TSTP Solution File: SET159+3 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET159+3 : TPTP v8.1.2. Released v2.2.0.
% 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 : n007.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 15:38:22 EDT 2023
% Result : Theorem 0.22s 0.58s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 75 ( 16 unt; 0 def)
% Number of atoms : 188 ( 24 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 182 ( 69 ~; 89 |; 17 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 99 (; 90 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5908,plain,
$false,
inference(unit_resulting_resolution,[],[f49,f4233,f5875]) ).
fof(f5875,plain,
( ~ subset(sF5,sF8)
| sF6 = sF8 ),
inference(resolution,[],[f5851,f4958]) ).
fof(f4958,plain,
( ~ subset(sF6,sF8)
| sF6 = sF8 ),
inference(resolution,[],[f4783,f4415]) ).
fof(f4415,plain,
subset(sF7,sF6),
inference(duplicate_literal_removal,[],[f4402]) ).
fof(f4402,plain,
( subset(sF7,sF6)
| subset(sF7,sF6) ),
inference(resolution,[],[f4386,f96]) ).
fof(f96,plain,
! [X0] :
( ~ member(sK4(X0,sF6),sK1)
| subset(X0,sF6) ),
inference(resolution,[],[f75,f69]) ).
fof(f69,plain,
! [X6] :
( member(X6,sF5)
| ~ member(X6,sK1) ),
inference(superposition,[],[f40,f45]) ).
fof(f45,plain,
union(sK0,sK1) = sF5,
introduced(function_definition,[]) ).
fof(f40,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox/tmp/tmp.NYZDkoB2ei/Vampire---4.8_21143',union_defn) ).
fof(f75,plain,
! [X0] :
( ~ member(sK4(X0,sF6),sF5)
| subset(X0,sF6) ),
inference(resolution,[],[f63,f37]) ).
fof(f37,plain,
! [X0,X1] :
( ~ member(sK4(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f20,f21]) ).
fof(f21,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f10,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.NYZDkoB2ei/Vampire---4.8_21143',subset_defn) ).
fof(f63,plain,
! [X10] :
( member(X10,sF6)
| ~ member(X10,sF5) ),
inference(superposition,[],[f39,f46]) ).
fof(f46,plain,
union(sF5,sK2) = sF6,
introduced(function_definition,[]) ).
fof(f39,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f4386,plain,
( member(sK4(sF7,sF6),sK1)
| subset(sF7,sF6) ),
inference(duplicate_literal_removal,[],[f4375]) ).
fof(f4375,plain,
( subset(sF7,sF6)
| member(sK4(sF7,sF6),sK1)
| subset(sF7,sF6) ),
inference(resolution,[],[f834,f79]) ).
fof(f79,plain,
! [X0] :
( ~ member(sK4(X0,sF6),sK2)
| subset(X0,sF6) ),
inference(resolution,[],[f62,f37]) ).
fof(f62,plain,
! [X9] :
( member(X9,sF6)
| ~ member(X9,sK2) ),
inference(superposition,[],[f39,f50]) ).
fof(f50,plain,
sF6 = union(sK2,sF5),
inference(superposition,[],[f27,f46]) ).
fof(f27,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox/tmp/tmp.NYZDkoB2ei/Vampire---4.8_21143',commutativity_of_union) ).
fof(f834,plain,
! [X8] :
( member(sK4(sF7,X8),sK2)
| subset(sF7,X8)
| member(sK4(sF7,X8),sK1) ),
inference(superposition,[],[f148,f47]) ).
fof(f47,plain,
union(sK1,sK2) = sF7,
introduced(function_definition,[]) ).
fof(f148,plain,
! [X2,X0,X1] :
( subset(union(X0,X1),X2)
| member(sK4(union(X0,X1),X2),X1)
| member(sK4(union(X0,X1),X2),X0) ),
inference(resolution,[],[f38,f36]) ).
fof(f36,plain,
! [X0,X1] :
( member(sK4(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f4783,plain,
( ~ subset(sF7,sF6)
| ~ subset(sF6,sF8)
| sF6 = sF8 ),
inference(resolution,[],[f4757,f30]) ).
fof(f30,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f13]) ).
fof(f13,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.NYZDkoB2ei/Vampire---4.8_21143',equal_defn) ).
fof(f4757,plain,
( subset(sF8,sF6)
| ~ subset(sF7,sF6) ),
inference(duplicate_literal_removal,[],[f4748]) ).
fof(f4748,plain,
( subset(sF8,sF6)
| ~ subset(sF7,sF6)
| subset(sF8,sF6) ),
inference(resolution,[],[f4282,f97]) ).
fof(f97,plain,
! [X1] :
( ~ member(sK4(X1,sF6),sK0)
| subset(X1,sF6) ),
inference(resolution,[],[f75,f59]) ).
fof(f59,plain,
! [X6] :
( member(X6,sF5)
| ~ member(X6,sK0) ),
inference(superposition,[],[f39,f45]) ).
fof(f4282,plain,
! [X5] :
( member(sK4(sF8,X5),sK0)
| subset(sF8,X5)
| ~ subset(sF7,X5) ),
inference(duplicate_literal_removal,[],[f4281]) ).
fof(f4281,plain,
! [X5] :
( subset(sF8,X5)
| member(sK4(sF8,X5),sK0)
| ~ subset(sF7,X5)
| subset(sF8,X5) ),
inference(resolution,[],[f833,f119]) ).
fof(f119,plain,
! [X2,X0,X1] :
( ~ member(sK4(X0,X1),X2)
| ~ subset(X2,X1)
| subset(X0,X1) ),
inference(resolution,[],[f35,f37]) ).
fof(f35,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f833,plain,
! [X7] :
( member(sK4(sF8,X7),sF7)
| subset(sF8,X7)
| member(sK4(sF8,X7),sK0) ),
inference(superposition,[],[f148,f48]) ).
fof(f48,plain,
union(sK0,sF7) = sF8,
introduced(function_definition,[]) ).
fof(f5851,plain,
( subset(sF6,sF8)
| ~ subset(sF5,sF8) ),
inference(duplicate_literal_removal,[],[f5844]) ).
fof(f5844,plain,
( subset(sF6,sF8)
| ~ subset(sF5,sF8)
| subset(sF6,sF8) ),
inference(resolution,[],[f4519,f106]) ).
fof(f106,plain,
! [X0] :
( ~ member(sK4(X0,sF8),sK2)
| subset(X0,sF8) ),
inference(resolution,[],[f77,f71]) ).
fof(f71,plain,
! [X8] :
( member(X8,sF7)
| ~ member(X8,sK2) ),
inference(superposition,[],[f40,f47]) ).
fof(f77,plain,
! [X0] :
( ~ member(sK4(X0,sF8),sF7)
| subset(X0,sF8) ),
inference(resolution,[],[f70,f37]) ).
fof(f70,plain,
! [X7] :
( member(X7,sF8)
| ~ member(X7,sF7) ),
inference(superposition,[],[f40,f48]) ).
fof(f4519,plain,
! [X5] :
( member(sK4(sF6,X5),sK2)
| subset(sF6,X5)
| ~ subset(sF5,X5) ),
inference(duplicate_literal_removal,[],[f4518]) ).
fof(f4518,plain,
! [X5] :
( subset(sF6,X5)
| member(sK4(sF6,X5),sK2)
| ~ subset(sF5,X5)
| subset(sF6,X5) ),
inference(resolution,[],[f835,f119]) ).
fof(f835,plain,
! [X9] :
( member(sK4(sF6,X9),sF5)
| subset(sF6,X9)
| member(sK4(sF6,X9),sK2) ),
inference(superposition,[],[f148,f50]) ).
fof(f4233,plain,
subset(sF5,sF8),
inference(duplicate_literal_removal,[],[f4222]) ).
fof(f4222,plain,
( subset(sF5,sF8)
| subset(sF5,sF8) ),
inference(resolution,[],[f4182,f65]) ).
fof(f65,plain,
! [X0] :
( ~ member(sK4(X0,sF8),sK0)
| subset(X0,sF8) ),
inference(resolution,[],[f60,f37]) ).
fof(f60,plain,
! [X7] :
( member(X7,sF8)
| ~ member(X7,sK0) ),
inference(superposition,[],[f39,f48]) ).
fof(f4182,plain,
( member(sK4(sF5,sF8),sK0)
| subset(sF5,sF8) ),
inference(duplicate_literal_removal,[],[f4175]) ).
fof(f4175,plain,
( subset(sF5,sF8)
| member(sK4(sF5,sF8),sK0)
| subset(sF5,sF8) ),
inference(resolution,[],[f832,f107]) ).
fof(f107,plain,
! [X1] :
( ~ member(sK4(X1,sF8),sK1)
| subset(X1,sF8) ),
inference(resolution,[],[f77,f61]) ).
fof(f61,plain,
! [X8] :
( member(X8,sF7)
| ~ member(X8,sK1) ),
inference(superposition,[],[f39,f47]) ).
fof(f832,plain,
! [X6] :
( member(sK4(sF5,X6),sK1)
| subset(sF5,X6)
| member(sK4(sF5,X6),sK0) ),
inference(superposition,[],[f148,f45]) ).
fof(f49,plain,
sF6 != sF8,
inference(definition_folding,[],[f25,f48,f47,f46,f45]) ).
fof(f25,plain,
union(union(sK0,sK1),sK2) != union(sK0,union(sK1,sK2)),
inference(cnf_transformation,[],[f12]) ).
fof(f12,plain,
union(union(sK0,sK1),sK2) != union(sK0,union(sK1,sK2)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f11]) ).
fof(f11,plain,
( ? [X0,X1,X2] : union(union(X0,X1),X2) != union(X0,union(X1,X2))
=> union(union(sK0,sK1),sK2) != union(sK0,union(sK1,sK2)) ),
introduced(choice_axiom,[]) ).
fof(f9,plain,
? [X0,X1,X2] : union(union(X0,X1),X2) != union(X0,union(X1,X2)),
inference(ennf_transformation,[],[f8]) ).
fof(f8,negated_conjecture,
~ ! [X0,X1,X2] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
inference(negated_conjecture,[],[f7]) ).
fof(f7,conjecture,
! [X0,X1,X2] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
file('/export/starexec/sandbox/tmp/tmp.NYZDkoB2ei/Vampire---4.8_21143',prove_associativity_of_union) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET159+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36 % Computer : n007.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 14:44:11 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.NYZDkoB2ei/Vampire---4.8_21143
% 0.15/0.37 % (21256)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (21263)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)
% 0.22/0.43 % (21259)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)
% 0.22/0.43 % (21260)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)
% 0.22/0.43 % (21261)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)
% 0.22/0.43 % (21258)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)
% 0.22/0.43 % (21261)Refutation not found, incomplete strategy% (21261)------------------------------
% 0.22/0.43 % (21261)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.43 % (21261)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.43 % (21261)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.43
% 0.22/0.43 % (21261)Memory used [KB]: 895
% 0.22/0.43 % (21261)Time elapsed: 0.004 s
% 0.22/0.43 % (21261)------------------------------
% 0.22/0.43 % (21261)------------------------------
% 0.22/0.43 % (21257)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)
% 0.22/0.44 % (21262)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)
% 0.22/0.49 % (21264)ott+4_40_av=off:bce=on:fsd=off:fde=unused:nm=4:nwc=1.1:sos=all:sp=frequency_375 on Vampire---4 for (375ds/0Mi)
% 0.22/0.49 % (21264)Refutation not found, incomplete strategy% (21264)------------------------------
% 0.22/0.49 % (21264)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.49 % (21264)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.49 % (21264)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.49
% 0.22/0.49 % (21264)Memory used [KB]: 895
% 0.22/0.49 % (21264)Time elapsed: 0.004 s
% 0.22/0.49 % (21264)------------------------------
% 0.22/0.49 % (21264)------------------------------
% 0.22/0.53 % (21265)lrs-11_16_av=off:bs=on:bsr=on:drc=off:fsd=off:fsr=off:nm=4:sp=scramble:tgt=ground:stl=62_367 on Vampire---4 for (367ds/0Mi)
% 0.22/0.58 % (21259)First to succeed.
% 0.22/0.58 % (21259)Refutation found. Thanks to Tanya!
% 0.22/0.58 % SZS status Theorem for Vampire---4
% 0.22/0.58 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.58 % (21259)------------------------------
% 0.22/0.58 % (21259)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.58 % (21259)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.58 % (21259)Termination reason: Refutation
% 0.22/0.58
% 0.22/0.58 % (21259)Memory used [KB]: 4477
% 0.22/0.58 % (21259)Time elapsed: 0.153 s
% 0.22/0.58 % (21259)------------------------------
% 0.22/0.58 % (21259)------------------------------
% 0.22/0.58 % (21256)Success in time 0.211 s
% 0.22/0.58 % Vampire---4.8 exiting
%------------------------------------------------------------------------------