TSTP Solution File: SEU147+2 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU147+2 : 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 : n028.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 : Sat Sep 2 00:06:49 EDT 2023
% Result : Theorem 15.13s 2.62s
% Output : Refutation 15.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 66 ( 22 unt; 0 def)
% Number of atoms : 219 ( 49 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 247 ( 94 ~; 90 |; 44 &)
% ( 15 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 126 (; 117 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f128418,plain,
$false,
inference(subsumption_resolution,[],[f128347,f15580]) ).
fof(f15580,plain,
~ in(sK14(powerset(empty_set),singleton(empty_set)),singleton(empty_set)),
inference(unit_resulting_resolution,[],[f15453,f266]) ).
fof(f266,plain,
! [X0,X1] :
( ~ in(sK14(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f149]) ).
fof(f149,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK14(X0,X1),X1)
& in(sK14(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f147,f148]) ).
fof(f148,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK14(X0,X1),X1)
& in(sK14(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f147,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,[],[f146]) ).
fof(f146,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,[],[f105]) ).
fof(f105,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.T9R0Q4WTN7/Vampire---4.8_7327',d3_tarski) ).
fof(f15453,plain,
~ subset(powerset(empty_set),singleton(empty_set)),
inference(unit_resulting_resolution,[],[f196,f14865,f258]) ).
fof(f258,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| X0 = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f141]) ).
fof(f141,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.T9R0Q4WTN7/Vampire---4.8_7327',d10_xboole_0) ).
fof(f14865,plain,
! [X0] : subset(singleton(empty_set),powerset(X0)),
inference(unit_resulting_resolution,[],[f14787,f221]) ).
fof(f221,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
! [X0,X1] :
( ( subset(singleton(X0),X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| ~ subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.T9R0Q4WTN7/Vampire---4.8_7327',l2_zfmisc_1) ).
fof(f14787,plain,
! [X0] : in(empty_set,powerset(X0)),
inference(unit_resulting_resolution,[],[f197,f713,f268]) ).
fof(f268,plain,
! [X3,X0,X1] :
( ~ sP0(X0,X1)
| ~ subset(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f153]) ).
fof(f153,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( ~ subset(sK15(X0,X1),X0)
| ~ in(sK15(X0,X1),X1) )
& ( subset(sK15(X0,X1),X0)
| in(sK15(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f151,f152]) ).
fof(f152,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) )
=> ( ( ~ subset(sK15(X0,X1),X0)
| ~ in(sK15(X0,X1),X1) )
& ( subset(sK15(X0,X1),X0)
| in(sK15(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f151,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f150]) ).
fof(f150,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ subset(X2,X0) )
& ( subset(X2,X0)
| ~ in(X2,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f713,plain,
! [X0] : sP0(X0,powerset(X0)),
inference(forward_demodulation,[],[f711,f238]) ).
fof(f238,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0] : set_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox/tmp/tmp.T9R0Q4WTN7/Vampire---4.8_7327',t3_boole) ).
fof(f711,plain,
! [X0] : sP0(X0,set_difference(powerset(X0),empty_set)),
inference(unit_resulting_resolution,[],[f238,f271]) ).
fof(f271,plain,
! [X0,X1] :
( powerset(X0) != X1
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| powerset(X0) != X1 ) ),
inference(nnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0,X1] :
( powerset(X0) = X1
<=> sP0(X0,X1) ),
inference(definition_folding,[],[f9,f108]) ).
fof(f9,axiom,
! [X0,X1] :
( powerset(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox/tmp/tmp.T9R0Q4WTN7/Vampire---4.8_7327',d1_zfmisc_1) ).
fof(f197,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox/tmp/tmp.T9R0Q4WTN7/Vampire---4.8_7327',t2_xboole_1) ).
fof(f196,plain,
powerset(empty_set) != singleton(empty_set),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
powerset(empty_set) != singleton(empty_set),
inference(flattening,[],[f45]) ).
fof(f45,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(negated_conjecture,[],[f44]) ).
fof(f44,conjecture,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox/tmp/tmp.T9R0Q4WTN7/Vampire---4.8_7327',t1_zfmisc_1) ).
fof(f128347,plain,
in(sK14(powerset(empty_set),singleton(empty_set)),singleton(empty_set)),
inference(unit_resulting_resolution,[],[f128027,f22358]) ).
fof(f22358,plain,
! [X0,X1] :
( X0 != X1
| in(X1,singleton(X0)) ),
inference(resolution,[],[f274,f731]) ).
fof(f731,plain,
! [X0] : sP1(X0,singleton(X0)),
inference(forward_demodulation,[],[f729,f238]) ).
fof(f729,plain,
! [X0] : sP1(X0,set_difference(singleton(X0),empty_set)),
inference(unit_resulting_resolution,[],[f238,f277]) ).
fof(f277,plain,
! [X0,X1] :
( singleton(X0) != X1
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f159]) ).
fof(f159,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ~ sP1(X0,X1) )
& ( sP1(X0,X1)
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0,X1] :
( singleton(X0) = X1
<=> sP1(X0,X1) ),
inference(definition_folding,[],[f7,f110]) ).
fof(f110,plain,
! [X0,X1] :
( sP1(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f7,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.T9R0Q4WTN7/Vampire---4.8_7327',d1_tarski) ).
fof(f274,plain,
! [X3,X0,X1] :
( ~ sP1(X0,X1)
| X0 != X3
| in(X3,X1) ),
inference(cnf_transformation,[],[f158]) ).
fof(f158,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ( ( sK16(X0,X1) != X0
| ~ in(sK16(X0,X1),X1) )
& ( sK16(X0,X1) = X0
| in(sK16(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| ~ sP1(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f156,f157]) ).
fof(f157,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK16(X0,X1) != X0
| ~ in(sK16(X0,X1),X1) )
& ( sK16(X0,X1) = X0
| in(sK16(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f156,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| ~ sP1(X0,X1) ) ),
inference(rectify,[],[f155]) ).
fof(f155,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| ~ sP1(X0,X1) ) ),
inference(nnf_transformation,[],[f110]) ).
fof(f128027,plain,
empty_set = sK14(powerset(empty_set),singleton(empty_set)),
inference(unit_resulting_resolution,[],[f348,f127734,f261]) ).
fof(f261,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| X0 = X1
| proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
! [X0,X1] :
( ( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) )
& ( ( X0 != X1
& subset(X0,X1) )
| ~ proper_subset(X0,X1) ) ),
inference(flattening,[],[f143]) ).
fof(f143,plain,
! [X0,X1] :
( ( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) )
& ( ( X0 != X1
& subset(X0,X1) )
| ~ proper_subset(X0,X1) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
<=> ( X0 != X1
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.T9R0Q4WTN7/Vampire---4.8_7327',d8_xboole_0) ).
fof(f127734,plain,
subset(sK14(powerset(empty_set),singleton(empty_set)),empty_set),
inference(unit_resulting_resolution,[],[f713,f15579,f267]) ).
fof(f267,plain,
! [X3,X0,X1] :
( ~ sP0(X0,X1)
| ~ in(X3,X1)
| subset(X3,X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f15579,plain,
in(sK14(powerset(empty_set),singleton(empty_set)),powerset(empty_set)),
inference(unit_resulting_resolution,[],[f15453,f265]) ).
fof(f265,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK14(X0,X1),X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f348,plain,
! [X0] : ~ proper_subset(X0,empty_set),
inference(unit_resulting_resolution,[],[f197,f226]) ).
fof(f226,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ proper_subset(X1,X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f63]) ).
fof(f63,axiom,
! [X0,X1] :
~ ( proper_subset(X1,X0)
& subset(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.T9R0Q4WTN7/Vampire---4.8_7327',t60_xboole_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU147+2 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.12 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.12/0.32 % Computer : n028.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Wed Aug 30 14:25:27 EDT 2023
% 0.12/0.32 % CPUTime :
% 0.17/0.38 % (7454)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.38 % (7462)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.17/0.38 % (7468)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.17/0.38 % (7466)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.17/0.38 % (7473)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.17/0.38 % (7479)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 0.17/0.38 % (7476)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.17/0.38 TRYING [1]
% 0.17/0.38 TRYING [2]
% 0.17/0.39 TRYING [3]
% 0.17/0.39 % (7458)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.17/0.40 TRYING [4]
% 0.17/0.42 TRYING [1]
% 0.17/0.43 TRYING [2]
% 0.17/0.44 TRYING [5]
% 0.17/0.46 TRYING [3]
% 0.17/0.54 TRYING [6]
% 0.17/0.66 TRYING [4]
% 0.17/0.75 TRYING [7]
% 4.41/1.01 TRYING [5]
% 5.29/1.20 TRYING [8]
% 7.69/1.49 TRYING [1]
% 7.69/1.49 TRYING [2]
% 7.69/1.50 TRYING [3]
% 7.98/1.51 TRYING [4]
% 8.25/1.54 TRYING [5]
% 8.92/1.64 TRYING [6]
% 10.33/1.91 TRYING [7]
% 10.33/1.99 TRYING [6]
% 12.37/2.14 TRYING [9]
% 15.13/2.52 TRYING [8]
% 15.13/2.61 % (7479)First to succeed.
% 15.13/2.62 % (7479)Refutation found. Thanks to Tanya!
% 15.13/2.62 % SZS status Theorem for Vampire---4
% 15.13/2.62 % SZS output start Proof for Vampire---4
% See solution above
% 15.13/2.62 % (7479)------------------------------
% 15.13/2.62 % (7479)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 15.13/2.62 % (7479)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 15.13/2.62 % (7479)Termination reason: Refutation
% 15.13/2.62
% 15.13/2.62 % (7479)Memory used [KB]: 56033
% 15.13/2.62 % (7479)Time elapsed: 2.227 s
% 15.13/2.62 % (7479)------------------------------
% 15.13/2.62 % (7479)------------------------------
% 15.13/2.62 % (7454)Success in time 2.269 s
% 15.13/2.62 % Vampire---4.8 exiting
%------------------------------------------------------------------------------