TSTP Solution File: SEU321+1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU321+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 : n027.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 17:58:01 EDT 2023
% Result : Theorem 0.19s 0.41s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 54 ( 14 unt; 0 def)
% Number of atoms : 195 ( 19 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 220 ( 79 ~; 70 |; 52 &)
% ( 2 <=>; 15 =>; 0 <=; 2 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 59 (; 38 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f854,plain,
$false,
inference(subsumption_resolution,[],[f797,f123]) ).
fof(f123,plain,
empty(empty_set),
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
( v5_membered(empty_set)
& v4_membered(empty_set)
& v3_membered(empty_set)
& v2_membered(empty_set)
& v1_membered(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/tmp/tmp.HWUNZrYnLZ/Vampire---4.8_13173',fc6_membered) ).
fof(f797,plain,
~ empty(empty_set),
inference(backward_demodulation,[],[f200,f792]) ).
fof(f792,plain,
empty_set = sF11,
inference(subsumption_resolution,[],[f791,f742]) ).
fof(f742,plain,
( in(sK4,sK3)
| empty_set = sF11 ),
inference(forward_literal_rewriting,[],[f741,f186]) ).
fof(f186,plain,
( ~ in(sK4,sF12)
| in(sK4,sK3) ),
inference(definition_folding,[],[f122,f185,f184]) ).
fof(f184,plain,
the_carrier(sK2) = sF11,
introduced(function_definition,[]) ).
fof(f185,plain,
subset_complement(sF11,sK3) = sF12,
introduced(function_definition,[]) ).
fof(f122,plain,
( in(sK4,sK3)
| ~ in(sK4,subset_complement(the_carrier(sK2),sK3)) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
( ( in(sK4,sK3)
| ~ in(sK4,subset_complement(the_carrier(sK2),sK3)) )
& ( ~ in(sK4,sK3)
| in(sK4,subset_complement(the_carrier(sK2),sK3)) )
& element(sK4,the_carrier(sK2))
& element(sK3,powerset(the_carrier(sK2)))
& one_sorted_str(sK2)
& ~ empty_carrier(sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f99,f102,f101,f100]) ).
fof(f100,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,X1)
| ~ in(X2,subset_complement(the_carrier(X0),X1)) )
& ( ~ in(X2,X1)
| in(X2,subset_complement(the_carrier(X0),X1)) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ( ? [X1] :
( ? [X2] :
( ( in(X2,X1)
| ~ in(X2,subset_complement(the_carrier(sK2),X1)) )
& ( ~ in(X2,X1)
| in(X2,subset_complement(the_carrier(sK2),X1)) )
& element(X2,the_carrier(sK2)) )
& element(X1,powerset(the_carrier(sK2))) )
& one_sorted_str(sK2)
& ~ empty_carrier(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
( ? [X1] :
( ? [X2] :
( ( in(X2,X1)
| ~ in(X2,subset_complement(the_carrier(sK2),X1)) )
& ( ~ in(X2,X1)
| in(X2,subset_complement(the_carrier(sK2),X1)) )
& element(X2,the_carrier(sK2)) )
& element(X1,powerset(the_carrier(sK2))) )
=> ( ? [X2] :
( ( in(X2,sK3)
| ~ in(X2,subset_complement(the_carrier(sK2),sK3)) )
& ( ~ in(X2,sK3)
| in(X2,subset_complement(the_carrier(sK2),sK3)) )
& element(X2,the_carrier(sK2)) )
& element(sK3,powerset(the_carrier(sK2))) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
( ? [X2] :
( ( in(X2,sK3)
| ~ in(X2,subset_complement(the_carrier(sK2),sK3)) )
& ( ~ in(X2,sK3)
| in(X2,subset_complement(the_carrier(sK2),sK3)) )
& element(X2,the_carrier(sK2)) )
=> ( ( in(sK4,sK3)
| ~ in(sK4,subset_complement(the_carrier(sK2),sK3)) )
& ( ~ in(sK4,sK3)
| in(sK4,subset_complement(the_carrier(sK2),sK3)) )
& element(sK4,the_carrier(sK2)) ) ),
introduced(choice_axiom,[]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,X1)
| ~ in(X2,subset_complement(the_carrier(X0),X1)) )
& ( ~ in(X2,X1)
| in(X2,subset_complement(the_carrier(X0),X1)) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& one_sorted_str(X0)
& ~ empty_carrier(X0) ),
inference(flattening,[],[f98]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,X1)
| ~ in(X2,subset_complement(the_carrier(X0),X1)) )
& ( ~ in(X2,X1)
| in(X2,subset_complement(the_carrier(X0),X1)) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& one_sorted_str(X0)
& ~ empty_carrier(X0) ),
inference(nnf_transformation,[],[f62]) ).
fof(f62,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,subset_complement(the_carrier(X0),X1))
<~> ~ in(X2,X1) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& one_sorted_str(X0)
& ~ empty_carrier(X0) ),
inference(flattening,[],[f61]) ).
fof(f61,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,subset_complement(the_carrier(X0),X1))
<~> ~ in(X2,X1) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& one_sorted_str(X0)
& ~ empty_carrier(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,negated_conjecture,
~ ! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,subset_complement(the_carrier(X0),X1))
<=> ~ in(X2,X1) ) ) ) ),
inference(negated_conjecture,[],[f40]) ).
fof(f40,conjecture,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,subset_complement(the_carrier(X0),X1))
<=> ~ in(X2,X1) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWUNZrYnLZ/Vampire---4.8_13173',l40_tops_1) ).
fof(f741,plain,
( in(sK4,sF12)
| empty_set = sF11 ),
inference(subsumption_resolution,[],[f740,f187]) ).
fof(f187,plain,
( ~ in(sK4,sK3)
| in(sK4,sF12) ),
inference(definition_folding,[],[f121,f185,f184]) ).
fof(f121,plain,
( ~ in(sK4,sK3)
| in(sK4,subset_complement(the_carrier(sK2),sK3)) ),
inference(cnf_transformation,[],[f103]) ).
fof(f740,plain,
( in(sK4,sF12)
| in(sK4,sK3)
| empty_set = sF11 ),
inference(forward_demodulation,[],[f733,f185]) ).
fof(f733,plain,
( in(sK4,sK3)
| in(sK4,subset_complement(sF11,sK3))
| empty_set = sF11 ),
inference(resolution,[],[f588,f190]) ).
fof(f190,plain,
element(sK3,sF13),
inference(definition_folding,[],[f119,f189,f184]) ).
fof(f189,plain,
powerset(sF11) = sF13,
introduced(function_definition,[]) ).
fof(f119,plain,
element(sK3,powerset(the_carrier(sK2))),
inference(cnf_transformation,[],[f103]) ).
fof(f588,plain,
! [X0] :
( ~ element(X0,sF13)
| in(sK4,X0)
| in(sK4,subset_complement(sF11,X0))
| empty_set = sF11 ),
inference(resolution,[],[f408,f188]) ).
fof(f188,plain,
element(sK4,sF11),
inference(definition_folding,[],[f120,f184]) ).
fof(f120,plain,
element(sK4,the_carrier(sK2)),
inference(cnf_transformation,[],[f103]) ).
fof(f408,plain,
! [X0,X1] :
( ~ element(X1,sF11)
| in(X1,X0)
| ~ element(X0,sF13)
| in(X1,subset_complement(sF11,X0))
| empty_set = sF11 ),
inference(superposition,[],[f156,f189]) ).
fof(f156,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X0))
| in(X2,X1)
| ~ element(X2,X0)
| in(X2,subset_complement(X0,X1))
| empty_set = X0 ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0) )
| ~ element(X1,powerset(X0)) )
| empty_set = X0 ),
inference(flattening,[],[f74]) ).
fof(f74,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0) )
| ~ element(X1,powerset(X0)) )
| empty_set = X0 ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] :
( empty_set != X0
=> ! [X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,X0)
=> ( ~ in(X2,X1)
=> in(X2,subset_complement(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWUNZrYnLZ/Vampire---4.8_13173',t50_subset_1) ).
fof(f791,plain,
( ~ in(sK4,sK3)
| empty_set = sF11 ),
inference(forward_literal_rewriting,[],[f790,f187]) ).
fof(f790,plain,
( ~ in(sK4,sF12)
| empty_set = sF11 ),
inference(subsumption_resolution,[],[f789,f190]) ).
fof(f789,plain,
( ~ element(sK3,sF13)
| ~ in(sK4,sF12)
| empty_set = sF11 ),
inference(forward_demodulation,[],[f788,f189]) ).
fof(f788,plain,
( ~ in(sK4,sF12)
| empty_set = sF11
| ~ element(sK3,powerset(sF11)) ),
inference(superposition,[],[f746,f185]) ).
fof(f746,plain,
! [X0] :
( ~ in(sK4,subset_complement(X0,sK3))
| empty_set = sF11
| ~ element(sK3,powerset(X0)) ),
inference(resolution,[],[f742,f170]) ).
fof(f170,plain,
! [X2,X0,X1] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f89]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0,X1,X2] :
( element(X2,powerset(X0))
=> ~ ( in(X1,X2)
& in(X1,subset_complement(X0,X2)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWUNZrYnLZ/Vampire---4.8_13173',t54_subset_1) ).
fof(f200,plain,
~ empty(sF11),
inference(subsumption_resolution,[],[f199,f117]) ).
fof(f117,plain,
~ empty_carrier(sK2),
inference(cnf_transformation,[],[f103]) ).
fof(f199,plain,
( ~ empty(sF11)
| empty_carrier(sK2) ),
inference(subsumption_resolution,[],[f198,f118]) ).
fof(f118,plain,
one_sorted_str(sK2),
inference(cnf_transformation,[],[f103]) ).
fof(f198,plain,
( ~ empty(sF11)
| ~ one_sorted_str(sK2)
| empty_carrier(sK2) ),
inference(superposition,[],[f157,f184]) ).
fof(f157,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f76]) ).
fof(f76,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWUNZrYnLZ/Vampire---4.8_13173',fc1_struct_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU321+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 23 22:00:17 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.33 This is a FOF_THM_RFO_SEQ problem
% 0.12/0.33 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.HWUNZrYnLZ/Vampire---4.8_13173
% 0.12/0.33 % (13426)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.38 % (13436)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)
% 0.19/0.39 % (13431)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)
% 0.19/0.39 % (13430)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)
% 0.19/0.39 % (13435)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.19/0.39 % (13432)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)
% 0.19/0.39 % (13433)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)
% 0.19/0.40 % (13434)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)
% 0.19/0.41 % (13436)First to succeed.
% 0.19/0.41 % (13435)Also succeeded, but the first one will report.
% 0.19/0.41 % (13436)Refutation found. Thanks to Tanya!
% 0.19/0.41 % SZS status Theorem for Vampire---4
% 0.19/0.41 % SZS output start Proof for Vampire---4
% See solution above
% 0.19/0.41 % (13436)------------------------------
% 0.19/0.41 % (13436)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.19/0.41 % (13436)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.19/0.41 % (13436)Termination reason: Refutation
% 0.19/0.41
% 0.19/0.41 % (13436)Memory used [KB]: 1663
% 0.19/0.41 % (13436)Time elapsed: 0.026 s
% 0.19/0.41 % (13436)------------------------------
% 0.19/0.41 % (13436)------------------------------
% 0.19/0.41 % (13426)Success in time 0.076 s
% 0.19/0.41 % Vampire---4.8 exiting
%------------------------------------------------------------------------------