TSTP Solution File: SEU147+2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---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 : n001.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 17:56:02 EDT 2023
% Result : Theorem 0.23s 0.48s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 63 ( 20 unt; 0 def)
% Number of atoms : 201 ( 61 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 227 ( 89 ~; 89 |; 36 &)
% ( 8 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 106 (; 97 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1995,plain,
$false,
inference(subsumption_resolution,[],[f1980,f336]) ).
fof(f336,plain,
in(empty_set,sF14),
inference(superposition,[],[f309,f326]) ).
fof(f326,plain,
unordered_pair(empty_set,empty_set) = sF14,
introduced(function_definition,[]) ).
fof(f309,plain,
! [X3] : in(X3,unordered_pair(X3,X3)),
inference(equality_resolution,[],[f308]) ).
fof(f308,plain,
! [X3,X1] :
( in(X3,X1)
| unordered_pair(X3,X3) != X1 ),
inference(equality_resolution,[],[f293]) ).
fof(f293,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| unordered_pair(X0,X0) != X1 ),
inference(definition_unfolding,[],[f241,f170]) ).
fof(f170,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f65]) ).
fof(f65,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/tmp/tmp.MPa953ff2Z/Vampire---4.8_31303',t69_enumset1) ).
fof(f241,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK6(X0,X1) != X0
| ~ in(sK6(X0,X1),X1) )
& ( sK6(X0,X1) = X0
| in(sK6(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f140,f141]) ).
fof(f141,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK6(X0,X1) != X0
| ~ in(sK6(X0,X1),X1) )
& ( sK6(X0,X1) = X0
| in(sK6(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f140,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,[],[f139]) ).
fof(f139,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,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.MPa953ff2Z/Vampire---4.8_31303',d1_tarski) ).
fof(f1980,plain,
~ in(empty_set,sF14),
inference(resolution,[],[f1978,f955]) ).
fof(f955,plain,
~ subset(sF13,sF14),
inference(subsumption_resolution,[],[f954,f327]) ).
fof(f327,plain,
sF13 != sF14,
inference(definition_folding,[],[f272,f326,f325]) ).
fof(f325,plain,
powerset(empty_set) = sF13,
introduced(function_definition,[]) ).
fof(f272,plain,
powerset(empty_set) != unordered_pair(empty_set,empty_set),
inference(definition_unfolding,[],[f167,f170]) ).
fof(f167,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/sandbox2/tmp/tmp.MPa953ff2Z/Vampire---4.8_31303',t1_zfmisc_1) ).
fof(f954,plain,
( sF13 = sF14
| ~ subset(sF13,sF14) ),
inference(resolution,[],[f229,f534]) ).
fof(f534,plain,
subset(sF14,sF13),
inference(forward_demodulation,[],[f532,f326]) ).
fof(f532,plain,
subset(unordered_pair(empty_set,empty_set),sF13),
inference(resolution,[],[f281,f398]) ).
fof(f398,plain,
in(empty_set,sF13),
inference(resolution,[],[f394,f168]) ).
fof(f168,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox2/tmp/tmp.MPa953ff2Z/Vampire---4.8_31303',t2_xboole_1) ).
fof(f394,plain,
! [X0] :
( ~ subset(X0,empty_set)
| in(X0,sF13) ),
inference(superposition,[],[f306,f325]) ).
fof(f306,plain,
! [X3,X0] :
( in(X3,powerset(X0))
| ~ subset(X3,X0) ),
inference(equality_resolution,[],[f237]) ).
fof(f237,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ subset(X3,X0)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f138]) ).
fof(f138,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ( ( ~ subset(sK5(X0,X1),X0)
| ~ in(sK5(X0,X1),X1) )
& ( subset(sK5(X0,X1),X0)
| in(sK5(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f136,f137]) ).
fof(f137,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) )
=> ( ( ~ subset(sK5(X0,X1),X0)
| ~ in(sK5(X0,X1),X1) )
& ( subset(sK5(X0,X1),X0)
| in(sK5(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f136,plain,
! [X0,X1] :
( ( powerset(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) ) )
| powerset(X0) != X1 ) ),
inference(rectify,[],[f135]) ).
fof(f135,plain,
! [X0,X1] :
( ( powerset(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) ) )
| powerset(X0) != X1 ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( powerset(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MPa953ff2Z/Vampire---4.8_31303',d1_zfmisc_1) ).
fof(f281,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(unordered_pair(X0,X0),X1) ),
inference(definition_unfolding,[],[f192,f170]) ).
fof(f192,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f118,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/sandbox2/tmp/tmp.MPa953ff2Z/Vampire---4.8_31303',l2_zfmisc_1) ).
fof(f229,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| X0 = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f128]) ).
fof(f128,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/sandbox2/tmp/tmp.MPa953ff2Z/Vampire---4.8_31303',d10_xboole_0) ).
fof(f1978,plain,
! [X1] :
( subset(sF13,X1)
| ~ in(empty_set,X1) ),
inference(duplicate_literal_removal,[],[f1975]) ).
fof(f1975,plain,
! [X1] :
( ~ in(empty_set,X1)
| subset(sF13,X1)
| subset(sF13,X1) ),
inference(superposition,[],[f235,f589]) ).
fof(f589,plain,
! [X7] :
( empty_set = sK4(sF13,X7)
| subset(sF13,X7) ),
inference(resolution,[],[f234,f396]) ).
fof(f396,plain,
! [X0] :
( ~ in(X0,sF13)
| empty_set = X0 ),
inference(forward_demodulation,[],[f395,f325]) ).
fof(f395,plain,
! [X0] :
( ~ in(X0,powerset(empty_set))
| empty_set = X0 ),
inference(resolution,[],[f307,f171]) ).
fof(f171,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0] :
( subset(X0,empty_set)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/tmp/tmp.MPa953ff2Z/Vampire---4.8_31303',t3_xboole_1) ).
fof(f307,plain,
! [X3,X0] :
( subset(X3,X0)
| ~ in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f236]) ).
fof(f236,plain,
! [X3,X0,X1] :
( subset(X3,X0)
| ~ in(X3,X1)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f138]) ).
fof(f234,plain,
! [X0,X1] :
( in(sK4(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK4(X0,X1),X1)
& in(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f132,f133]) ).
fof(f133,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK4(X0,X1),X1)
& in(sK4(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f132,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,[],[f131]) ).
fof(f131,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,[],[f108]) ).
fof(f108,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/sandbox2/tmp/tmp.MPa953ff2Z/Vampire---4.8_31303',d3_tarski) ).
fof(f235,plain,
! [X0,X1] :
( ~ in(sK4(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU147+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.16 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.36 % Computer : n001.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 21:24:40 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/sandbox2/tmp/tmp.MPa953ff2Z/Vampire---4.8_31303
% 0.16/0.37 % (31418)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.43 % (31424)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 % (31421)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)
% 0.23/0.43 % (31422)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)
% 0.23/0.43 % (31419)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)
% 0.23/0.43 % (31420)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)
% 0.23/0.43 % (31425)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)
% 0.23/0.44 % (31423)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)
% 0.23/0.48 % (31424)First to succeed.
% 0.23/0.48 % (31424)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 % (31424)------------------------------
% 0.23/0.48 % (31424)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.48 % (31424)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.48 % (31424)Termination reason: Refutation
% 0.23/0.48
% 0.23/0.48 % (31424)Memory used [KB]: 6268
% 0.23/0.48 % (31424)Time elapsed: 0.048 s
% 0.23/0.48 % (31424)------------------------------
% 0.23/0.48 % (31424)------------------------------
% 0.23/0.48 % (31418)Success in time 0.109 s
% 0.23/0.48 31421 Aborted by signal SIGHUP on /export/starexec/sandbox2/tmp/tmp.MPa953ff2Z/Vampire---4.8_31303
% 0.23/0.48 % (31421)------------------------------
% 0.23/0.48 % (31421)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.48 31420 Aborted by signal SIGHUP on /export/starexec/sandbox2/tmp/tmp.MPa953ff2Z/Vampire---4.8_31303
% 0.23/0.48 % (31420)------------------------------
% 0.23/0.48 % (31420)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.48 % (31421)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.48 % (31420)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.48 % (31420)Termination reason: Unknown
% 0.23/0.48 % (31420)Termination phase: Saturation
% 0.23/0.48 % (31421)Termination reason: Unknown
% 0.23/0.48
% 0.23/0.48 % (31421)Termination phase: Saturation
% 0.23/0.48
% 0.23/0.48 % (31420)Memory used [KB]: 1023
% 0.23/0.48 % (31421)Memory used [KB]: 1151
% 0.23/0.48 % (31420)Time elapsed: 0.051 s
% 0.23/0.48 % (31421)Time elapsed: 0.050 s
% 0.23/0.48 % (31420)------------------------------
% 0.23/0.48 % (31420)------------------------------
% 0.23/0.48 % (31421)------------------------------
% 0.23/0.48 % (31421)------------------------------
% 0.23/0.48 % Vampire---4.8 exiting
%------------------------------------------------------------------------------