TSTP Solution File: SEU251+1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU251+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 : n002.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 17:57:21 EDT 2023
% Result : Theorem 0.22s 0.45s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 66 ( 12 unt; 0 def)
% Number of atoms : 232 ( 39 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 267 ( 101 ~; 100 |; 46 &)
% ( 11 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 134 (; 121 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f472,plain,
$false,
inference(subsumption_resolution,[],[f227,f471]) ).
fof(f471,plain,
! [X2] : ~ sP0(X2,sK3,sF15),
inference(subsumption_resolution,[],[f459,f152]) ).
fof(f152,plain,
~ subset(sF15,sF16),
inference(definition_folding,[],[f96,f151,f150,f149]) ).
fof(f149,plain,
relation_restriction(sK4,sK2) = sF14,
introduced(function_definition,[]) ).
fof(f150,plain,
fiber(sF14,sK3) = sF15,
introduced(function_definition,[]) ).
fof(f151,plain,
fiber(sK4,sK3) = sF16,
introduced(function_definition,[]) ).
fof(f96,plain,
~ subset(fiber(relation_restriction(sK4,sK2),sK3),fiber(sK4,sK3)),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
( ~ subset(fiber(relation_restriction(sK4,sK2),sK3),fiber(sK4,sK3))
& relation(sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f46,f68]) ).
fof(f68,plain,
( ? [X0,X1,X2] :
( ~ subset(fiber(relation_restriction(X2,X0),X1),fiber(X2,X1))
& relation(X2) )
=> ( ~ subset(fiber(relation_restriction(sK4,sK2),sK3),fiber(sK4,sK3))
& relation(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
? [X0,X1,X2] :
( ~ subset(fiber(relation_restriction(X2,X0),X1),fiber(X2,X1))
& relation(X2) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> subset(fiber(relation_restriction(X2,X0),X1),fiber(X2,X1)) ),
inference(negated_conjecture,[],[f32]) ).
fof(f32,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> subset(fiber(relation_restriction(X2,X0),X1),fiber(X2,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.5Oq4BMVqfW/Vampire---4.8_30559',t21_wellord1) ).
fof(f459,plain,
! [X2] :
( ~ sP0(X2,sK3,sF15)
| subset(sF15,sF16) ),
inference(superposition,[],[f182,f449]) ).
fof(f449,plain,
sK3 = sK7(sF15,sF16),
inference(subsumption_resolution,[],[f448,f152]) ).
fof(f448,plain,
( sK3 = sK7(sF15,sF16)
| subset(sF15,sF16) ),
inference(duplicate_literal_removal,[],[f444]) ).
fof(f444,plain,
( sK3 = sK7(sF15,sF16)
| subset(sF15,sF16)
| subset(sF15,sF16) ),
inference(resolution,[],[f390,f126]) ).
fof(f126,plain,
! [X0,X1] :
( ~ in(sK7(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK7(X0,X1),X1)
& in(sK7(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f79,f80]) ).
fof(f80,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK7(X0,X1),X1)
& in(sK7(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.5Oq4BMVqfW/Vampire---4.8_30559',d3_tarski) ).
fof(f390,plain,
! [X1] :
( in(sK7(sF15,X1),sF16)
| sK3 = sK7(sF15,X1)
| subset(sF15,X1) ),
inference(resolution,[],[f379,f373]) ).
fof(f373,plain,
! [X1] :
( in(ordered_pair(sK7(sF15,X1),sK3),sK4)
| subset(sF15,X1) ),
inference(resolution,[],[f336,f248]) ).
fof(f248,plain,
! [X0] :
( ~ in(X0,sF14)
| in(X0,sK4) ),
inference(subsumption_resolution,[],[f247,f95]) ).
fof(f95,plain,
relation(sK4),
inference(cnf_transformation,[],[f69]) ).
fof(f247,plain,
! [X0] :
( ~ in(X0,sF14)
| in(X0,sK4)
| ~ relation(sK4) ),
inference(superposition,[],[f131,f149]) ).
fof(f131,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_restriction(X2,X1))
| in(X0,X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_restriction(X2,X1))
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2) )
& ( ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) )
| ~ in(X0,relation_restriction(X2,X1)) ) )
| ~ relation(X2) ),
inference(flattening,[],[f83]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_restriction(X2,X1))
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2) )
& ( ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) )
| ~ in(X0,relation_restriction(X2,X1)) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5Oq4BMVqfW/Vampire---4.8_30559',t16_wellord1) ).
fof(f336,plain,
! [X0] :
( in(ordered_pair(sK7(sF15,X0),sK3),sF14)
| subset(sF15,X0) ),
inference(resolution,[],[f332,f125]) ).
fof(f125,plain,
! [X0,X1] :
( in(sK7(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f332,plain,
! [X3] :
( ~ in(X3,sF15)
| in(ordered_pair(X3,sK3),sF14) ),
inference(resolution,[],[f105,f227]) ).
fof(f105,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ in(X4,X2)
| in(ordered_pair(X4,X1),X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ~ in(ordered_pair(sK5(X0,X1,X2),X1),X0)
| sK5(X0,X1,X2) = X1
| ~ in(sK5(X0,X1,X2),X2) )
& ( ( in(ordered_pair(sK5(X0,X1,X2),X1),X0)
& sK5(X0,X1,X2) != X1 )
| in(sK5(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(ordered_pair(X4,X1),X0)
| X1 = X4 )
& ( ( in(ordered_pair(X4,X1),X0)
& X1 != X4 )
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f73,f74]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(ordered_pair(X3,X1),X0)
| X1 = X3
| ~ in(X3,X2) )
& ( ( in(ordered_pair(X3,X1),X0)
& X1 != X3 )
| in(X3,X2) ) )
=> ( ( ~ in(ordered_pair(sK5(X0,X1,X2),X1),X0)
| sK5(X0,X1,X2) = X1
| ~ in(sK5(X0,X1,X2),X2) )
& ( ( in(ordered_pair(sK5(X0,X1,X2),X1),X0)
& sK5(X0,X1,X2) != X1 )
| in(sK5(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ~ in(ordered_pair(X3,X1),X0)
| X1 = X3
| ~ in(X3,X2) )
& ( ( in(ordered_pair(X3,X1),X0)
& X1 != X3 )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(ordered_pair(X4,X1),X0)
| X1 = X4 )
& ( ( in(ordered_pair(X4,X1),X0)
& X1 != X4 )
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f72]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ~ in(ordered_pair(X3,X1),X0)
| X1 = X3
| ~ in(X3,X2) )
& ( ( in(ordered_pair(X3,X1),X0)
& X1 != X3 )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(ordered_pair(X3,X1),X0)
| X1 = X3 )
& ( ( in(ordered_pair(X3,X1),X0)
& X1 != X3 )
| ~ in(X3,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(flattening,[],[f71]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ~ in(ordered_pair(X3,X1),X0)
| X1 = X3
| ~ in(X3,X2) )
& ( ( in(ordered_pair(X3,X1),X0)
& X1 != X3 )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(ordered_pair(X3,X1),X0)
| X1 = X3 )
& ( ( in(ordered_pair(X3,X1),X0)
& X1 != X3 )
| ~ in(X3,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1,X2] :
( sP0(X0,X1,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(ordered_pair(X3,X1),X0)
& X1 != X3 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f379,plain,
! [X4] :
( ~ in(ordered_pair(X4,sK3),sK4)
| sK3 = X4
| in(X4,sF16) ),
inference(resolution,[],[f106,f228]) ).
fof(f228,plain,
sP0(sK4,sK3,sF16),
inference(subsumption_resolution,[],[f226,f95]) ).
fof(f226,plain,
( sP0(sK4,sK3,sF16)
| ~ relation(sK4) ),
inference(superposition,[],[f189,f151]) ).
fof(f189,plain,
! [X0,X1] :
( sP0(X0,X1,fiber(X0,X1))
| ~ relation(X0) ),
inference(resolution,[],[f145,f110]) ).
fof(f110,plain,
! [X0] :
( sP1(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0] :
( sP1(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f50,f66,f65]) ).
fof(f66,plain,
! [X0] :
( ! [X1,X2] :
( fiber(X0,X1) = X2
<=> sP0(X0,X1,X2) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f50,plain,
! [X0] :
( ! [X1,X2] :
( fiber(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(ordered_pair(X3,X1),X0)
& X1 != X3 ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( fiber(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(ordered_pair(X3,X1),X0)
& X1 != X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5Oq4BMVqfW/Vampire---4.8_30559',d1_wellord1) ).
fof(f145,plain,
! [X0,X1] :
( ~ sP1(X0)
| sP0(X0,X1,fiber(X0,X1)) ),
inference(equality_resolution,[],[f102]) ).
fof(f102,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| fiber(X0,X1) != X2
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0] :
( ! [X1,X2] :
( ( fiber(X0,X1) = X2
| ~ sP0(X0,X1,X2) )
& ( sP0(X0,X1,X2)
| fiber(X0,X1) != X2 ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f66]) ).
fof(f106,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ in(ordered_pair(X4,X1),X0)
| X1 = X4
| in(X4,X2) ),
inference(cnf_transformation,[],[f75]) ).
fof(f182,plain,
! [X2,X0,X1] :
( ~ sP0(X2,sK7(X0,X1),X0)
| subset(X0,X1) ),
inference(resolution,[],[f125,f146]) ).
fof(f146,plain,
! [X2,X0,X4] :
( ~ in(X4,X2)
| ~ sP0(X0,X4,X2) ),
inference(equality_resolution,[],[f104]) ).
fof(f104,plain,
! [X2,X0,X1,X4] :
( X1 != X4
| ~ in(X4,X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f75]) ).
fof(f227,plain,
sP0(sF14,sK3,sF15),
inference(subsumption_resolution,[],[f225,f162]) ).
fof(f162,plain,
relation(sF14),
inference(subsumption_resolution,[],[f161,f95]) ).
fof(f161,plain,
( relation(sF14)
| ~ relation(sK4) ),
inference(superposition,[],[f120,f149]) ).
fof(f120,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_restriction(X0,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.5Oq4BMVqfW/Vampire---4.8_30559',dt_k2_wellord1) ).
fof(f225,plain,
( sP0(sF14,sK3,sF15)
| ~ relation(sF14) ),
inference(superposition,[],[f189,f150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU251+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.36 % Computer : n002.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Wed Aug 23 21:07:01 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.16/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.16/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.5Oq4BMVqfW/Vampire---4.8_30559
% 0.16/0.37 % (30666)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.40 % (30668)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)
% 0.22/0.43 % (30669)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)
% 0.22/0.43 % (30672)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.22/0.43 % (30671)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)
% 0.22/0.43 % (30667)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)
% 0.22/0.43 % (30670)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)
% 0.22/0.43 % (30673)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)
% 0.22/0.44 % (30673)First to succeed.
% 0.22/0.45 % (30673)Refutation found. Thanks to Tanya!
% 0.22/0.45 % SZS status Theorem for Vampire---4
% 0.22/0.45 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.45 % (30673)------------------------------
% 0.22/0.45 % (30673)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.45 % (30673)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.45 % (30673)Termination reason: Refutation
% 0.22/0.45
% 0.22/0.45 % (30673)Memory used [KB]: 1407
% 0.22/0.45 % (30673)Time elapsed: 0.022 s
% 0.22/0.45 % (30673)------------------------------
% 0.22/0.45 % (30673)------------------------------
% 0.22/0.45 % (30666)Success in time 0.08 s
% 0.22/0.45 30668 Aborted by signal SIGHUP on /export/starexec/sandbox/tmp/tmp.5Oq4BMVqfW/Vampire---4.8_30559
% 0.22/0.45 % (30668)------------------------------
% 0.22/0.45 % (30668)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.45 % (30668)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.45 % (30668)Termination reason: Unknown
% 0.22/0.45 % (30668)Termination phase: Saturation
% 0.22/0.45
% 0.22/0.45 % (30668)Memory used [KB]: 1279
% 0.22/0.45 % (30668)Time elapsed: 0.047 s
% 0.22/0.45 % (30668)------------------------------
% 0.22/0.45 % (30668)------------------------------
% 0.22/0.45 % Vampire---4.8 exiting
%------------------------------------------------------------------------------