TSTP Solution File: SET776+4 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET776+4 : TPTP v8.1.2. Released v2.2.0.
% 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 : n015.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 : Thu Aug 31 15:45:33 EDT 2023
% Result : Theorem 0.24s 0.45s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 4
% Syntax : Number of formulae : 46 ( 12 unt; 0 def)
% Number of atoms : 318 ( 0 equ)
% Maximal formula atoms : 34 ( 6 avg)
% Number of connectives : 404 ( 132 ~; 103 |; 138 &)
% ( 7 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 147 (; 97 !; 50 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f320,plain,
$false,
inference(subsumption_resolution,[],[f319,f75]) ).
fof(f75,plain,
member(sK4,sK0),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
( ~ apply(sK1,sK5,sK6)
& apply(sK1,sK3,sK4)
& apply(sK2,sK4,sK6)
& apply(sK2,sK3,sK5)
& member(sK6,sK0)
& member(sK5,sK0)
& member(sK4,sK0)
& member(sK3,sK0)
& ! [X7,X8] :
( ( ( apply(sK2,X7,X8)
| ~ apply(sK1,X8,X7)
| ~ apply(sK1,X7,X8) )
& ( ( apply(sK1,X8,X7)
& apply(sK1,X7,X8) )
| ~ apply(sK2,X7,X8) ) )
| ~ member(X8,sK0)
| ~ member(X7,sK0) )
& pre_order(sK1,sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f42,f44,f43]) ).
fof(f43,plain,
( ? [X0,X1,X2] :
( ? [X3,X4,X5,X6] :
( ~ apply(X1,X5,X6)
& apply(X1,X3,X4)
& apply(X2,X4,X6)
& apply(X2,X3,X5)
& member(X6,X0)
& member(X5,X0)
& member(X4,X0)
& member(X3,X0) )
& ! [X7,X8] :
( ( ( apply(X2,X7,X8)
| ~ apply(X1,X8,X7)
| ~ apply(X1,X7,X8) )
& ( ( apply(X1,X8,X7)
& apply(X1,X7,X8) )
| ~ apply(X2,X7,X8) ) )
| ~ member(X8,X0)
| ~ member(X7,X0) )
& pre_order(X1,X0) )
=> ( ? [X6,X5,X4,X3] :
( ~ apply(sK1,X5,X6)
& apply(sK1,X3,X4)
& apply(sK2,X4,X6)
& apply(sK2,X3,X5)
& member(X6,sK0)
& member(X5,sK0)
& member(X4,sK0)
& member(X3,sK0) )
& ! [X8,X7] :
( ( ( apply(sK2,X7,X8)
| ~ apply(sK1,X8,X7)
| ~ apply(sK1,X7,X8) )
& ( ( apply(sK1,X8,X7)
& apply(sK1,X7,X8) )
| ~ apply(sK2,X7,X8) ) )
| ~ member(X8,sK0)
| ~ member(X7,sK0) )
& pre_order(sK1,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f44,plain,
( ? [X6,X5,X4,X3] :
( ~ apply(sK1,X5,X6)
& apply(sK1,X3,X4)
& apply(sK2,X4,X6)
& apply(sK2,X3,X5)
& member(X6,sK0)
& member(X5,sK0)
& member(X4,sK0)
& member(X3,sK0) )
=> ( ~ apply(sK1,sK5,sK6)
& apply(sK1,sK3,sK4)
& apply(sK2,sK4,sK6)
& apply(sK2,sK3,sK5)
& member(sK6,sK0)
& member(sK5,sK0)
& member(sK4,sK0)
& member(sK3,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f42,plain,
? [X0,X1,X2] :
( ? [X3,X4,X5,X6] :
( ~ apply(X1,X5,X6)
& apply(X1,X3,X4)
& apply(X2,X4,X6)
& apply(X2,X3,X5)
& member(X6,X0)
& member(X5,X0)
& member(X4,X0)
& member(X3,X0) )
& ! [X7,X8] :
( ( ( apply(X2,X7,X8)
| ~ apply(X1,X8,X7)
| ~ apply(X1,X7,X8) )
& ( ( apply(X1,X8,X7)
& apply(X1,X7,X8) )
| ~ apply(X2,X7,X8) ) )
| ~ member(X8,X0)
| ~ member(X7,X0) )
& pre_order(X1,X0) ),
inference(rectify,[],[f41]) ).
fof(f41,plain,
? [X0,X1,X2] :
( ? [X5,X6,X7,X8] :
( ~ apply(X1,X7,X8)
& apply(X1,X5,X6)
& apply(X2,X6,X8)
& apply(X2,X5,X7)
& member(X8,X0)
& member(X7,X0)
& member(X6,X0)
& member(X5,X0) )
& ! [X3,X4] :
( ( ( apply(X2,X3,X4)
| ~ apply(X1,X4,X3)
| ~ apply(X1,X3,X4) )
& ( ( apply(X1,X4,X3)
& apply(X1,X3,X4) )
| ~ apply(X2,X3,X4) ) )
| ~ member(X4,X0)
| ~ member(X3,X0) )
& pre_order(X1,X0) ),
inference(flattening,[],[f40]) ).
fof(f40,plain,
? [X0,X1,X2] :
( ? [X5,X6,X7,X8] :
( ~ apply(X1,X7,X8)
& apply(X1,X5,X6)
& apply(X2,X6,X8)
& apply(X2,X5,X7)
& member(X8,X0)
& member(X7,X0)
& member(X6,X0)
& member(X5,X0) )
& ! [X3,X4] :
( ( ( apply(X2,X3,X4)
| ~ apply(X1,X4,X3)
| ~ apply(X1,X3,X4) )
& ( ( apply(X1,X4,X3)
& apply(X1,X3,X4) )
| ~ apply(X2,X3,X4) ) )
| ~ member(X4,X0)
| ~ member(X3,X0) )
& pre_order(X1,X0) ),
inference(nnf_transformation,[],[f35]) ).
fof(f35,plain,
? [X0,X1,X2] :
( ? [X5,X6,X7,X8] :
( ~ apply(X1,X7,X8)
& apply(X1,X5,X6)
& apply(X2,X6,X8)
& apply(X2,X5,X7)
& member(X8,X0)
& member(X7,X0)
& member(X6,X0)
& member(X5,X0) )
& ! [X3,X4] :
( ( apply(X2,X3,X4)
<=> ( apply(X1,X4,X3)
& apply(X1,X3,X4) ) )
| ~ member(X4,X0)
| ~ member(X3,X0) )
& pre_order(X1,X0) ),
inference(flattening,[],[f34]) ).
fof(f34,plain,
? [X0,X1,X2] :
( ? [X5,X6,X7,X8] :
( ~ apply(X1,X7,X8)
& apply(X1,X5,X6)
& apply(X2,X6,X8)
& apply(X2,X5,X7)
& member(X8,X0)
& member(X7,X0)
& member(X6,X0)
& member(X5,X0) )
& ! [X3,X4] :
( ( apply(X2,X3,X4)
<=> ( apply(X1,X4,X3)
& apply(X1,X3,X4) ) )
| ~ member(X4,X0)
| ~ member(X3,X0) )
& pre_order(X1,X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,plain,
~ ! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( member(X4,X0)
& member(X3,X0) )
=> ( apply(X2,X3,X4)
<=> ( apply(X1,X4,X3)
& apply(X1,X3,X4) ) ) )
& pre_order(X1,X0) )
=> ! [X5,X6,X7,X8] :
( ( member(X8,X0)
& member(X7,X0)
& member(X6,X0)
& member(X5,X0) )
=> ( ( apply(X1,X5,X6)
& apply(X2,X6,X8)
& apply(X2,X5,X7) )
=> apply(X1,X7,X8) ) ) ),
inference(rectify,[],[f18]) ).
fof(f18,negated_conjecture,
~ ! [X3,X7,X6] :
( ( ! [X0,X1] :
( ( member(X1,X3)
& member(X0,X3) )
=> ( apply(X6,X0,X1)
<=> ( apply(X7,X1,X0)
& apply(X7,X0,X1) ) ) )
& pre_order(X7,X3) )
=> ! [X8,X9,X10,X11] :
( ( member(X11,X3)
& member(X10,X3)
& member(X9,X3)
& member(X8,X3) )
=> ( ( apply(X7,X8,X9)
& apply(X6,X9,X11)
& apply(X6,X8,X10) )
=> apply(X7,X10,X11) ) ) ),
inference(negated_conjecture,[],[f17]) ).
fof(f17,conjecture,
! [X3,X7,X6] :
( ( ! [X0,X1] :
( ( member(X1,X3)
& member(X0,X3) )
=> ( apply(X6,X0,X1)
<=> ( apply(X7,X1,X0)
& apply(X7,X0,X1) ) ) )
& pre_order(X7,X3) )
=> ! [X8,X9,X10,X11] :
( ( member(X11,X3)
& member(X10,X3)
& member(X9,X3)
& member(X8,X3) )
=> ( ( apply(X7,X8,X9)
& apply(X6,X9,X11)
& apply(X6,X8,X10) )
=> apply(X7,X10,X11) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ZDcw0W10Lw/Vampire---4.8_14893',thIII12) ).
fof(f319,plain,
~ member(sK4,sK0),
inference(subsumption_resolution,[],[f315,f80]) ).
fof(f80,plain,
apply(sK1,sK3,sK4),
inference(cnf_transformation,[],[f45]) ).
fof(f315,plain,
( ~ apply(sK1,sK3,sK4)
| ~ member(sK4,sK0) ),
inference(resolution,[],[f307,f79]) ).
fof(f79,plain,
apply(sK2,sK4,sK6),
inference(cnf_transformation,[],[f45]) ).
fof(f307,plain,
! [X3] :
( ~ apply(sK2,X3,sK6)
| ~ apply(sK1,sK3,X3)
| ~ member(X3,sK0) ),
inference(subsumption_resolution,[],[f302,f77]) ).
fof(f77,plain,
member(sK6,sK0),
inference(cnf_transformation,[],[f45]) ).
fof(f302,plain,
! [X3] :
( ~ member(X3,sK0)
| ~ apply(sK1,sK3,X3)
| ~ apply(sK2,X3,sK6)
| ~ member(sK6,sK0) ),
inference(duplicate_literal_removal,[],[f300]) ).
fof(f300,plain,
! [X3] :
( ~ member(X3,sK0)
| ~ apply(sK1,sK3,X3)
| ~ apply(sK2,X3,sK6)
| ~ member(sK6,sK0)
| ~ member(X3,sK0) ),
inference(resolution,[],[f286,f71]) ).
fof(f71,plain,
! [X8,X7] :
( apply(sK1,X7,X8)
| ~ apply(sK2,X7,X8)
| ~ member(X8,sK0)
| ~ member(X7,sK0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f286,plain,
! [X0] :
( ~ apply(sK1,X0,sK6)
| ~ member(X0,sK0)
| ~ apply(sK1,sK3,X0) ),
inference(subsumption_resolution,[],[f285,f74]) ).
fof(f74,plain,
member(sK3,sK0),
inference(cnf_transformation,[],[f45]) ).
fof(f285,plain,
! [X0] :
( ~ apply(sK1,sK3,X0)
| ~ member(X0,sK0)
| ~ member(sK3,sK0)
| ~ apply(sK1,X0,sK6) ),
inference(subsumption_resolution,[],[f282,f77]) ).
fof(f282,plain,
! [X0] :
( ~ apply(sK1,sK3,X0)
| ~ member(sK6,sK0)
| ~ member(X0,sK0)
| ~ member(sK3,sK0)
| ~ apply(sK1,X0,sK6) ),
inference(resolution,[],[f281,f224]) ).
fof(f224,plain,
! [X2,X0,X1] :
( apply(sK1,X2,X1)
| ~ apply(sK1,X2,X0)
| ~ member(X1,sK0)
| ~ member(X0,sK0)
| ~ member(X2,sK0)
| ~ apply(sK1,X0,X1) ),
inference(resolution,[],[f87,f70]) ).
fof(f70,plain,
pre_order(sK1,sK0),
inference(cnf_transformation,[],[f45]) ).
fof(f87,plain,
! [X2,X3,X0,X1,X4] :
( ~ pre_order(X0,X1)
| ~ apply(X0,X3,X4)
| ~ apply(X0,X2,X3)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ member(X2,X1)
| apply(X0,X2,X4) ),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0,X1] :
( ( ! [X2,X3,X4] :
( apply(X0,X2,X4)
| ~ apply(X0,X3,X4)
| ~ apply(X0,X2,X3)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ member(X2,X1) )
& ! [X5] :
( apply(X0,X5,X5)
| ~ member(X5,X1) ) )
| ~ pre_order(X0,X1) ),
inference(flattening,[],[f37]) ).
fof(f37,plain,
! [X0,X1] :
( ( ! [X2,X3,X4] :
( apply(X0,X2,X4)
| ~ apply(X0,X3,X4)
| ~ apply(X0,X2,X3)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ member(X2,X1) )
& ! [X5] :
( apply(X0,X5,X5)
| ~ member(X5,X1) ) )
| ~ pre_order(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1] :
( pre_order(X0,X1)
=> ( ! [X2,X3,X4] :
( ( member(X4,X1)
& member(X3,X1)
& member(X2,X1) )
=> ( ( apply(X0,X3,X4)
& apply(X0,X2,X3) )
=> apply(X0,X2,X4) ) )
& ! [X5] :
( member(X5,X1)
=> apply(X0,X5,X5) ) ) ),
inference(unused_predicate_definition_removal,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( pre_order(X0,X1)
<=> ( ! [X2,X3,X4] :
( ( member(X4,X1)
& member(X3,X1)
& member(X2,X1) )
=> ( ( apply(X0,X3,X4)
& apply(X0,X2,X3) )
=> apply(X0,X2,X4) ) )
& ! [X5] :
( member(X5,X1)
=> apply(X0,X5,X5) ) ) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X6,X3] :
( pre_order(X6,X3)
<=> ( ! [X2,X4,X5] :
( ( member(X5,X3)
& member(X4,X3)
& member(X2,X3) )
=> ( ( apply(X6,X4,X5)
& apply(X6,X2,X4) )
=> apply(X6,X2,X5) ) )
& ! [X2] :
( member(X2,X3)
=> apply(X6,X2,X2) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ZDcw0W10Lw/Vampire---4.8_14893',pre_order) ).
fof(f281,plain,
~ apply(sK1,sK3,sK6),
inference(subsumption_resolution,[],[f277,f74]) ).
fof(f277,plain,
( ~ apply(sK1,sK3,sK6)
| ~ member(sK3,sK0) ),
inference(resolution,[],[f275,f78]) ).
fof(f78,plain,
apply(sK2,sK3,sK5),
inference(cnf_transformation,[],[f45]) ).
fof(f275,plain,
! [X2] :
( ~ apply(sK2,X2,sK5)
| ~ apply(sK1,X2,sK6)
| ~ member(X2,sK0) ),
inference(subsumption_resolution,[],[f272,f76]) ).
fof(f76,plain,
member(sK5,sK0),
inference(cnf_transformation,[],[f45]) ).
fof(f272,plain,
! [X2] :
( ~ member(X2,sK0)
| ~ apply(sK1,X2,sK6)
| ~ apply(sK2,X2,sK5)
| ~ member(sK5,sK0) ),
inference(duplicate_literal_removal,[],[f268]) ).
fof(f268,plain,
! [X2] :
( ~ member(X2,sK0)
| ~ apply(sK1,X2,sK6)
| ~ apply(sK2,X2,sK5)
| ~ member(sK5,sK0)
| ~ member(X2,sK0) ),
inference(resolution,[],[f266,f72]) ).
fof(f72,plain,
! [X8,X7] :
( apply(sK1,X8,X7)
| ~ apply(sK2,X7,X8)
| ~ member(X8,sK0)
| ~ member(X7,sK0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f266,plain,
! [X0] :
( ~ apply(sK1,sK5,X0)
| ~ member(X0,sK0)
| ~ apply(sK1,X0,sK6) ),
inference(subsumption_resolution,[],[f265,f76]) ).
fof(f265,plain,
! [X0] :
( ~ apply(sK1,sK5,X0)
| ~ member(X0,sK0)
| ~ member(sK5,sK0)
| ~ apply(sK1,X0,sK6) ),
inference(subsumption_resolution,[],[f264,f77]) ).
fof(f264,plain,
! [X0] :
( ~ apply(sK1,sK5,X0)
| ~ member(sK6,sK0)
| ~ member(X0,sK0)
| ~ member(sK5,sK0)
| ~ apply(sK1,X0,sK6) ),
inference(resolution,[],[f224,f81]) ).
fof(f81,plain,
~ apply(sK1,sK5,sK6),
inference(cnf_transformation,[],[f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET776+4 : TPTP v8.1.2. Released v2.2.0.
% 0.14/0.16 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.17/0.37 % Computer : n015.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Sat Aug 26 16:28:23 EDT 2023
% 0.23/0.37 % CPUTime :
% 0.23/0.37 This is a FOF_THM_RFO_SEQ problem
% 0.23/0.37 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.ZDcw0W10Lw/Vampire---4.8_14893
% 0.23/0.38 % (15058)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.44 % (15062)lrs-3_8_anc=none:bce=on:cond=on:drc=off:flr=on:fsd=off:fsr=off:fde=unused:gsp=on:gs=on:gsaa=full_model:lcm=predicate:lma=on:nm=16:sos=all:sp=weighted_frequency:tgt=ground:urr=ec_only:stl=188_482 on Vampire---4 for (482ds/0Mi)
% 0.24/0.44 % (15060)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_680 on Vampire---4 for (680ds/0Mi)
% 0.24/0.44 % (15061)dis-11_4:1_aac=none:add=off:afr=on:anc=none:bd=preordered:bs=on:bsr=on:drc=off:fsr=off:fde=none:gsp=on:irw=on:lcm=reverse:lma=on:nm=0:nwc=1.7:nicw=on:sas=z3:sims=off:sos=all:sac=on:sp=weighted_frequency:tgt=full_602 on Vampire---4 for (602ds/0Mi)
% 0.24/0.44 % (15063)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_424 on Vampire---4 for (424ds/0Mi)
% 0.24/0.44 % (15059)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_730 on Vampire---4 for (730ds/0Mi)
% 0.24/0.44 % (15065)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_386 on Vampire---4 for (386ds/0Mi)
% 0.24/0.44 % (15064)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.24/0.45 % (15064)First to succeed.
% 0.24/0.45 % (15064)Refutation found. Thanks to Tanya!
% 0.24/0.45 % SZS status Theorem for Vampire---4
% 0.24/0.45 % SZS output start Proof for Vampire---4
% See solution above
% 0.24/0.45 % (15064)------------------------------
% 0.24/0.45 % (15064)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.24/0.45 % (15064)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.24/0.45 % (15064)Termination reason: Refutation
% 0.24/0.45
% 0.24/0.45 % (15064)Memory used [KB]: 5628
% 0.24/0.45 % (15064)Time elapsed: 0.014 s
% 0.24/0.45 % (15064)------------------------------
% 0.24/0.45 % (15064)------------------------------
% 0.24/0.45 % (15058)Success in time 0.074 s
% 0.24/0.45 % Vampire---4.8 exiting
%------------------------------------------------------------------------------