TSTP Solution File: SEU106+1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU106+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 : n013.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 17:55:44 EDT 2023
% Result : Theorem 0.23s 0.48s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 9 unt; 0 def)
% Number of atoms : 170 ( 6 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 211 ( 87 ~; 72 |; 37 &)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 91 (; 82 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1781,plain,
$false,
inference(unit_resulting_resolution,[],[f123,f1780,f245]) ).
fof(f245,plain,
! [X4] :
( element(sK4(X4),X4)
| preboolean(X4) ),
inference(resolution,[],[f171,f147]) ).
fof(f147,plain,
! [X0] :
( in(sK4(X0),X0)
| preboolean(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0] :
( ( preboolean(X0)
| ( ( ~ in(set_difference(sK4(X0),sK5(X0)),X0)
| ~ in(set_union2(sK4(X0),sK5(X0)),X0) )
& in(sK5(X0),X0)
& in(sK4(X0),X0) ) )
& ( ! [X3,X4] :
( ( in(set_difference(X3,X4),X0)
& in(set_union2(X3,X4),X0) )
| ~ in(X4,X0)
| ~ in(X3,X0) )
| ~ preboolean(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f103,f104]) ).
fof(f104,plain,
! [X0] :
( ? [X1,X2] :
( ( ~ in(set_difference(X1,X2),X0)
| ~ in(set_union2(X1,X2),X0) )
& in(X2,X0)
& in(X1,X0) )
=> ( ( ~ in(set_difference(sK4(X0),sK5(X0)),X0)
| ~ in(set_union2(sK4(X0),sK5(X0)),X0) )
& in(sK5(X0),X0)
& in(sK4(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f103,plain,
! [X0] :
( ( preboolean(X0)
| ? [X1,X2] :
( ( ~ in(set_difference(X1,X2),X0)
| ~ in(set_union2(X1,X2),X0) )
& in(X2,X0)
& in(X1,X0) ) )
& ( ! [X3,X4] :
( ( in(set_difference(X3,X4),X0)
& in(set_union2(X3,X4),X0) )
| ~ in(X4,X0)
| ~ in(X3,X0) )
| ~ preboolean(X0) ) ),
inference(rectify,[],[f102]) ).
fof(f102,plain,
! [X0] :
( ( preboolean(X0)
| ? [X1,X2] :
( ( ~ in(set_difference(X1,X2),X0)
| ~ in(set_union2(X1,X2),X0) )
& in(X2,X0)
& in(X1,X0) ) )
& ( ! [X1,X2] :
( ( in(set_difference(X1,X2),X0)
& in(set_union2(X1,X2),X0) )
| ~ in(X2,X0)
| ~ in(X1,X0) )
| ~ preboolean(X0) ) ),
inference(nnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0] :
( preboolean(X0)
<=> ! [X1,X2] :
( ( in(set_difference(X1,X2),X0)
& in(set_union2(X1,X2),X0) )
| ~ in(X2,X0)
| ~ in(X1,X0) ) ),
inference(flattening,[],[f73]) ).
fof(f73,plain,
! [X0] :
( preboolean(X0)
<=> ! [X1,X2] :
( ( in(set_difference(X1,X2),X0)
& in(set_union2(X1,X2),X0) )
| ~ in(X2,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0] :
( preboolean(X0)
<=> ! [X1,X2] :
( ( in(X2,X0)
& in(X1,X0) )
=> ( in(set_difference(X1,X2),X0)
& in(set_union2(X1,X2),X0) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qpuYB6MTa8/Vampire---4.8_18960',t10_finsub_1) ).
fof(f171,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.qpuYB6MTa8/Vampire---4.8_18960',t1_subset) ).
fof(f1780,plain,
~ element(sK4(sK0),sK0),
inference(subsumption_resolution,[],[f1778,f123]) ).
fof(f1778,plain,
( ~ element(sK4(sK0),sK0)
| preboolean(sK0) ),
inference(resolution,[],[f1772,f246]) ).
fof(f246,plain,
! [X5] :
( element(sK5(X5),X5)
| preboolean(X5) ),
inference(resolution,[],[f171,f148]) ).
fof(f148,plain,
! [X0] :
( in(sK5(X0),X0)
| preboolean(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f1772,plain,
( ~ element(sK5(sK0),sK0)
| ~ element(sK4(sK0),sK0) ),
inference(subsumption_resolution,[],[f1771,f122]) ).
fof(f122,plain,
! [X2,X1] :
( in(set_union2(X1,X2),sK0)
| ~ element(X2,sK0)
| ~ element(X1,sK0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
( ~ preboolean(sK0)
& ! [X1] :
( ! [X2] :
( ( in(set_union2(X1,X2),sK0)
& in(symmetric_difference(X1,X2),sK0) )
| ~ element(X2,sK0) )
| ~ element(X1,sK0) )
& ~ empty(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f63,f94]) ).
fof(f94,plain,
( ? [X0] :
( ~ preboolean(X0)
& ! [X1] :
( ! [X2] :
( ( in(set_union2(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) )
| ~ element(X2,X0) )
| ~ element(X1,X0) )
& ~ empty(X0) )
=> ( ~ preboolean(sK0)
& ! [X1] :
( ! [X2] :
( ( in(set_union2(X1,X2),sK0)
& in(symmetric_difference(X1,X2),sK0) )
| ~ element(X2,sK0) )
| ~ element(X1,sK0) )
& ~ empty(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
? [X0] :
( ~ preboolean(X0)
& ! [X1] :
( ! [X2] :
( ( in(set_union2(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) )
| ~ element(X2,X0) )
| ~ element(X1,X0) )
& ~ empty(X0) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
? [X0] :
( ~ preboolean(X0)
& ! [X1] :
( ! [X2] :
( ( in(set_union2(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) )
| ~ element(X2,X0) )
| ~ element(X1,X0) )
& ~ empty(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,negated_conjecture,
~ ! [X0] :
( ~ empty(X0)
=> ( ! [X1] :
( element(X1,X0)
=> ! [X2] :
( element(X2,X0)
=> ( in(set_union2(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) ) ) )
=> preboolean(X0) ) ),
inference(negated_conjecture,[],[f34]) ).
fof(f34,conjecture,
! [X0] :
( ~ empty(X0)
=> ( ! [X1] :
( element(X1,X0)
=> ! [X2] :
( element(X2,X0)
=> ( in(set_union2(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) ) ) )
=> preboolean(X0) ) ),
file('/export/starexec/sandbox/tmp/tmp.qpuYB6MTa8/Vampire---4.8_18960',t17_finsub_1) ).
fof(f1771,plain,
( ~ in(set_union2(sK4(sK0),sK5(sK0)),sK0)
| ~ element(sK4(sK0),sK0)
| ~ element(sK5(sK0),sK0) ),
inference(subsumption_resolution,[],[f1762,f123]) ).
fof(f1762,plain,
( preboolean(sK0)
| ~ in(set_union2(sK4(sK0),sK5(sK0)),sK0)
| ~ element(sK4(sK0),sK0)
| ~ element(sK5(sK0),sK0) ),
inference(resolution,[],[f149,f871]) ).
fof(f871,plain,
! [X4,X5] :
( in(set_difference(X5,X4),sK0)
| ~ element(X5,sK0)
| ~ element(X4,sK0) ),
inference(duplicate_literal_removal,[],[f853]) ).
fof(f853,plain,
! [X4,X5] :
( ~ element(X4,sK0)
| ~ element(X5,sK0)
| in(set_difference(X5,X4),sK0)
| ~ element(X5,sK0) ),
inference(resolution,[],[f839,f516]) ).
fof(f516,plain,
! [X6,X7] :
( ~ element(set_intersection2(X7,X6),sK0)
| in(set_difference(X6,X7),sK0)
| ~ element(X6,sK0) ),
inference(superposition,[],[f492,f159]) ).
fof(f159,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/tmp/tmp.qpuYB6MTa8/Vampire---4.8_18960',commutativity_k3_xboole_0) ).
fof(f492,plain,
! [X0,X1] :
( ~ element(set_intersection2(X0,X1),sK0)
| in(set_difference(X0,X1),sK0)
| ~ element(X0,sK0) ),
inference(superposition,[],[f121,f162]) ).
fof(f162,plain,
! [X0,X1] : set_difference(X0,X1) = symmetric_difference(X0,set_intersection2(X0,X1)),
inference(cnf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1] : set_difference(X0,X1) = symmetric_difference(X0,set_intersection2(X0,X1)),
file('/export/starexec/sandbox/tmp/tmp.qpuYB6MTa8/Vampire---4.8_18960',t100_xboole_1) ).
fof(f121,plain,
! [X2,X1] :
( in(symmetric_difference(X1,X2),sK0)
| ~ element(X2,sK0)
| ~ element(X1,sK0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f839,plain,
! [X0,X1] :
( element(set_intersection2(X1,X0),sK0)
| ~ element(X1,sK0)
| ~ element(X0,sK0) ),
inference(resolution,[],[f735,f171]) ).
fof(f735,plain,
! [X0,X1] :
( in(set_intersection2(X0,X1),sK0)
| ~ element(X1,sK0)
| ~ element(X0,sK0) ),
inference(subsumption_resolution,[],[f725,f243]) ).
fof(f243,plain,
! [X2,X3] :
( element(set_union2(X2,X3),sK0)
| ~ element(X3,sK0)
| ~ element(X2,sK0) ),
inference(resolution,[],[f171,f122]) ).
fof(f725,plain,
! [X0,X1] :
( ~ element(set_union2(X0,X1),sK0)
| in(set_intersection2(X0,X1),sK0)
| ~ element(X1,sK0)
| ~ element(X0,sK0) ),
inference(resolution,[],[f703,f242]) ).
fof(f242,plain,
! [X0,X1] :
( element(symmetric_difference(X0,X1),sK0)
| ~ element(X1,sK0)
| ~ element(X0,sK0) ),
inference(resolution,[],[f171,f121]) ).
fof(f703,plain,
! [X0,X1] :
( ~ element(symmetric_difference(X0,X1),sK0)
| ~ element(set_union2(X0,X1),sK0)
| in(set_intersection2(X0,X1),sK0) ),
inference(superposition,[],[f121,f163]) ).
fof(f163,plain,
! [X0,X1] : set_intersection2(X0,X1) = symmetric_difference(symmetric_difference(X0,X1),set_union2(X0,X1)),
inference(cnf_transformation,[],[f49]) ).
fof(f49,axiom,
! [X0,X1] : set_intersection2(X0,X1) = symmetric_difference(symmetric_difference(X0,X1),set_union2(X0,X1)),
file('/export/starexec/sandbox/tmp/tmp.qpuYB6MTa8/Vampire---4.8_18960',t95_xboole_1) ).
fof(f149,plain,
! [X0] :
( ~ in(set_difference(sK4(X0),sK5(X0)),X0)
| preboolean(X0)
| ~ in(set_union2(sK4(X0),sK5(X0)),X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f123,plain,
~ preboolean(sK0),
inference(cnf_transformation,[],[f95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU106+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.37 % Computer : n013.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu Aug 24 01:01:47 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.16/0.37 This is a FOF_THM_RFO_SEQ problem
% 0.16/0.37 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.qpuYB6MTa8/Vampire---4.8_18960
% 0.16/0.37 % (19267)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.43 % (19274)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)
% 0.23/0.43 % (19272)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)
% 0.23/0.43 % (19273)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.23/0.43 % (19268)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)
% 0.23/0.44 % (19271)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)
% 0.23/0.44 % (19270)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)
% 0.23/0.48 % (19269)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)
% 0.23/0.48 % (19272)First to succeed.
% 0.23/0.48 % (19272)Refutation found. Thanks to Tanya!
% 0.23/0.48 % SZS status Theorem for Vampire---4
% 0.23/0.48 % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.48 % (19272)------------------------------
% 0.23/0.48 % (19272)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.48 % (19272)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.48 % (19272)Termination reason: Refutation
% 0.23/0.48
% 0.23/0.48 % (19272)Memory used [KB]: 1535
% 0.23/0.48 % (19272)Time elapsed: 0.048 s
% 0.23/0.48 % (19272)------------------------------
% 0.23/0.48 % (19272)------------------------------
% 0.23/0.48 % (19267)Success in time 0.109 s
% 0.23/0.49 % Vampire---4.8 exiting
%------------------------------------------------------------------------------