus(vmul(vd411,X0),vsucc(vplus(X0,vd411)))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) )
| ~ spl1_8
| ~ spl1_12 ),
inference(forward_demodulation,[],[f171,f107]) ).
fof(f171,plain,
( ! [X0] :
( vplus(vmul(vsucc(vd411),X0),vsucc(vd411)) = vplus(vmul(vd411,X0),vplus(X0,vsucc(vd411)))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) )
| ~ spl1_12 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f172,plain,
spl1_12,
inference(avatar_split_clause,[],[f59,f170]) ).
fof(f59,plain,
! [X0] :
( vplus(vmul(vsucc(vd411),X0),vsucc(vd411)) = vplus(vmul(vd411,X0),vplus(X0,vsucc(vd411)))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ),
inference(inner_rewriting,[],[f49]) ).
fof(f49,plain,
! [X0] :
( vplus(vplus(vmul(vd411,X0),X0),vsucc(vd411)) = vplus(vmul(vd411,X0),vplus(X0,vsucc(vd411)))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0] :
( vplus(vplus(vmul(vd411,X0),X0),vsucc(vd411)) = vplus(vmul(vd411,X0),vplus(X0,vsucc(vd411)))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0] :
( vmul(vsucc(vd411),X0) = vplus(vmul(vd411,X0),X0)
=> vplus(vplus(vmul(vd411,X0),X0),vsucc(vd411)) = vplus(vmul(vd411,X0),vplus(X0,vsucc(vd411))) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X1] :
( vmul(vsucc(vd411),X1) = vplus(vmul(vd411,X1),X1)
=> vplus(vmul(vd411,X1),vplus(X1,vsucc(vd411))) = vplus(vplus(vmul(vd411,X1),X1),vsucc(vd411)) ),
file('/export/starexec/sandbox2/tmp/tmp.oNnbrs1EEg/Vampire---4.8_15442','ass(cond(conseq(263), 1), 5)') ).
fof(f168,plain,
spl1_11,
inference(avatar_split_clause,[],[f46,f166]) ).
fof(f166,plain,
( spl1_11
<=> ! [X0] :
( vplus(vmul(vd411,vsucc(X0)),vsucc(X0)) = vplus(vplus(vmul(vd411,X0),vd411),vsucc(X0))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_11])]) ).
fof(f46,plain,
! [X0] :
( vplus(vmul(vd411,vsucc(X0)),vsucc(X0)) = vplus(vplus(vmul(vd411,X0),vd411),vsucc(X0))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0] :
( vplus(vmul(vd411,vsucc(X0)),vsucc(X0)) = vplus(vplus(vmul(vd411,X0),vd411),vsucc(X0))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0] :
( vmul(vsucc(vd411),X0) = vplus(vmul(vd411,X0),X0)
=> vplus(vmul(vd411,vsucc(X0)),vsucc(X0)) = vplus(vplus(vmul(vd411,X0),vd411),vsucc(X0)) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X1] :
( vmul(vsucc(vd411),X1) = vplus(vmul(vd411,X1),X1)
=> vplus(vplus(vmul(vd411,X1),vd411),vsucc(X1)) = vplus(vmul(vd411,vsucc(X1)),vsucc(X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.oNnbrs1EEg/Vampire---4.8_15442','ass(cond(conseq(263), 1), 0)') ).
fof(f135,plain,
spl1_10,
inference(avatar_split_clause,[],[f58,f133]) ).
fof(f58,plain,
! [X2,X0,X1] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1,X2] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X7,X8,X9] : vplus(vplus(X7,X8),X9) = vplus(X7,vplus(X8,X9)),
file('/export/starexec/sandbox2/tmp/tmp.oNnbrs1EEg/Vampire---4.8_15442','ass(cond(33, 0), 0)') ).
fof(f120,plain,
spl1_9,
inference(avatar_split_clause,[],[f56,f118]) ).
fof(f56,plain,
! [X0,X1] : vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( vmul(X0,v1) = X0
& vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X2,X3] :
( vmul(X2,v1) = X2
& vmul(X2,vsucc(X3)) = vplus(vmul(X2,X3),X2) ),
file('/export/starexec/sandbox2/tmp/tmp.oNnbrs1EEg/Vampire---4.8_15442','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).
fof(f108,plain,
spl1_8,
inference(avatar_split_clause,[],[f54,f106]) ).
fof(f54,plain,
! [X0,X1] : vplus(X0,vsucc(X1)) = vsucc(vplus(X0,X1)),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( vsucc(X0) = vplus(X0,v1)
& vplus(X0,vsucc(X1)) = vsucc(vplus(X0,X1)) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X10,X11] :
( vplus(X10,v1) = vsucc(X10)
& vplus(X10,vsucc(X11)) = vsucc(vplus(X10,X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.oNnbrs1EEg/Vampire---4.8_15442','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).
fof(f104,plain,
( spl1_7
| ~ spl1_1
| ~ spl1_6 ),
inference(avatar_split_clause,[],[f86,f83,f61,f101]) ).
fof(f86,plain,
( vmul(vsucc(vd411),sK0) = vplus(sK0,vmul(vd411,sK0))
| ~ spl1_1
| ~ spl1_6 ),
inference(superposition,[],[f84,f63]) ).
fof(f85,plain,
spl1_6,
inference(avatar_split_clause,[],[f53,f83]) ).
fof(f53,plain,
! [X0,X1] : vplus(X1,X0) = vplus(X0,X1),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] : vplus(X1,X0) = vplus(X0,X1),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X4,X5] : vplus(X5,X4) = vplus(X4,X5),
file('/export/starexec/sandbox2/tmp/tmp.oNnbrs1EEg/Vampire---4.8_15442','ass(cond(61, 0), 0)') ).
fof(f81,plain,
spl1_5,
inference(avatar_split_clause,[],[f55,f79]) ).
fof(f79,plain,
( spl1_5
<=> ! [X0] : vsucc(X0) = vplus(X0,v1) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).
fof(f55,plain,
! [X0] : vsucc(X0) = vplus(X0,v1),
inference(cnf_transformation,[],[f27]) ).
fof(f77,plain,
spl1_4,
inference(avatar_split_clause,[],[f44,f75]) ).
fof(f75,plain,
( spl1_4
<=> ! [X0] : vsucc(X0) = vplus(v1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).
fof(f44,plain,
! [X0] : vsucc(X0) = vplus(v1,X0),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0] : vsucc(X0) = vplus(v1,X0),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X6] : vplus(v1,X6) = vsucc(X6),
file('/export/starexec/sandbox2/tmp/tmp.oNnbrs1EEg/Vampire---4.8_15442','ass(cond(43, 0), 0)') ).
fof(f73,plain,
spl1_3,
inference(avatar_split_clause,[],[f57,f71]) ).
fof(f71,plain,
( spl1_3
<=> ! [X0] : vmul(X0,v1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).
fof(f57,plain,
! [X0] : vmul(X0,v1) = X0,
inference(cnf_transformation,[],[f28]) ).
fof(f69,plain,
~ spl1_2,
inference(avatar_split_clause,[],[f42,f66]) ).
fof(f42,plain,
vmul(vsucc(vd411),vsucc(sK0)) != vplus(vmul(vd411,vsucc(sK0)),vsucc(sK0)),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
( vmul(vsucc(vd411),vsucc(sK0)) != vplus(vmul(vd411,vsucc(sK0)),vsucc(sK0))
& vmul(vsucc(vd411),sK0) = vplus(vmul(vd411,sK0),sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f30,f39]) ).
fof(f39,plain,
( ? [X0] :
( vmul(vsucc(vd411),vsucc(X0)) != vplus(vmul(vd411,vsucc(X0)),vsucc(X0))
& vmul(vsucc(vd411),X0) = vplus(vmul(vd411,X0),X0) )
=> ( vmul(vsucc(vd411),vsucc(sK0)) != vplus(vmul(vd411,vsucc(sK0)),vsucc(sK0))
& vmul(vsucc(vd411),sK0) = vplus(vmul(vd411,sK0),sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
? [X0] :
( vmul(vsucc(vd411),vsucc(X0)) != vplus(vmul(vd411,vsucc(X0)),vsucc(X0))
& vmul(vsucc(vd411),X0) = vplus(vmul(vd411,X0),X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( vmul(vsucc(vd411),X0) = vplus(vmul(vd411,X0),X0)
=> vmul(vsucc(vd411),vsucc(X0)) = vplus(vmul(vd411,vsucc(X0)),vsucc(X0)) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
! [X0] :
( vmul(vsucc(vd411),X0) = vplus(vmul(vd411,X0),X0)
=> vmul(vsucc(vd411),vsucc(X0)) = vplus(vmul(vd411,vsucc(X0)),vsucc(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.oNnbrs1EEg/Vampire---4.8_15442','qu(ind(267), imp(267))') ).
fof(f64,plain,
spl1_1,
inference(avatar_split_clause,[],[f41,f61]) ).
fof(f41,plain,
vmul(vsucc(vd411),sK0) = vplus(vmul(vd411,sK0),sK0),
inference(cnf_transformation,[],[f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM845+2 : TPTP v8.1.2. Released v4.1.0.
% 0.03/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 30 15:13:41 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.42 % (15612)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (15635)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.21/0.42 % (15636)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.21/0.42 % (15638)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.21/0.42 % (15637)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 Vampire---4 for (569ds/0Mi)
% 0.21/0.42 % (15639)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 Vampire---4 for (531ds/0Mi)
% 0.21/0.42 % (15640)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 Vampire---4 for (522ds/0Mi)
% 0.21/0.42 % (15641)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 Vampire---4 for (497ds/0Mi)
% 0.21/0.43 TRYING [1]
% 0.21/0.43 TRYING [2]
% 0.21/0.43 % (15639)First to succeed.
% 0.21/0.44 % (15639)Refutation found. Thanks to Tanya!
% 0.21/0.44 % SZS status Theorem for Vampire---4
% 0.21/0.44 % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.44 % (15639)------------------------------
% 0.21/0.44 % (15639)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.44 % (15639)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.44 % (15639)Termination reason: Refutation
% 0.21/0.44
% 0.21/0.44 % (15639)Memory used [KB]: 5500
% 0.21/0.44 % (15639)Time elapsed: 0.011 s
% 0.21/0.44 % (15639)------------------------------
% 0.21/0.44 % (15639)------------------------------
% 0.21/0.44 % (15612)Success in time 0.071 s
% 0.21/0.44 % Vampire---4.8 exiting
%------------------------------------------------------------------------------