TSTP Solution File: SEU292+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU292+1 : TPTP v8.1.2. Released v3.3.0.
% 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 17:57:39 EDT 2023
% Result : Theorem 0.23s 0.45s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 16 unt; 0 def)
% Number of atoms : 203 ( 62 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 232 ( 81 ~; 65 |; 61 &)
% ( 7 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 90 (; 73 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f464,plain,
$false,
inference(subsumption_resolution,[],[f460,f304]) ).
fof(f304,plain,
~ relation(sK3),
inference(subsumption_resolution,[],[f302,f149]) ).
fof(f149,plain,
in(sK2,sK0),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
( apply(relation_composition(sK3,sK4),sK2) != apply(sK4,apply(sK3,sK2))
& empty_set != sK1
& in(sK2,sK0)
& function(sK4)
& relation(sK4)
& relation_of2_as_subset(sK3,sK0,sK1)
& quasi_total(sK3,sK0,sK1)
& function(sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f67,f106,f105]) ).
fof(f105,plain,
( ? [X0,X1,X2,X3] :
( ? [X4] :
( apply(relation_composition(X3,X4),X2) != apply(X4,apply(X3,X2))
& empty_set != X1
& in(X2,X0)
& function(X4)
& relation(X4) )
& relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) )
=> ( ? [X4] :
( apply(relation_composition(sK3,X4),sK2) != apply(X4,apply(sK3,sK2))
& empty_set != sK1
& in(sK2,sK0)
& function(X4)
& relation(X4) )
& relation_of2_as_subset(sK3,sK0,sK1)
& quasi_total(sK3,sK0,sK1)
& function(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f106,plain,
( ? [X4] :
( apply(relation_composition(sK3,X4),sK2) != apply(X4,apply(sK3,sK2))
& empty_set != sK1
& in(sK2,sK0)
& function(X4)
& relation(X4) )
=> ( apply(relation_composition(sK3,sK4),sK2) != apply(sK4,apply(sK3,sK2))
& empty_set != sK1
& in(sK2,sK0)
& function(sK4)
& relation(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
? [X0,X1,X2,X3] :
( ? [X4] :
( apply(relation_composition(X3,X4),X2) != apply(X4,apply(X3,X2))
& empty_set != X1
& in(X2,X0)
& function(X4)
& relation(X4) )
& relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) ),
inference(flattening,[],[f66]) ).
fof(f66,plain,
? [X0,X1,X2,X3] :
( ? [X4] :
( apply(relation_composition(X3,X4),X2) != apply(X4,apply(X3,X2))
& empty_set != X1
& in(X2,X0)
& function(X4)
& relation(X4) )
& relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) )
=> ! [X4] :
( ( function(X4)
& relation(X4) )
=> ( in(X2,X0)
=> ( apply(relation_composition(X3,X4),X2) = apply(X4,apply(X3,X2))
| empty_set = X1 ) ) ) ),
inference(negated_conjecture,[],[f48]) ).
fof(f48,conjecture,
! [X0,X1,X2,X3] :
( ( relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) )
=> ! [X4] :
( ( function(X4)
& relation(X4) )
=> ( in(X2,X0)
=> ( apply(relation_composition(X3,X4),X2) = apply(X4,apply(X3,X2))
| empty_set = X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WFKJoTAzJl/Vampire---4.8_16679',t21_funct_2) ).
fof(f302,plain,
( ~ in(sK2,sK0)
| ~ relation(sK3) ),
inference(backward_demodulation,[],[f288,f301]) ).
fof(f301,plain,
sK0 = relation_dom(sK3),
inference(forward_demodulation,[],[f299,f279]) ).
fof(f279,plain,
sK0 = relation_dom_as_subset(sK0,sK1,sK3),
inference(subsumption_resolution,[],[f278,f146]) ).
fof(f146,plain,
relation_of2_as_subset(sK3,sK0,sK1),
inference(cnf_transformation,[],[f107]) ).
fof(f278,plain,
( sK0 = relation_dom_as_subset(sK0,sK1,sK3)
| ~ relation_of2_as_subset(sK3,sK0,sK1) ),
inference(subsumption_resolution,[],[f277,f150]) ).
fof(f150,plain,
empty_set != sK1,
inference(cnf_transformation,[],[f107]) ).
fof(f277,plain,
( sK0 = relation_dom_as_subset(sK0,sK1,sK3)
| empty_set = sK1
| ~ relation_of2_as_subset(sK3,sK0,sK1) ),
inference(resolution,[],[f145,f197]) ).
fof(f197,plain,
! [X2,X0,X1] :
( relation_dom_as_subset(X0,X1,X2) = X0
| ~ quasi_total(X2,X0,X1)
| empty_set = X1
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0,X1,X2] :
( ( ( ( ( quasi_total(X2,X0,X1)
| empty_set != X2 )
& ( empty_set = X2
| ~ quasi_total(X2,X0,X1) ) )
| empty_set = X0
| empty_set != X1 )
& ( ( ( quasi_total(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) != X0 )
& ( relation_dom_as_subset(X0,X1,X2) = X0
| ~ quasi_total(X2,X0,X1) ) )
| ( empty_set != X0
& empty_set = X1 ) ) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(nnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ( ( ( quasi_total(X2,X0,X1)
<=> empty_set = X2 )
| empty_set = X0
| empty_set != X1 )
& ( ( quasi_total(X2,X0,X1)
<=> relation_dom_as_subset(X0,X1,X2) = X0 )
| ( empty_set != X0
& empty_set = X1 ) ) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(flattening,[],[f97]) ).
fof(f97,plain,
! [X0,X1,X2] :
( ( ( ( quasi_total(X2,X0,X1)
<=> empty_set = X2 )
| empty_set = X0
| empty_set != X1 )
& ( ( quasi_total(X2,X0,X1)
<=> relation_dom_as_subset(X0,X1,X2) = X0 )
| ( empty_set != X0
& empty_set = X1 ) ) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( ( empty_set = X1
=> ( ( quasi_total(X2,X0,X1)
<=> empty_set = X2 )
| empty_set = X0 ) )
& ( ( empty_set = X1
=> empty_set = X0 )
=> ( quasi_total(X2,X0,X1)
<=> relation_dom_as_subset(X0,X1,X2) = X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WFKJoTAzJl/Vampire---4.8_16679',d1_funct_2) ).
fof(f145,plain,
quasi_total(sK3,sK0,sK1),
inference(cnf_transformation,[],[f107]) ).
fof(f299,plain,
relation_dom(sK3) = relation_dom_as_subset(sK0,sK1,sK3),
inference(resolution,[],[f280,f203]) ).
fof(f203,plain,
! [X2,X0,X1] :
( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0,X1,X2] :
( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
file('/export/starexec/sandbox/tmp/tmp.WFKJoTAzJl/Vampire---4.8_16679',redefinition_k4_relset_1) ).
fof(f280,plain,
relation_of2(sK3,sK0,sK1),
inference(resolution,[],[f146,f207]) ).
fof(f207,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) )
& ( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.WFKJoTAzJl/Vampire---4.8_16679',redefinition_m2_relset_1) ).
fof(f288,plain,
( ~ in(sK2,relation_dom(sK3))
| ~ relation(sK3) ),
inference(subsumption_resolution,[],[f287,f144]) ).
fof(f144,plain,
function(sK3),
inference(cnf_transformation,[],[f107]) ).
fof(f287,plain,
( ~ in(sK2,relation_dom(sK3))
| ~ function(sK3)
| ~ relation(sK3) ),
inference(subsumption_resolution,[],[f286,f147]) ).
fof(f147,plain,
relation(sK4),
inference(cnf_transformation,[],[f107]) ).
fof(f286,plain,
( ~ in(sK2,relation_dom(sK3))
| ~ relation(sK4)
| ~ function(sK3)
| ~ relation(sK3) ),
inference(subsumption_resolution,[],[f285,f148]) ).
fof(f148,plain,
function(sK4),
inference(cnf_transformation,[],[f107]) ).
fof(f285,plain,
( ~ in(sK2,relation_dom(sK3))
| ~ function(sK4)
| ~ relation(sK4)
| ~ function(sK3)
| ~ relation(sK3) ),
inference(trivial_inequality_removal,[],[f284]) ).
fof(f284,plain,
( apply(sK4,apply(sK3,sK2)) != apply(sK4,apply(sK3,sK2))
| ~ in(sK2,relation_dom(sK3))
| ~ function(sK4)
| ~ relation(sK4)
| ~ function(sK3)
| ~ relation(sK3) ),
inference(superposition,[],[f151,f182]) ).
fof(f182,plain,
! [X2,X0,X1] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(X1))
=> apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WFKJoTAzJl/Vampire---4.8_16679',t23_funct_1) ).
fof(f151,plain,
apply(relation_composition(sK3,sK4),sK2) != apply(sK4,apply(sK3,sK2)),
inference(cnf_transformation,[],[f107]) ).
fof(f460,plain,
relation(sK3),
inference(resolution,[],[f283,f205]) ).
fof(f205,plain,
! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox/tmp/tmp.WFKJoTAzJl/Vampire---4.8_16679',cc1_relset_1) ).
fof(f283,plain,
element(sK3,powerset(cartesian_product2(sK0,sK1))),
inference(resolution,[],[f146,f196]) ).
fof(f196,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox/tmp/tmp.WFKJoTAzJl/Vampire---4.8_16679',dt_m2_relset_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU292+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.38 % Computer : n015.cluster.edu
% 0.15/0.38 % Model : x86_64 x86_64
% 0.15/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38 % Memory : 8042.1875MB
% 0.15/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38 % CPULimit : 300
% 0.15/0.38 % WCLimit : 300
% 0.15/0.38 % DateTime : Wed Aug 23 20:16:05 EDT 2023
% 0.15/0.38 % CPUTime :
% 0.15/0.38 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.38 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.WFKJoTAzJl/Vampire---4.8_16679
% 0.23/0.38 % (16803)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.44 % (16815)lrs+2_5:4_anc=none:br=off:fde=unused:gsp=on:nm=32:nwc=1.3:sims=off:sos=all:urr=on:stl=62_558 on Vampire---4 for (558ds/0Mi)
% 0.23/0.44 % (16805)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_1192 on Vampire---4 for (1192ds/0Mi)
% 0.23/0.44 % (16818)lrs-1010_20_afr=on:anc=all_dependent:bs=on:bsr=on:cond=on:er=known:fde=none:nm=4:nwc=1.3:sims=off:sp=frequency:urr=on:stl=62_533 on Vampire---4 for (533ds/0Mi)
% 0.23/0.44 % (16809)ott+3_2:7_add=large:amm=off:anc=all:bce=on:drc=off:fsd=off:fde=unused:gs=on:irw=on:lcm=predicate:lma=on:msp=off:nwc=10.0:sac=on_598 on Vampire---4 for (598ds/0Mi)
% 0.23/0.44 % (16822)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_520 on Vampire---4 for (520ds/0Mi)
% 0.23/0.44 % (16811)lrs+11_10:1_bs=unit_only:drc=off:fsd=off:fde=none:gs=on:msp=off:nm=16:nwc=2.0:nicw=on:sos=all:sac=on:sp=reverse_frequency:stl=62_575 on Vampire---4 for (575ds/0Mi)
% 0.23/0.44 % (16823)ott+1010_1_aac=none:bce=on:ep=RS:fsd=off:nm=4:nwc=2.0:nicw=on:sas=z3:sims=off_453 on Vampire---4 for (453ds/0Mi)
% 0.23/0.45 % (16811)First to succeed.
% 0.23/0.45 % (16811)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 % (16811)------------------------------
% 0.23/0.45 % (16811)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.45 % (16811)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.45 % (16811)Termination reason: Refutation
% 0.23/0.45
% 0.23/0.45 % (16811)Memory used [KB]: 10362
% 0.23/0.45 % (16811)Time elapsed: 0.013 s
% 0.23/0.45 % (16811)------------------------------
% 0.23/0.45 % (16811)------------------------------
% 0.23/0.45 % (16803)Success in time 0.072 s
% 0.23/0.46 % Vampire---4.8 exiting
%------------------------------------------------------------------------------