TSTP Solution File: DAT026_1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : DAT026_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 : n021.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 22:21:29 EDT 2023
% Result : Theorem 0.23s 0.44s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 19
% Syntax : Number of formulae : 63 ( 30 unt; 9 typ; 0 def)
% Number of atoms : 141 ( 27 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 138 ( 51 ~; 30 |; 42 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 210 ( 49 atm; 32 fun; 69 num; 60 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 5 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 7 usr; 8 con; 0-2 aty)
% Number of variables : 84 (; 66 !; 18 ?; 84 :)
% 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_8,type,
sK0: collection ).
tff(func_def_9,type,
sK1: collection ).
tff(func_def_10,type,
sK2: $int ).
tff(func_def_11,type,
sK3: $int ).
tff(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(f427,plain,
$false,
inference(subsumption_resolution,[],[f423,f174]) ).
tff(f174,plain,
~ $less(2,sK3),
inference(evaluation,[],[f171]) ).
tff(f171,plain,
~ $less($sum(1,1),sK3),
inference(unit_resulting_resolution,[],[f68,f142,f15]) ).
tff(f15,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X0,X2)
| ~ $less(X1,X2)
| ~ $less(X0,X1) ),
introduced(theory_axiom_146,[]) ).
tff(f142,plain,
~ $less(1,sK3),
inference(unit_resulting_resolution,[],[f68,f83,f15]) ).
tff(f83,plain,
~ $less(1,$sum(1,sK3)),
inference(forward_demodulation,[],[f75,f9]) ).
tff(f9,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_138,[]) ).
tff(f75,plain,
~ $less(1,$sum(sK3,1)),
inference(unit_resulting_resolution,[],[f67,f20]) ).
tff(f20,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) ),
introduced(theory_axiom_164,[]) ).
tff(f67,plain,
$less(sK3,1),
inference(evaluation,[],[f62]) ).
tff(f62,plain,
$less(sK3,$sum(0,1)),
inference(unit_resulting_resolution,[],[f39,f18]) ).
tff(f18,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) ),
introduced(theory_axiom_150,[]) ).
tff(f39,plain,
~ $less(0,sK3),
inference(cnf_transformation,[],[f30]) ).
tff(f30,plain,
( ~ $less(0,sK3)
& in(sK3,sK0)
& ( sK0 = add($sum(sK2,2),remove(sK2,sK1)) )
& in(sK2,sK1)
& ! [X4: $int] :
( $less(0,X4)
| ~ in(X4,sK1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f27,f29,f28]) ).
tff(f28,plain,
( ? [X0: collection,X1: collection,X2: $int] :
( ? [X3: $int] :
( ~ $less(0,X3)
& in(X3,X0) )
& ( add($sum(X2,2),remove(X2,X1)) = X0 )
& in(X2,X1)
& ! [X4: $int] :
( $less(0,X4)
| ~ in(X4,X1) ) )
=> ( ? [X3: $int] :
( ~ $less(0,X3)
& in(X3,sK0) )
& ( sK0 = add($sum(sK2,2),remove(sK2,sK1)) )
& in(sK2,sK1)
& ! [X4: $int] :
( $less(0,X4)
| ~ in(X4,sK1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f29,plain,
( ? [X3: $int] :
( ~ $less(0,X3)
& in(X3,sK0) )
=> ( ~ $less(0,sK3)
& in(sK3,sK0) ) ),
introduced(choice_axiom,[]) ).
tff(f27,plain,
? [X0: collection,X1: collection,X2: $int] :
( ? [X3: $int] :
( ~ $less(0,X3)
& in(X3,X0) )
& ( add($sum(X2,2),remove(X2,X1)) = X0 )
& in(X2,X1)
& ! [X4: $int] :
( $less(0,X4)
| ~ in(X4,X1) ) ),
inference(rectify,[],[f26]) ).
tff(f26,plain,
? [X0: collection,X1: collection,X2: $int] :
( ? [X4: $int] :
( ~ $less(0,X4)
& in(X4,X0) )
& ( add($sum(X2,2),remove(X2,X1)) = X0 )
& in(X2,X1)
& ! [X3: $int] :
( $less(0,X3)
| ~ in(X3,X1) ) ),
inference(flattening,[],[f25]) ).
tff(f25,plain,
? [X0: collection,X1: collection,X2: $int] :
( ? [X4: $int] :
( ~ $less(0,X4)
& in(X4,X0) )
& ( add($sum(X2,2),remove(X2,X1)) = X0 )
& in(X2,X1)
& ! [X3: $int] :
( $less(0,X3)
| ~ in(X3,X1) ) ),
inference(ennf_transformation,[],[f8]) ).
tff(f8,plain,
~ ! [X0: collection,X1: collection,X2: $int] :
( ( ( add($sum(X2,2),remove(X2,X1)) = X0 )
& in(X2,X1)
& ! [X3: $int] :
( in(X3,X1)
=> $less(0,X3) ) )
=> ! [X4: $int] :
( in(X4,X0)
=> $less(0,X4) ) ),
inference(theory_normalization,[],[f7]) ).
tff(f7,negated_conjecture,
~ ! [X0: collection,X1: collection,X2: $int] :
( ( ( add($sum(X2,2),remove(X2,X1)) = X0 )
& in(X2,X1)
& ! [X3: $int] :
( in(X3,X1)
=> $greater(X3,0) ) )
=> ! [X4: $int] :
( in(X4,X0)
=> $greater(X4,0) ) ),
inference(negated_conjecture,[],[f6]) ).
tff(f6,conjecture,
! [X0: collection,X1: collection,X2: $int] :
( ( ( add($sum(X2,2),remove(X2,X1)) = X0 )
& in(X2,X1)
& ! [X3: $int] :
( in(X3,X1)
=> $greater(X3,0) ) )
=> ! [X4: $int] :
( in(X4,X0)
=> $greater(X4,0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.APCKrO65Jd/Vampire---4.8_2922',co1) ).
tff(f68,plain,
! [X0: $int] : $less(X0,$sum(1,X0)),
inference(superposition,[],[f64,f9]) ).
tff(f64,plain,
! [X0: $int] : $less(X0,$sum(X0,1)),
inference(unit_resulting_resolution,[],[f14,f18]) ).
tff(f14,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_145,[]) ).
tff(f423,plain,
$less(2,sK3),
inference(backward_demodulation,[],[f106,f419]) ).
tff(f419,plain,
sK3 = $sum(2,sK2),
inference(unit_resulting_resolution,[],[f38,f90,f373]) ).
tff(f373,plain,
! [X0: $int] :
( in(X0,remove(sK2,sK1))
| ~ in(X0,sK0)
| ( $sum(2,sK2) = X0 ) ),
inference(superposition,[],[f48,f51]) ).
tff(f51,plain,
sK0 = add($sum(2,sK2),remove(sK2,sK1)),
inference(forward_demodulation,[],[f37,f9]) ).
tff(f37,plain,
sK0 = add($sum(sK2,2),remove(sK2,sK1)),
inference(cnf_transformation,[],[f30]) ).
tff(f48,plain,
! [X2: $int,X0: $int,X1: collection] :
( ~ in(X0,add(X2,X1))
| in(X0,X1)
| ( X0 = X2 ) ),
inference(cnf_transformation,[],[f34]) ).
tff(f34,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 = X2 )
| in(X0,X1)
| ~ in(X0,add(X2,X1)) )
& ( in(X0,add(X2,X1))
| ( ( X0 != X2 )
& ~ in(X0,X1) ) ) ),
inference(flattening,[],[f33]) ).
tff(f33,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 = X2 )
| in(X0,X1)
| ~ in(X0,add(X2,X1)) )
& ( in(X0,add(X2,X1))
| ( ( X0 != X2 )
& ~ in(X0,X1) ) ) ),
inference(nnf_transformation,[],[f24]) ).
tff(f24,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 = X2 )
| in(X0,X1) )
<=> in(X0,add(X2,X1)) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X5: $int,X6: collection,X7: $int] :
( ( ( X5 = X7 )
| in(X5,X6) )
<=> in(X5,add(X7,X6)) ),
file('/export/starexec/sandbox2/tmp/tmp.APCKrO65Jd/Vampire---4.8_2922',ax4) ).
tff(f90,plain,
! [X0: $int] : ~ in(sK3,remove(X0,sK1)),
inference(unit_resulting_resolution,[],[f53,f44]) ).
tff(f44,plain,
! [X2: $int,X0: $int,X1: collection] :
( ~ in(X0,remove(X2,X1))
| in(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tff(f32,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( ( X0 != X2 )
& in(X0,X1) )
| ~ in(X0,remove(X2,X1)) )
& ( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ) ),
inference(flattening,[],[f31]) ).
tff(f31,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( ( X0 != X2 )
& in(X0,X1) )
| ~ in(X0,remove(X2,X1)) )
& ( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f23]) ).
tff(f23,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 != X2 )
& in(X0,X1) )
<=> in(X0,remove(X2,X1)) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X8: $int,X9: collection,X10: $int] :
( ( ( X8 != X10 )
& in(X8,X9) )
<=> in(X8,remove(X10,X9)) ),
file('/export/starexec/sandbox2/tmp/tmp.APCKrO65Jd/Vampire---4.8_2922',ax5) ).
tff(f53,plain,
~ in(sK3,sK1),
inference(unit_resulting_resolution,[],[f39,f35]) ).
tff(f35,plain,
! [X4: $int] :
( $less(0,X4)
| ~ in(X4,sK1) ),
inference(cnf_transformation,[],[f30]) ).
tff(f38,plain,
in(sK3,sK0),
inference(cnf_transformation,[],[f30]) ).
tff(f106,plain,
$less(2,$sum(2,sK2)),
inference(evaluation,[],[f105]) ).
tff(f105,plain,
$less(2,$sum($sum(1,sK2),1)),
inference(unit_resulting_resolution,[],[f89,f18]) ).
tff(f89,plain,
~ $less($sum(1,sK2),2),
inference(evaluation,[],[f88]) ).
tff(f88,plain,
~ $less($sum(1,sK2),$sum(1,1)),
inference(unit_resulting_resolution,[],[f85,f20]) ).
tff(f85,plain,
$less(1,$sum(1,sK2)),
inference(forward_demodulation,[],[f84,f9]) ).
tff(f84,plain,
$less(1,$sum(sK2,1)),
inference(unit_resulting_resolution,[],[f82,f18]) ).
tff(f82,plain,
~ $less(sK2,1),
inference(evaluation,[],[f74]) ).
tff(f74,plain,
~ $less(sK2,$sum(0,1)),
inference(unit_resulting_resolution,[],[f52,f20]) ).
tff(f52,plain,
$less(0,sK2),
inference(unit_resulting_resolution,[],[f36,f35]) ).
tff(f36,plain,
in(sK2,sK1),
inference(cnf_transformation,[],[f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : DAT026_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
% 0.14/0.36 % Computer : n021.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 : Thu Aug 24 14:17:10 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.14/0.37 This is a TF0_THM_EQU_ARI problem
% 0.14/0.37 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.APCKrO65Jd/Vampire---4.8_2922
% 0.14/0.37 % (3032)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.43 % (3037)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 % (3039)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 % (3034)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 % (3038)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)
% 0.23/0.43 % (3033)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 % (3035)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 % (3036)dis-11_10:1_canc=force:fsd=off:nwc=1.5:sas=z3:tha=off:uwa=all_472 on Vampire---4 for (472ds/0Mi)
% 0.23/0.44 % (3039)First to succeed.
% 0.23/0.44 % (3039)Refutation found. Thanks to Tanya!
% 0.23/0.44 % SZS status Theorem for Vampire---4
% 0.23/0.44 % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.44 % (3039)------------------------------
% 0.23/0.44 % (3039)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.44 % (3039)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.44 % (3039)Termination reason: Refutation
% 0.23/0.44
% 0.23/0.44 % (3039)Memory used [KB]: 1279
% 0.23/0.44 % (3039)Time elapsed: 0.013 s
% 0.23/0.44 % (3039)------------------------------
% 0.23/0.44 % (3039)------------------------------
% 0.23/0.44 % (3032)Success in time 0.072 s
% 0.23/0.44 % Vampire---4.8 exiting
%------------------------------------------------------------------------------