TSTP Solution File: DAT036_1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : DAT036_1 : TPTP v8.1.2. Released v5.0.0.
% 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 : n014.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 : Wed Aug 30 22:21:32 EDT 2023
% Result : Theorem 0.23s 0.45s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 21
% Syntax : Number of formulae : 56 ( 27 unt; 9 typ; 0 def)
% Number of atoms : 74 ( 15 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 52 ( 25 ~; 13 |; 6 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 170 ( 42 atm; 50 fun; 34 num; 44 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 6 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 62 (; 56 !; 6 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
collection: $tType ).
tff(func_def_0,type,
empty: collection ).
tff(func_def_1,type,
add: ( $int * collection ) > collection ).
tff(func_def_2,type,
remove: ( $int * collection ) > collection ).
tff(func_def_3,type,
count: collection > $int ).
tff(func_def_9,type,
sK0: collection ).
tff(func_def_10,type,
sK1: $int ).
tff(func_def_11,type,
sK2: $int ).
tff(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(f821,plain,
$false,
inference(subsumption_resolution,[],[f813,f330]) ).
tff(f330,plain,
! [X0: $int] : $less($sum(1,X0),$sum(1,$sum(sK2,X0))),
inference(forward_demodulation,[],[f300,f19]) ).
tff(f19,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_139,[]) ).
tff(f300,plain,
! [X0: $int] : $less($sum(1,X0),$sum($sum(1,sK2),X0)),
inference(unit_resulting_resolution,[],[f122,f26]) ).
tff(f26,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) ),
introduced(theory_axiom_148,[]) ).
tff(f122,plain,
$less(1,$sum(1,sK2)),
inference(forward_demodulation,[],[f121,f18]) ).
tff(f18,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_138,[]) ).
tff(f121,plain,
$less(1,$sum(sK2,1)),
inference(unit_resulting_resolution,[],[f118,f27]) ).
tff(f27,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) ),
introduced(theory_axiom_150,[]) ).
tff(f118,plain,
~ $less(sK2,1),
inference(evaluation,[],[f109]) ).
tff(f109,plain,
~ $less(sK2,$sum(0,1)),
inference(unit_resulting_resolution,[],[f54,f29]) ).
tff(f29,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) ),
introduced(theory_axiom_164,[]) ).
tff(f54,plain,
$less(0,sK2),
inference(cnf_transformation,[],[f44]) ).
tff(f44,plain,
( $less($sum(count(sK0),sK2),count(add(sK1,add(sK1,sK0))))
& $less(0,sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f41,f43]) ).
tff(f43,plain,
( ? [X0: collection,X1: $int,X2: $int] :
( $less($sum(count(X0),X2),count(add(X1,add(X1,X0))))
& $less(0,X2) )
=> ( $less($sum(count(sK0),sK2),count(add(sK1,add(sK1,sK0))))
& $less(0,sK2) ) ),
introduced(choice_axiom,[]) ).
tff(f41,plain,
? [X0: collection,X1: $int,X2: $int] :
( $less($sum(count(X0),X2),count(add(X1,add(X1,X0))))
& $less(0,X2) ),
inference(ennf_transformation,[],[f15]) ).
tff(f15,plain,
~ ! [X0: collection,X1: $int,X2: $int] :
( $less(0,X2)
=> ~ $less($sum(count(X0),X2),count(add(X1,add(X1,X0)))) ),
inference(theory_normalization,[],[f14]) ).
tff(f14,negated_conjecture,
~ ! [X0: collection,X1: $int,X2: $int] :
( $greater(X2,0)
=> $greatereq($sum(count(X0),X2),count(add(X1,add(X1,X0)))) ),
inference(negated_conjecture,[],[f13]) ).
tff(f13,conjecture,
! [X0: collection,X1: $int,X2: $int] :
( $greater(X2,0)
=> $greatereq($sum(count(X0),X2),count(add(X1,add(X1,X0)))) ),
file('/export/starexec/sandbox/tmp/tmp.jNhXtoETyc/Vampire---4.8_10320',co1) ).
tff(f813,plain,
~ $less($sum(1,count(sK0)),$sum(1,$sum(sK2,count(sK0)))),
inference(backward_demodulation,[],[f526,f800]) ).
tff(f800,plain,
count(add(sK1,sK0)) = $sum(1,count(sK0)),
inference(unit_resulting_resolution,[],[f573,f84]) ).
tff(f84,plain,
! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| in(X0,X1) ),
inference(forward_demodulation,[],[f65,f18]) ).
tff(f65,plain,
! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(count(X1),1) )
| in(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
tff(f47,plain,
! [X0: $int,X1: collection] :
( ( ~ in(X0,X1)
| ( count(add(X0,X1)) != $sum(count(X1),1) ) )
& ( ( count(add(X0,X1)) = $sum(count(X1),1) )
| in(X0,X1) ) ),
inference(nnf_transformation,[],[f36]) ).
tff(f36,plain,
! [X0: $int,X1: collection] :
( ~ in(X0,X1)
<=> ( count(add(X0,X1)) = $sum(count(X1),1) ) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X13: $int,X14: collection] :
( ~ in(X13,X14)
<=> ( count(add(X13,X14)) = $sum(count(X14),1) ) ),
file('/export/starexec/sandbox/tmp/tmp.jNhXtoETyc/Vampire---4.8_10320',ax3) ).
tff(f573,plain,
~ in(sK1,sK0),
inference(subsumption_resolution,[],[f569,f368]) ).
tff(f368,plain,
! [X0: $int] : ~ $less($sum(sK2,X0),X0),
inference(unit_resulting_resolution,[],[f23,f320,f24]) ).
tff(f24,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X0,X2)
| ~ $less(X1,X2)
| ~ $less(X0,X1) ),
introduced(theory_axiom_146,[]) ).
tff(f320,plain,
! [X0: $int] : $less(X0,$sum(sK2,X0)),
inference(evaluation,[],[f296]) ).
tff(f296,plain,
! [X0: $int] : $less($sum(0,X0),$sum(sK2,X0)),
inference(unit_resulting_resolution,[],[f54,f26]) ).
tff(f23,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_145,[]) ).
tff(f569,plain,
( $less($sum(sK2,count(sK0)),count(sK0))
| ~ in(sK1,sK0) ),
inference(superposition,[],[f525,f67]) ).
tff(f67,plain,
! [X0: $int,X1: collection] :
( ( count(X1) = count(add(X0,X1)) )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tff(f48,plain,
! [X0: $int,X1: collection] :
( ( in(X0,X1)
| ( count(X1) != count(add(X0,X1)) ) )
& ( ( count(X1) = count(add(X0,X1)) )
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f37]) ).
tff(f37,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
<=> ( count(X1) = count(add(X0,X1)) ) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X15: $int,X16: collection] :
( in(X15,X16)
<=> ( count(add(X15,X16)) = count(X16) ) ),
file('/export/starexec/sandbox/tmp/tmp.jNhXtoETyc/Vampire---4.8_10320',ax4) ).
tff(f525,plain,
$less($sum(sK2,count(sK0)),count(add(sK1,sK0))),
inference(backward_demodulation,[],[f82,f519]) ).
tff(f519,plain,
! [X0: $int,X1: collection] : ( count(add(X0,X1)) = count(add(X0,add(X0,X1))) ),
inference(unit_resulting_resolution,[],[f61,f67]) ).
tff(f61,plain,
! [X0: $int,X1: collection] : in(X0,add(X0,X1)),
inference(cnf_transformation,[],[f33]) ).
tff(f33,plain,
! [X0: $int,X1: collection] : in(X0,add(X0,X1)),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X1: $int,X2: collection] : in(X1,add(X1,X2)),
file('/export/starexec/sandbox/tmp/tmp.jNhXtoETyc/Vampire---4.8_10320',ax2) ).
tff(f82,plain,
$less($sum(sK2,count(sK0)),count(add(sK1,add(sK1,sK0)))),
inference(forward_demodulation,[],[f55,f18]) ).
tff(f55,plain,
$less($sum(count(sK0),sK2),count(add(sK1,add(sK1,sK0)))),
inference(cnf_transformation,[],[f44]) ).
tff(f526,plain,
~ $less(count(add(sK1,sK0)),$sum(1,$sum(sK2,count(sK0)))),
inference(backward_demodulation,[],[f120,f519]) ).
tff(f120,plain,
~ $less(count(add(sK1,add(sK1,sK0))),$sum(1,$sum(sK2,count(sK0)))),
inference(forward_demodulation,[],[f111,f18]) ).
tff(f111,plain,
~ $less(count(add(sK1,add(sK1,sK0))),$sum($sum(sK2,count(sK0)),1)),
inference(unit_resulting_resolution,[],[f82,f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : DAT036_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36 % Computer : n014.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 24 13:57:48 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a TF0_THM_EQU_ARI problem
% 0.15/0.37 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.jNhXtoETyc/Vampire---4.8_10320
% 0.15/0.37 % (10653)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.43 % (10662)lrs-1010_3_av=off:br=off:drc=off:er=known:fsd=off:fde=unused:nm=4:nwc=3.0:sp=scramble:urr=on:stl=180_280 on Vampire---4 for (280ds/0Mi)
% 0.23/0.43 % (10658)dis-11_10:1_canc=force:fsd=off:nwc=1.5:sas=z3:tha=off:uwa=all_472 on Vampire---4 for (472ds/0Mi)
% 0.23/0.43 % (10659)lrs+1010_2:1_amm=off:bs=on:bsr=on:canc=force:fsd=off:fsr=off:gs=on:gsaa=full_model:gsem=on:nm=0:nwc=1.3:sas=z3:sac=on:tha=off:thi=overlap:tgt=ground:uwa=ground:stl=60_408 on Vampire---4 for (408ds/0Mi)
% 0.23/0.43 % (10655)lrs+2_32_add=large:amm=off:bd=off:bs=unit_only:drc=off:flr=on:fsd=off:fde=none:nm=0:nwc=1.1:sos=theory:sp=reverse_arity:tgt=ground:stl=180_1034 on Vampire---4 for (1034ds/0Mi)
% 0.23/0.43 % (10656)dis-1010_2:3_canc=force:fsd=off:fde=unused:gs=on:gsem=on:nm=0:nwc=1.3:sas=z3:tha=off:thf=on:uwa=ground_572 on Vampire---4 for (572ds/0Mi)
% 0.23/0.43 % (10657)dis-10_20_canc=force:fsd=off:gs=on:gsem=off:nm=0:sas=z3:sac=on:tha=off:thi=strong:tgt=ground_476 on Vampire---4 for (476ds/0Mi)
% 0.23/0.43 % (10660)ott+10_1024_av=off:bd=preordered:br=off:ep=RSTC:fsr=off:fde=none:nm=2:urr=on_318 on Vampire---4 for (318ds/0Mi)
% 0.23/0.45 % (10662)First to succeed.
% 0.23/0.45 % (10662)Refutation found. Thanks to Tanya!
% 0.23/0.45 % SZS status Theorem for Vampire---4
% 0.23/0.45 % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.45 % (10662)------------------------------
% 0.23/0.45 % (10662)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.45 % (10662)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.45 % (10662)Termination reason: Refutation
% 0.23/0.45
% 0.23/0.45 % (10662)Memory used [KB]: 1407
% 0.23/0.45 % (10662)Time elapsed: 0.023 s
% 0.23/0.45 % (10662)------------------------------
% 0.23/0.45 % (10662)------------------------------
% 0.23/0.45 % (10653)Success in time 0.082 s
% 0.23/0.45 % Vampire---4.8 exiting
%------------------------------------------------------------------------------