TSTP Solution File: SEU328+1 by SnakeForV---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SEU328+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n009.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 31 18:28:48 EDT 2022
% Result : Theorem 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 50 ( 20 unt; 0 def)
% Number of atoms : 99 ( 54 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 84 ( 35 ~; 20 |; 12 &)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 65 ( 59 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f442,plain,
$false,
inference(subsumption_resolution,[],[f440,f311]) ).
fof(f311,plain,
subset_complement(sK2,set_meet(sK1)) != union_of_subsets(sK2,complements_of_subsets(sK2,sK1)),
inference(backward_demodulation,[],[f184,f257]) ).
fof(f257,plain,
meet_of_subsets(sK2,sK1) = set_meet(sK1),
inference(unit_resulting_resolution,[],[f186,f240]) ).
fof(f240,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| meet_of_subsets(X0,X1) = set_meet(X1) ),
inference(cnf_transformation,[],[f160]) ).
fof(f160,plain,
! [X0,X1] :
( meet_of_subsets(X0,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(rectify,[],[f106]) ).
fof(f106,plain,
! [X1,X0] :
( set_meet(X0) = meet_of_subsets(X1,X0)
| ~ element(X0,powerset(powerset(X1))) ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,plain,
! [X1,X0] :
( element(X0,powerset(powerset(X1)))
=> set_meet(X0) = meet_of_subsets(X1,X0) ),
inference(rectify,[],[f45]) ).
fof(f45,axiom,
! [X1,X0] :
( element(X1,powerset(powerset(X0)))
=> meet_of_subsets(X0,X1) = set_meet(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
fof(f186,plain,
element(sK1,powerset(powerset(sK2))),
inference(cnf_transformation,[],[f149]) ).
fof(f149,plain,
( element(sK1,powerset(powerset(sK2)))
& empty_set != sK1
& subset_complement(sK2,meet_of_subsets(sK2,sK1)) != union_of_subsets(sK2,complements_of_subsets(sK2,sK1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f100,f148]) ).
fof(f148,plain,
( ? [X0,X1] :
( element(X0,powerset(powerset(X1)))
& empty_set != X0
& subset_complement(X1,meet_of_subsets(X1,X0)) != union_of_subsets(X1,complements_of_subsets(X1,X0)) )
=> ( element(sK1,powerset(powerset(sK2)))
& empty_set != sK1
& subset_complement(sK2,meet_of_subsets(sK2,sK1)) != union_of_subsets(sK2,complements_of_subsets(sK2,sK1)) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
? [X0,X1] :
( element(X0,powerset(powerset(X1)))
& empty_set != X0
& subset_complement(X1,meet_of_subsets(X1,X0)) != union_of_subsets(X1,complements_of_subsets(X1,X0)) ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
? [X1,X0] :
( subset_complement(X1,meet_of_subsets(X1,X0)) != union_of_subsets(X1,complements_of_subsets(X1,X0))
& empty_set != X0
& element(X0,powerset(powerset(X1))) ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,plain,
~ ! [X1,X0] :
( element(X0,powerset(powerset(X1)))
=> ( empty_set != X0
=> subset_complement(X1,meet_of_subsets(X1,X0)) = union_of_subsets(X1,complements_of_subsets(X1,X0)) ) ),
inference(rectify,[],[f49]) ).
fof(f49,negated_conjecture,
~ ! [X1,X0] :
( element(X1,powerset(powerset(X0)))
=> ( empty_set != X1
=> union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_complement(X0,meet_of_subsets(X0,X1)) ) ),
inference(negated_conjecture,[],[f48]) ).
fof(f48,conjecture,
! [X1,X0] :
( element(X1,powerset(powerset(X0)))
=> ( empty_set != X1
=> union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_complement(X0,meet_of_subsets(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_tops_2) ).
fof(f184,plain,
subset_complement(sK2,meet_of_subsets(sK2,sK1)) != union_of_subsets(sK2,complements_of_subsets(sK2,sK1)),
inference(cnf_transformation,[],[f149]) ).
fof(f440,plain,
subset_complement(sK2,set_meet(sK1)) = union_of_subsets(sK2,complements_of_subsets(sK2,sK1)),
inference(backward_demodulation,[],[f428,f383]) ).
fof(f383,plain,
set_difference(sK2,set_meet(sK1)) = subset_complement(sK2,set_meet(sK1)),
inference(unit_resulting_resolution,[],[f324,f177]) ).
fof(f177,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset_complement(X1,X0) = set_difference(X1,X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset_complement(X1,X0) = set_difference(X1,X0) ),
inference(ennf_transformation,[],[f65]) ).
fof(f65,plain,
! [X1,X0] :
( element(X0,powerset(X1))
=> subset_complement(X1,X0) = set_difference(X1,X0) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X1,X0] :
( element(X1,powerset(X0))
=> subset_complement(X0,X1) = set_difference(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
fof(f324,plain,
element(set_meet(sK1),powerset(sK2)),
inference(forward_demodulation,[],[f254,f257]) ).
fof(f254,plain,
element(meet_of_subsets(sK2,sK1),powerset(sK2)),
inference(unit_resulting_resolution,[],[f186,f178]) ).
fof(f178,plain,
! [X0,X1] :
( element(meet_of_subsets(X1,X0),powerset(X1))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
! [X0,X1] :
( element(meet_of_subsets(X1,X0),powerset(X1))
| ~ element(X0,powerset(powerset(X1))) ),
inference(ennf_transformation,[],[f78]) ).
fof(f78,plain,
! [X1,X0] :
( element(X0,powerset(powerset(X1)))
=> element(meet_of_subsets(X1,X0),powerset(X1)) ),
inference(rectify,[],[f27]) ).
fof(f27,axiom,
! [X1,X0] :
( element(X1,powerset(powerset(X0)))
=> element(meet_of_subsets(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
fof(f428,plain,
set_difference(sK2,set_meet(sK1)) = union_of_subsets(sK2,complements_of_subsets(sK2,sK1)),
inference(backward_demodulation,[],[f310,f427]) ).
fof(f427,plain,
set_difference(sK2,set_meet(sK1)) = subset_difference(sK2,sK2,set_meet(sK1)),
inference(forward_demodulation,[],[f384,f220]) ).
fof(f220,plain,
! [X0] : cast_to_subset(X0) = X0,
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] : cast_to_subset(X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).
fof(f384,plain,
subset_difference(sK2,cast_to_subset(sK2),set_meet(sK1)) = set_difference(cast_to_subset(sK2),set_meet(sK1)),
inference(unit_resulting_resolution,[],[f168,f324,f187]) ).
fof(f187,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0))
| set_difference(X2,X1) = subset_difference(X0,X2,X1) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X0))
| set_difference(X2,X1) = subset_difference(X0,X2,X1)
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f114]) ).
fof(f114,plain,
! [X2,X0,X1] :
( set_difference(X2,X1) = subset_difference(X0,X2,X1)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f66]) ).
fof(f66,plain,
! [X2,X0,X1] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> set_difference(X2,X1) = subset_difference(X0,X2,X1) ),
inference(rectify,[],[f46]) ).
fof(f46,axiom,
! [X0,X2,X1] :
( ( element(X1,powerset(X0))
& element(X2,powerset(X0)) )
=> subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(f168,plain,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).
fof(f310,plain,
subset_difference(sK2,sK2,set_meet(sK1)) = union_of_subsets(sK2,complements_of_subsets(sK2,sK1)),
inference(backward_demodulation,[],[f305,f257]) ).
fof(f305,plain,
subset_difference(sK2,sK2,meet_of_subsets(sK2,sK1)) = union_of_subsets(sK2,complements_of_subsets(sK2,sK1)),
inference(forward_demodulation,[],[f304,f220]) ).
fof(f304,plain,
subset_difference(sK2,cast_to_subset(sK2),meet_of_subsets(sK2,sK1)) = union_of_subsets(sK2,complements_of_subsets(sK2,sK1)),
inference(subsumption_resolution,[],[f282,f185]) ).
fof(f185,plain,
empty_set != sK1,
inference(cnf_transformation,[],[f149]) ).
fof(f282,plain,
( empty_set = sK1
| subset_difference(sK2,cast_to_subset(sK2),meet_of_subsets(sK2,sK1)) = union_of_subsets(sK2,complements_of_subsets(sK2,sK1)) ),
inference(resolution,[],[f186,f230]) ).
fof(f230,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1 ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f128]) ).
fof(f128,plain,
! [X1,X0] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X1,X0] :
( element(X1,powerset(powerset(X0)))
=> ( empty_set != X1
=> union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_setfam_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU328+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Tue Aug 30 15:10:05 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.19/0.45 % (26605)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.47 % (26613)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.47 % (26613)First to succeed.
% 0.19/0.49 % (26613)Refutation found. Thanks to Tanya!
% 0.19/0.49 % SZS status Theorem for theBenchmark
% 0.19/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49 % (26613)------------------------------
% 0.19/0.49 % (26613)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.49 % (26613)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.49 % (26613)Termination reason: Refutation
% 0.19/0.49
% 0.19/0.49 % (26613)Memory used [KB]: 6140
% 0.19/0.49 % (26613)Time elapsed: 0.079 s
% 0.19/0.49 % (26613)Instructions burned: 12 (million)
% 0.19/0.49 % (26613)------------------------------
% 0.19/0.49 % (26613)------------------------------
% 0.19/0.49 % (26591)Success in time 0.152 s
%------------------------------------------------------------------------------