TSTP Solution File: SET975+1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET975+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n026.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 15:46:36 EDT 2023
% Result : Theorem 0.24s 0.45s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 6 unt; 0 def)
% Number of atoms : 136 ( 51 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 163 ( 63 ~; 63 |; 29 &)
% ( 5 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 76 (; 57 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f83,plain,
$false,
inference(subsumption_resolution,[],[f49,f82]) ).
fof(f82,plain,
~ in(sK1,sK3),
inference(resolution,[],[f79,f44]) ).
fof(f44,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f43]) ).
fof(f43,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f35]) ).
fof(f35,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK4(X0,X1) != X0
| ~ in(sK4(X0,X1),X1) )
& ( sK4(X0,X1) = X0
| in(sK4(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f18,f19]) ).
fof(f19,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK4(X0,X1) != X0
| ~ in(sK4(X0,X1),X1) )
& ( sK4(X0,X1) = X0
| in(sK4(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.VRWTlGz14o/Vampire---4.8_18388',d1_tarski) ).
fof(f79,plain,
( ~ in(sK2,singleton(sK2))
| ~ in(sK1,sK3) ),
inference(resolution,[],[f40,f76]) ).
fof(f76,plain,
~ in(ordered_pair(sK2,sK1),cartesian_product2(singleton(sK2),sK3)),
inference(subsumption_resolution,[],[f50,f75]) ).
fof(f75,plain,
sK0 = sK2,
inference(duplicate_literal_removal,[],[f72]) ).
fof(f72,plain,
( sK0 = sK2
| sK0 = sK2 ),
inference(resolution,[],[f69,f45]) ).
fof(f45,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f34]) ).
fof(f34,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f69,plain,
( in(sK0,singleton(sK2))
| sK0 = sK2 ),
inference(resolution,[],[f27,f38]) ).
fof(f38,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f21]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VRWTlGz14o/Vampire---4.8_18388',l55_zfmisc_1) ).
fof(f27,plain,
( in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3))
| sK0 = sK2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
( ( ~ in(sK1,sK3)
| sK0 != sK2
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) )
& ( ( in(sK1,sK3)
& sK0 = sK2 )
| in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f14,f15]) ).
fof(f15,plain,
( ? [X0,X1,X2,X3] :
( ( ~ in(X1,X3)
| X0 != X2
| ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) )
& ( ( in(X1,X3)
& X0 = X2 )
| in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) ) )
=> ( ( ~ in(sK1,sK3)
| sK0 != sK2
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) )
& ( ( in(sK1,sK3)
& sK0 = sK2 )
| in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
? [X0,X1,X2,X3] :
( ( ~ in(X1,X3)
| X0 != X2
| ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) )
& ( ( in(X1,X3)
& X0 = X2 )
| in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) ) ),
inference(flattening,[],[f13]) ).
fof(f13,plain,
? [X0,X1,X2,X3] :
( ( ~ in(X1,X3)
| X0 != X2
| ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) )
& ( ( in(X1,X3)
& X0 = X2 )
| in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
? [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
<~> ( in(X1,X3)
& X0 = X2 ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
<=> ( in(X1,X3)
& X0 = X2 ) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
<=> ( in(X1,X3)
& X0 = X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.VRWTlGz14o/Vampire---4.8_18388',t128_zfmisc_1) ).
fof(f50,plain,
( sK0 != sK2
| ~ in(ordered_pair(sK2,sK1),cartesian_product2(singleton(sK2),sK3)) ),
inference(subsumption_resolution,[],[f46,f49]) ).
fof(f46,plain,
( ~ in(sK1,sK3)
| sK0 != sK2
| ~ in(ordered_pair(sK2,sK1),cartesian_product2(singleton(sK2),sK3)) ),
inference(inner_rewriting,[],[f29]) ).
fof(f29,plain,
( ~ in(sK1,sK3)
| sK0 != sK2
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f40,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f49,plain,
in(sK1,sK3),
inference(subsumption_resolution,[],[f28,f39]) ).
fof(f39,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f22]) ).
fof(f28,plain,
( in(sK1,sK3)
| in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) ),
inference(cnf_transformation,[],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SET975+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.16 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.17/0.37 % Computer : n026.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Sat Aug 26 12:38:48 EDT 2023
% 0.17/0.38 % CPUTime :
% 0.17/0.38 This is a FOF_THM_RFO_SEQ problem
% 0.17/0.38 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.VRWTlGz14o/Vampire---4.8_18388
% 0.17/0.38 % (18499)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.44 % (18500)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_1169 on Vampire---4 for (1169ds/0Mi)
% 0.24/0.44 % (18505)lrs-11_32_av=off:bd=off:bs=on:bsr=on:drc=off:flr=on:fsd=off:fsr=off:fde=none:gsp=on:irw=on:lcm=predicate:nm=4:sp=scramble:stl=125_825 on Vampire---4 for (825ds/0Mi)
% 0.24/0.44 % (18502)ott-4_11_av=off:bd=preordered:bce=on:drc=off:flr=on:fsr=off:lma=on:nwc=2.0:sp=occurrence:tgt=ground:urr=ec_only_1010 on Vampire---4 for (1010ds/0Mi)
% 0.24/0.44 % (18501)lrs-11_28_aac=none:afr=on:anc=none:bs=on:drc=off:fde=unused:gs=on:nm=2:nwc=1.3:sp=frequency:stl=188_1092 on Vampire---4 for (1092ds/0Mi)
% 0.24/0.44 % (18506)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_501 on Vampire---4 for (501ds/0Mi)
% 0.24/0.44 % (18503)lrs+3_20_av=off:bd=preordered:drc=off:fsd=off:fsr=off:fde=unused:irw=on:lcm=reverse:sos=theory:stl=315_961 on Vampire---4 for (961ds/0Mi)
% 0.24/0.44 % (18504)ott+1003_4:1_av=off:cond=on:drc=off:fsd=off:fsr=off:fde=none:gsp=on:nm=2:nwc=1.5:sos=all:sp=reverse_arity:tgt=full_871 on Vampire---4 for (871ds/0Mi)
% 0.24/0.44 % (18505)First to succeed.
% 0.24/0.45 % (18501)Also succeeded, but the first one will report.
% 0.24/0.45 % (18505)Refutation found. Thanks to Tanya!
% 0.24/0.45 % SZS status Theorem for Vampire---4
% 0.24/0.45 % SZS output start Proof for Vampire---4
% See solution above
% 0.24/0.45 % (18505)------------------------------
% 0.24/0.45 % (18505)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.24/0.45 % (18505)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.24/0.45 % (18505)Termination reason: Refutation
% 0.24/0.45
% 0.24/0.45 % (18505)Memory used [KB]: 1023
% 0.24/0.45 % (18505)Time elapsed: 0.006 s
% 0.24/0.45 % (18505)------------------------------
% 0.24/0.45 % (18505)------------------------------
% 0.24/0.45 % (18499)Success in time 0.064 s
% 0.24/0.45 % Vampire---4.8 exiting
%------------------------------------------------------------------------------